TSTP Solution File: ITP005^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP005^5 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:14:02 EDT 2023
% Result : Timeout 299.44s 300.21s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.46 % Problem : ITP005^5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.47 % Command : do_cvc5 %s %d
% 0.47/0.68 % Computer : n012.cluster.edu
% 0.47/0.68 % Model : x86_64 x86_64
% 0.47/0.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.47/0.68 % Memory : 8042.1875MB
% 0.47/0.68 % OS : Linux 3.10.0-693.el7.x86_64
% 0.47/0.68 % CPULimit : 300
% 0.47/0.68 % WCLimit : 300
% 0.47/0.68 % DateTime : Sun Aug 27 11:31:40 EDT 2023
% 0.47/0.68 % CPUTime :
% 0.65/1.31 %----Proving TH0
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 % File : ITP005^5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.65/1.32 % Domain : Interactive Theorem Proving
% 0.65/1.32 % Problem : HOL4 set theory export of thm_2Eset__relation_2Erel__to__reln__inv.p, chainy mode
% 0.65/1.32 % Version : [BG+19] axioms.
% 0.65/1.32 % English :
% 0.65/1.32
% 0.65/1.32 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.65/1.32 % : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% 0.65/1.32 % Source : [BG+19]
% 0.65/1.32 % Names : thm_2Eset__relation_2Erel__to__reln__inv.p [Gau20]
% 0.65/1.32 % : HL402001^5.p [TPAP]
% 0.65/1.32
% 0.65/1.32 % Status : Theorem
% 0.65/1.32 % Rating : 0.54 v8.1.0, 0.55 v7.5.0
% 0.65/1.32 % Syntax : Number of formulae : 3387 ( 335 unt; 494 typ; 0 def)
% 0.65/1.32 % Number of atoms : 43012 (2090 equ; 0 cnn)
% 0.65/1.32 % Maximal formula atoms : 110 ( 14 avg)
% 0.65/1.32 % Number of connectives : 86778 ( 369 ~; 262 |;1678 &;78007 @)
% 0.65/1.32 % ( 968 <=>;5494 =>; 0 <=; 0 <~>)
% 0.65/1.32 % Maximal formula depth : 42 ( 11 avg)
% 0.65/1.32 % Number of types : 10 ( 8 usr)
% 0.65/1.32 % Number of type conns : 514 ( 514 >; 0 *; 0 +; 0 <<)
% 0.65/1.32 % Number of symbols : 525 ( 522 usr; 170 con; 0-4 aty)
% 0.65/1.32 % Number of variables : 9302 ( 433 ^;8552 !; 317 ?;9302 :)
% 0.65/1.32 % SPC : TH0_THM_EQU_NAR
% 0.65/1.32
% 0.65/1.32 % Comments :
% 0.65/1.32 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 thf(del_tp,type,
% 0.65/1.32 del: $tType ).
% 0.65/1.32
% 0.65/1.32 thf(bool,type,
% 0.65/1.32 bool: del ).
% 0.65/1.32
% 0.65/1.32 thf(ind,type,
% 0.65/1.32 ind: del ).
% 0.65/1.32
% 0.65/1.32 thf(arr,type,
% 0.65/1.32 arr: del > del > del ).
% 0.65/1.32
% 0.65/1.32 thf(mem,type,
% 0.65/1.32 mem: $i > del > $o ).
% 0.65/1.32
% 0.65/1.32 thf(ap,type,
% 0.65/1.32 ap: $i > $i > $i ).
% 0.65/1.32
% 0.65/1.32 thf(lam,type,
% 0.65/1.32 lam: del > ( $i > $i ) > $i ).
% 0.65/1.32
% 0.65/1.32 thf(p,type,
% 0.65/1.32 p: $i > $o ).
% 0.65/1.32
% 0.65/1.32 thf(stp_inj_o,type,
% 0.65/1.32 inj__o: $o > $i ).
% 0.65/1.32
% 0.65/1.32 thf(stp_inj_surj_o,axiom,
% 0.65/1.32 ! [X: $o] :
% 0.65/1.32 ( ( p @ ( inj__o @ X ) )
% 0.65/1.32 = X ) ).
% 0.65/1.32
% 0.65/1.32 thf(stp_inj_mem_o,axiom,
% 0.65/1.32 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.65/1.32
% 0.65/1.32 thf(stp_iso_mem_o,axiom,
% 0.65/1.32 ! [X: $i] :
% 0.65/1.32 ( ( mem @ X @ bool )
% 0.65/1.32 => ( X
% 0.65/1.32 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ap_tp,axiom,
% 0.65/1.32 ! [A: del,B: del,F: $i] :
% 0.65/1.32 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.65/1.32 => ! [X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(lam_tp,axiom,
% 0.65/1.32 ! [A: del,B: del,F: $i > $i] :
% 0.65/1.32 ( ! [X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 => ( mem @ ( F @ X ) @ B ) )
% 0.65/1.32 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(funcext,axiom,
% 0.65/1.32 ! [A: del,B: del,F: $i] :
% 0.65/1.32 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.65/1.32 => ! [G: $i] :
% 0.65/1.32 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.65/1.32 => ( ! [X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 => ( ( ap @ F @ X )
% 0.65/1.32 = ( ap @ G @ X ) ) )
% 0.65/1.32 => ( F = G ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(beta,axiom,
% 0.65/1.32 ! [A: del,F: $i > $i,X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.65/1.32 = ( F @ X ) ) ) ).
% 0.65/1.32
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 thf(tp_c_2Emin_2E_3D,type,
% 0.65/1.32 c_2Emin_2E_3D: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Emin_2E_3D,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_eq_p,axiom,
% 0.65/1.32 ! [A: del,X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 => ! [Y: $i] :
% 0.65/1.32 ( ( mem @ Y @ A )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.65/1.32 <=> ( X = Y ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.65/1.32 c_2Emin_2E_3D_3D_3E: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.65/1.32 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_imp_p,axiom,
% 0.65/1.32 ! [Q: $i] :
% 0.65/1.32 ( ( mem @ Q @ bool )
% 0.65/1.32 => ! [R: $i] :
% 0.65/1.32 ( ( mem @ R @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.65/1.32 <=> ( ( p @ Q )
% 0.65/1.32 => ( p @ R ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Emin_2E_40,type,
% 0.65/1.32 c_2Emin_2E_40: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Emin_2E_40,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_40 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ).
% 0.65/1.32
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 %------------------------------------------------------------------------------
% 0.65/1.32 thf(tp_ty_2Ebool_2Eitself,type,
% 0.65/1.32 ty_2Ebool_2Eitself: del > del ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2E_21,type,
% 0.65/1.32 c_2Ebool_2E_21: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2E_21,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_all_p,axiom,
% 0.65/1.32 ! [A: del,Q: $i] :
% 0.65/1.32 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.65/1.32 <=> ! [X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.65/1.32 c_2Ebool_2E_2F_5C: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.65/1.32 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_and_p,axiom,
% 0.65/1.32 ! [Q: $i] :
% 0.65/1.32 ( ( mem @ Q @ bool )
% 0.65/1.32 => ! [R: $i] :
% 0.65/1.32 ( ( mem @ R @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.65/1.32 <=> ( ( p @ Q )
% 0.65/1.32 & ( p @ R ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2E_3F,type,
% 0.65/1.32 c_2Ebool_2E_3F: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2E_3F,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_ex_p,axiom,
% 0.65/1.32 ! [A: del,Q: $i] :
% 0.65/1.32 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
% 0.65/1.32 <=> ? [X: $i] :
% 0.65/1.32 ( ( mem @ X @ A )
% 0.65/1.32 & ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2E_3F_21,type,
% 0.65/1.32 c_2Ebool_2E_3F_21: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2E_3F_21,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EARB,type,
% 0.65/1.32 c_2Ebool_2EARB: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EARB,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EARB @ A_27a ) @ A_27a ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EBOUNDED,type,
% 0.65/1.32 c_2Ebool_2EBOUNDED: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EBOUNDED,axiom,
% 0.65/1.32 mem @ c_2Ebool_2EBOUNDED @ ( arr @ bool @ bool ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ECOND,type,
% 0.65/1.32 c_2Ebool_2ECOND: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ECOND,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EDATATYPE,type,
% 0.65/1.32 c_2Ebool_2EDATATYPE: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EDATATYPE,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ ( arr @ A_27a @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EF,type,
% 0.65/1.32 c_2Ebool_2EF: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EF,axiom,
% 0.65/1.32 mem @ c_2Ebool_2EF @ bool ).
% 0.65/1.32
% 0.65/1.32 thf(ax_false_p,axiom,
% 0.65/1.32 ~ ( p @ c_2Ebool_2EF ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EIN,type,
% 0.65/1.32 c_2Ebool_2EIN: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EIN,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ELET,type,
% 0.65/1.32 c_2Ebool_2ELET: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ELET,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EONE__ONE,type,
% 0.65/1.32 c_2Ebool_2EONE__ONE: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EONE__ONE,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2EONTO,type,
% 0.65/1.32 c_2Ebool_2EONTO: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2EONTO,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONTO @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ERES__ABSTRACT,type,
% 0.65/1.32 c_2Ebool_2ERES__ABSTRACT: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ERES__ABSTRACT,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ERES__EXISTS,type,
% 0.65/1.32 c_2Ebool_2ERES__EXISTS: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ERES__EXISTS,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ERES__EXISTS__UNIQUE,type,
% 0.65/1.32 c_2Ebool_2ERES__EXISTS__UNIQUE: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ERES__EXISTS__UNIQUE,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ERES__FORALL,type,
% 0.65/1.32 c_2Ebool_2ERES__FORALL: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ERES__FORALL,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ERES__SELECT,type,
% 0.65/1.32 c_2Ebool_2ERES__SELECT: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ERES__SELECT,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__SELECT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ET,type,
% 0.65/1.32 c_2Ebool_2ET: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ET,axiom,
% 0.65/1.32 mem @ c_2Ebool_2ET @ bool ).
% 0.65/1.32
% 0.65/1.32 thf(ax_true_p,axiom,
% 0.65/1.32 p @ c_2Ebool_2ET ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2ETYPE__DEFINITION,type,
% 0.65/1.32 c_2Ebool_2ETYPE__DEFINITION: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2ETYPE__DEFINITION,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ bool ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.65/1.32 c_2Ebool_2E_5C_2F: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.65/1.32 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_or_p,axiom,
% 0.65/1.32 ! [Q: $i] :
% 0.65/1.32 ( ( mem @ Q @ bool )
% 0.65/1.32 => ! [R: $i] :
% 0.65/1.32 ( ( mem @ R @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.65/1.32 <=> ( ( p @ Q )
% 0.65/1.32 | ( p @ R ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2Eitself__case,type,
% 0.65/1.32 c_2Ebool_2Eitself__case: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2Eitself__case,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eitself__case @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2Eliteral__case,type,
% 0.65/1.32 c_2Ebool_2Eliteral__case: del > del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2Eliteral__case,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2Ethe__value,type,
% 0.65/1.32 c_2Ebool_2Ethe__value: del > $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2Ethe__value,axiom,
% 0.65/1.32 ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(tp_c_2Ebool_2E_7E,type,
% 0.65/1.32 c_2Ebool_2E_7E: $i ).
% 0.65/1.32
% 0.65/1.32 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.65/1.32 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_neg_p,axiom,
% 0.65/1.32 ! [Q: $i] :
% 0.65/1.32 ( ( mem @ Q @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.65/1.32 <=> ~ ( p @ Q ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ET__DEF,axiom,
% 0.65/1.32 ( $true
% 0.65/1.32 <=> ( ( lam @ bool
% 0.65/1.32 @ ^ [V0x: $i] : V0x )
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V1x: $i] : V1x ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EFORALL__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0P: $i] :
% 0.65/1.32 ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0P )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : c_2Ebool_2ET ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EEXISTS__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2E_3F @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0P: $i] : ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EAND__DEF,axiom,
% 0.65/1.32 ( c_2Ebool_2E_2F_5C
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V0t1: $i] :
% 0.65/1.32 ( lam @ bool
% 0.65/1.32 @ ^ [V1t2: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ bool )
% 0.65/1.32 @ ( lam @ bool
% 0.65/1.32 @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) ) @ V2t ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EOR__DEF,axiom,
% 0.65/1.32 ( c_2Ebool_2E_5C_2F
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V0t1: $i] :
% 0.65/1.32 ( lam @ bool
% 0.65/1.32 @ ^ [V1t2: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ bool )
% 0.65/1.32 @ ( lam @ bool
% 0.65/1.32 @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ V2t ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) @ V2t ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EF__DEF,axiom,
% 0.65/1.32 ( $false
% 0.65/1.32 <=> ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ENOT__DEF,axiom,
% 0.65/1.32 ( c_2Ebool_2E_7E
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V0t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t ) @ c_2Ebool_2EF ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0P: $i] :
% 0.65/1.32 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0P ) )
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V1x ) ) @ ( ap @ V0P @ V2y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ELET__DEF,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] :
% 0.65/1.32 ( ( c_2Ebool_2ELET @ A_27a @ A_27b )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.65/1.32 @ ^ [V0f: $i] :
% 0.65/1.32 ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ECOND__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2ECOND @ A_27a )
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V0t: $i] :
% 0.65/1.32 ( lam @ A_27a
% 0.65/1.32 @ ^ [V1t1: $i] :
% 0.65/1.32 ( lam @ A_27a
% 0.65/1.32 @ ^ [V2t2: $i] :
% 0.65/1.32 ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V1t1 ) ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2t2 ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EONE__ONE__DEF,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] :
% 0.65/1.32 ( ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.65/1.32 @ ^ [V0f: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x1: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x2: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V1x1 ) ) @ ( ap @ V0f @ V2x2 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x1 ) @ V2x2 ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EONTO__DEF,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] :
% 0.65/1.32 ( ( c_2Ebool_2EONTO @ A_27a @ A_27b )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.65/1.32 @ ^ [V0f: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ A_27b )
% 0.65/1.32 @ ( lam @ A_27b
% 0.65/1.32 @ ^ [V1y: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1y ) @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ETYPE__DEFINITION,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] :
% 0.65/1.32 ( ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0P: $i] :
% 0.65/1.32 ( lam @ ( arr @ A_27b @ A_27a )
% 0.65/1.32 @ ^ [V1rep: $i] :
% 0.65/1.32 ( ap
% 0.65/1.32 @ ( ap @ c_2Ebool_2E_2F_5C
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_21 @ A_27b )
% 0.65/1.32 @ ( lam @ A_27b
% 0.65/1.32 @ ^ [V2x_27: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ A_27b )
% 0.65/1.32 @ ( lam @ A_27b
% 0.65/1.32 @ ^ [V3x_27_27: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1rep @ V2x_27 ) ) @ ( ap @ V1rep @ V3x_27_27 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V2x_27 ) @ V3x_27_27 ) ) ) ) ) ) )
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V4x: $i] :
% 0.65/1.32 ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V0P @ V4x ) )
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
% 0.65/1.32 @ ( lam @ A_27b
% 0.65/1.32 @ ^ [V5x_27: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ ( ap @ V1rep @ V5x_27 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( p @ V0t )
% 0.65/1.32 <=> $true )
% 0.65/1.32 | ( ( p @ V0t )
% 0.65/1.32 <=> $false ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EETA__AX,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
% 0.65/1.32 = V0t ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ESELECT__AX,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V1x ) )
% 0.65/1.32 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(stp_i,type,
% 0.65/1.32 tp__i: $tType ).
% 0.65/1.32
% 0.65/1.32 thf(stp_inj_i,type,
% 0.65/1.32 inj__i: tp__i > $i ).
% 0.65/1.32
% 0.65/1.32 thf(stp_surj_i,type,
% 0.65/1.32 surj__i: $i > tp__i ).
% 0.65/1.32
% 0.65/1.32 thf(stp_inj_surj_i,axiom,
% 0.65/1.32 ! [X: tp__i] :
% 0.65/1.32 ( ( surj__i @ ( inj__i @ X ) )
% 0.65/1.32 = X ) ).
% 0.65/1.32
% 0.65/1.32 thf(stp_inj_mem_i,axiom,
% 0.65/1.32 ! [X: tp__i] : ( mem @ ( inj__i @ X ) @ ind ) ).
% 0.65/1.32
% 0.65/1.32 thf(stp_iso_mem_i,axiom,
% 0.65/1.32 ! [X: $i] :
% 0.65/1.32 ( ( mem @ X @ ind )
% 0.65/1.32 => ( X
% 0.65/1.32 = ( inj__i @ ( surj__i @ X ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EINFINITY__AX,axiom,
% 0.65/1.32 ? [V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ ind @ ind ) )
% 0.65/1.32 & ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ V0f ) )
% 0.65/1.32 & ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ V0f ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2Eliteral__case__DEF,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] :
% 0.65/1.32 ( ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.65/1.32 @ ^ [V0f: $i] :
% 0.65/1.32 ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EIN__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2EIN @ A_27a )
% 0.65/1.32 = ( lam @ A_27a
% 0.65/1.32 @ ^ [V0x: $i] :
% 0.65/1.32 ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V1f: $i] : ( ap @ V1f @ V0x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ERES__FORALL__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2ERES__FORALL @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0p: $i] :
% 0.65/1.32 ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V1m: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ERES__EXISTS__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2ERES__EXISTS @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0p: $i] :
% 0.65/1.32 ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V1m: $i] :
% 0.65/1.32 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0p: $i] :
% 0.65/1.32 ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V1m: $i] :
% 0.65/1.32 ( ap
% 0.65/1.32 @ ( ap @ c_2Ebool_2E_2F_5C
% 0.65/1.32 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0p )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ V1m @ V2x ) ) ) )
% 0.65/1.32 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] :
% 0.65/1.32 ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V4y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1m @ V3x ) ) @ ( ap @ V1m @ V4y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ERES__SELECT__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2ERES__SELECT @ A_27a )
% 0.65/1.32 = ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V0p: $i] :
% 0.65/1.32 ( lam @ ( arr @ A_27a @ bool )
% 0.65/1.32 @ ^ [V1m: $i] :
% 0.65/1.32 ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EBOUNDED__DEF,axiom,
% 0.65/1.32 ( c_2Ebool_2EBOUNDED
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V0v: $i] : c_2Ebool_2ET ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2EDATATYPE__TAG__DEF,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ( c_2Ebool_2EDATATYPE @ A_27a )
% 0.65/1.32 = ( lam @ A_27a
% 0.65/1.32 @ ^ [V0x: $i] : c_2Ebool_2ET ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.65/1.32 $true ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 => ( p @ V1t2 ) )
% 0.65/1.32 => ( ( ( p @ V1t2 )
% 0.65/1.32 => ( p @ V0t1 ) )
% 0.65/1.32 => ( ( p @ V0t1 )
% 0.65/1.32 <=> ( p @ V1t2 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EFALSITY,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( $false
% 0.65/1.32 => ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EETA__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0M: $i] :
% 0.65/1.32 ( ( mem @ V0M @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ V0M @ V1x ) )
% 0.65/1.32 = V0M ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( p @ V0t )
% 0.65/1.32 | ~ ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBETA__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ A_27a )
% 0.65/1.32 => ( ( ap
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ V0f @ V2x ) )
% 0.65/1.32 @ V1y )
% 0.65/1.32 = ( ap @ V0f @ V1y ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELET__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ( ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ V0f ) @ V1x )
% 0.65/1.32 = ( ap @ V0f @ V1x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EFORALL__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A_27a ) @ V0f ) )
% 0.65/1.32 <=> ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V0f @ V1x ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXISTS__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0f ) )
% 0.65/1.32 <=> ? [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0f @ V1x ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EABS__SIMP,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ A_27a )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ A_27b )
% 0.65/1.32 => ( ( ap
% 0.65/1.32 @ ( lam @ A_27b
% 0.65/1.32 @ ^ [V2x: $i] : V0t1 )
% 0.65/1.32 @ V1t2 )
% 0.65/1.32 = V0t1 ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.65/1.32 ! [A_27a: del,V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXISTS__SIMP,axiom,
% 0.65/1.32 ! [A_27a: del,V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ? [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 & ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EAND__INTRO__THM,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( p @ V0t1 )
% 0.65/1.32 => ( ( p @ V1t2 )
% 0.65/1.32 => ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EAND1__THM,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) )
% 0.65/1.32 => ( p @ V0t1 ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EAND2__THM,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) )
% 0.65/1.32 => ( p @ V1t2 ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECONJ__SYM,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) )
% 0.65/1.32 <=> ( ( p @ V1t2 )
% 0.65/1.32 & ( p @ V0t1 ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECONJ__COMM,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) )
% 0.65/1.32 <=> ( ( p @ V1t2 )
% 0.65/1.32 & ( p @ V0t1 ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECONJ__ASSOC,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ! [V2t3: $i] :
% 0.65/1.32 ( ( mem @ V2t3 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 )
% 0.65/1.32 & ( p @ V2t3 ) )
% 0.65/1.32 <=> ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 )
% 0.65/1.32 & ( p @ V2t3 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EOR__INTRO__THM1,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( p @ V0t1 )
% 0.65/1.32 => ( ( p @ V0t1 )
% 0.65/1.32 | ( p @ V1t2 ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EOR__INTRO__THM2,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( p @ V1t2 )
% 0.65/1.32 => ( ( p @ V0t1 )
% 0.65/1.32 | ( p @ V1t2 ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EOR__ELIM__THM,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ! [V1t1: $i] :
% 0.65/1.32 ( ( mem @ V1t1 @ bool )
% 0.65/1.32 => ! [V2t2: $i] :
% 0.65/1.32 ( ( mem @ V2t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V1t1 )
% 0.65/1.32 | ( p @ V2t2 ) )
% 0.65/1.32 => ( ( ( p @ V1t1 )
% 0.65/1.32 => ( p @ V0t ) )
% 0.65/1.32 => ( ( ( p @ V2t2 )
% 0.65/1.32 => ( p @ V0t ) )
% 0.65/1.32 => ( p @ V0t ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__F,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( p @ V0t )
% 0.65/1.32 => $false )
% 0.65/1.32 => ~ ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EF__IMP,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ~ ( p @ V0t )
% 0.65/1.32 => ( ( p @ V0t )
% 0.65/1.32 => $false ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ENOT__F,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ~ ( p @ V0t )
% 0.65/1.32 => ( ( p @ V0t )
% 0.65/1.32 <=> $false ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ENOT__AND,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ~ ( ( p @ V0t )
% 0.65/1.32 & ~ ( p @ V0t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( $true
% 0.65/1.32 & ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 & $true )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( $false
% 0.65/1.32 & ( p @ V0t ) )
% 0.65/1.32 <=> $false )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 & $false )
% 0.65/1.32 <=> $false )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 & ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EOR__CLAUSES,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( $true
% 0.65/1.32 | ( p @ V0t ) )
% 0.65/1.32 <=> $true )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 | $true )
% 0.65/1.32 <=> $true )
% 0.65/1.32 & ( ( $false
% 0.65/1.32 | ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 | $false )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 | ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( $true
% 0.65/1.32 => ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 => $true )
% 0.65/1.32 <=> $true )
% 0.65/1.32 & ( ( $false
% 0.65/1.32 => ( p @ V0t ) )
% 0.65/1.32 <=> $true )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 => ( p @ V0t ) )
% 0.65/1.32 <=> $true )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 => $false )
% 0.65/1.32 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.65/1.32 ( ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ~ ~ ( p @ V0t )
% 0.65/1.32 <=> ( p @ V0t ) ) )
% 0.65/1.32 & ( ~ $true
% 0.65/1.32 <=> $false )
% 0.65/1.32 & ( ~ $false
% 0.65/1.32 <=> $true ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__REFL,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ( V0x = V0x ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ( ( V0x = V0x )
% 0.65/1.32 <=> $true ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__SYM,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ A_27a )
% 0.65/1.32 => ( ( V0x = V1y )
% 0.65/1.32 => ( V1y = V0x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ A_27a )
% 0.65/1.32 => ( ( V0x = V1y )
% 0.65/1.32 <=> ( V1y = V0x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__EXT,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V1g: $i] :
% 0.65/1.32 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( ap @ V0f @ V2x )
% 0.65/1.32 = ( ap @ V1g @ V2x ) ) )
% 0.65/1.32 => ( V0f = V1g ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EFUN__EQ__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V1g: $i] :
% 0.65/1.32 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ( V0f = V1g )
% 0.65/1.32 <=> ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( ap @ V0f @ V2x )
% 0.65/1.32 = ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__TRANS,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ A_27a )
% 0.65/1.32 => ! [V2z: $i] :
% 0.65/1.32 ( ( mem @ V2z @ A_27a )
% 0.65/1.32 => ( ( ( V0x = V1y )
% 0.65/1.32 & ( V1y = V2z ) )
% 0.65/1.32 => ( V0x = V2z ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT,axiom,
% 0.65/1.32 ( ~ ( $true
% 0.65/1.32 <=> $false )
% 0.65/1.32 & ~ ( $false
% 0.65/1.32 <=> $true ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( $true
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 <=> $true )
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 & ( ( $false
% 0.65/1.32 <=> ( p @ V0t ) )
% 0.65/1.32 <=> ~ ( p @ V0t ) )
% 0.65/1.32 & ( ( ( p @ V0t )
% 0.65/1.32 <=> $false )
% 0.65/1.32 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
% 0.65/1.32 ! [A_27a: del,V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ A_27a )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ A_27a )
% 0.65/1.32 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
% 0.65/1.32 = V0t1 )
% 0.65/1.32 & ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V0t1 ) @ V1t2 )
% 0.65/1.32 = V1t2 ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__ID,axiom,
% 0.65/1.32 ! [A_27a: del,V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1t: $i] :
% 0.65/1.32 ( ( mem @ V1t @ A_27a )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0b ) @ V1t ) @ V1t )
% 0.65/1.32 = V1t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESELECT__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ V0P
% 0.65/1.32 @ ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ V0P @ V1x ) ) ) ) )
% 0.65/1.32 <=> ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESELECT__REFL,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ( ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1y ) @ V0x ) ) )
% 0.65/1.32 = V0x ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESELECT__REFL__2,axiom,
% 0.65/1.32 ! [A_27a: del,V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ A_27a )
% 0.65/1.32 => ( ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0x ) @ V1y ) ) )
% 0.65/1.32 = V0x ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESELECT__UNIQUE,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ( ! [V2y: $i] :
% 0.65/1.32 ( ( mem @ V2y @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V2y ) )
% 0.65/1.32 <=> ( V2y = V1x ) ) )
% 0.65/1.32 => ( ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P )
% 0.65/1.32 = V1x ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESELECT__ELIM__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.32 & ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V3x ) )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V3x ) ) ) ) )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ENOT__FORALL__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ~ ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V1x ) ) )
% 0.65/1.32 <=> ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ~ ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ENOT__EXISTS__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ~ ? [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V1x ) ) )
% 0.65/1.32 <=> ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ~ ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EFORALL__AND__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ( ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 & ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.32 & ( p @ V1Q ) )
% 0.65/1.32 <=> ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V3x ) )
% 0.65/1.32 & ( p @ V1Q ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 & ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXISTS__OR__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 | ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ( ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 | ? [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.32 | ( p @ V1Q ) )
% 0.65/1.32 <=> ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( ( p @ ( ap @ V0P @ V3x ) )
% 0.65/1.32 | ( p @ V1Q ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 | ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( ( p @ V0P )
% 0.65/1.32 | ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBOTH__EXISTS__AND__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ V0P )
% 0.65/1.32 & ( p @ V1Q ) )
% 0.65/1.32 <=> ( ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ V0P ) )
% 0.65/1.32 & ? [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 & ( p @ V1Q ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 & ( p @ V1Q ) )
% 0.65/1.32 <=> ( ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 & ( p @ V1Q ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ V0P )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V2x ) ) )
% 0.65/1.32 <=> ( ( p @ V0P )
% 0.65/1.32 & ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBOTH__FORALL__OR__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 | ( p @ V1Q ) ) )
% 0.65/1.32 <=> ( ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ V0P ) )
% 0.65/1.32 | ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( p @ V1Q ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0Q: $i] :
% 0.65/1.32 ( ( mem @ V0Q @ bool )
% 0.65/1.32 => ! [V1P: $i] :
% 0.65/1.32 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V1P @ V2x ) )
% 0.65/1.32 | ( p @ V0Q ) ) )
% 0.65/1.32 <=> ( ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V1P @ V3x ) ) )
% 0.65/1.32 | ( p @ V0Q ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 | ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ( ( p @ V0P )
% 0.65/1.32 | ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBOTH__FORALL__IMP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 => ( p @ V1Q ) ) )
% 0.65/1.32 <=> ( ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ V0P ) )
% 0.65/1.32 => ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( p @ V1Q ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__FORALL__IMP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 => ( p @ V1Q ) ) )
% 0.65/1.32 <=> ( ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 => ( p @ V1Q ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__FORALL__IMP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ( ( p @ V0P )
% 0.65/1.32 => ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBOTH__EXISTS__IMP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( ( p @ V0P )
% 0.65/1.32 => ( p @ V1Q ) ) )
% 0.65/1.32 <=> ( ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ V0P ) )
% 0.65/1.32 => ? [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 & ( p @ V1Q ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__EXISTS__IMP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 => ( p @ V1Q ) ) )
% 0.65/1.32 <=> ( ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 => ( p @ V1Q ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__EXISTS__IMP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( ( p @ V0P )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 <=> ( ( p @ V0P )
% 0.65/1.32 => ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EOR__IMP__THM,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 <=> ( ( p @ V1B )
% 0.65/1.32 | ( p @ V0A ) ) )
% 0.65/1.32 <=> ( ( p @ V1B )
% 0.65/1.32 => ( p @ V0A ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ENOT__IMP,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ( ~ ( ( p @ V0A )
% 0.65/1.32 => ( p @ V1B ) )
% 0.65/1.32 <=> ( ( p @ V0A )
% 0.65/1.32 & ~ ( p @ V1B ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EDISJ__ASSOC,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ! [V2C: $i] :
% 0.65/1.32 ( ( mem @ V2C @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 | ( p @ V1B )
% 0.65/1.32 | ( p @ V2C ) )
% 0.65/1.32 <=> ( ( p @ V0A )
% 0.65/1.32 | ( p @ V1B )
% 0.65/1.32 | ( p @ V2C ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EDISJ__SYM,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 | ( p @ V1B ) )
% 0.65/1.32 <=> ( ( p @ V1B )
% 0.65/1.32 | ( p @ V0A ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EDISJ__COMM,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 | ( p @ V1B ) )
% 0.65/1.32 <=> ( ( p @ V1B )
% 0.65/1.32 | ( p @ V0A ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ( ( ~ ( ( p @ V0A )
% 0.65/1.32 & ( p @ V1B ) )
% 0.65/1.32 <=> ( ~ ( p @ V0A )
% 0.65/1.32 | ~ ( p @ V1B ) ) )
% 0.65/1.32 & ( ~ ( ( p @ V0A )
% 0.65/1.32 | ( p @ V1B ) )
% 0.65/1.32 <=> ( ~ ( p @ V0A )
% 0.65/1.32 & ~ ( p @ V1B ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__AND__OVER__OR,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ! [V2C: $i] :
% 0.65/1.32 ( ( mem @ V2C @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 & ( ( p @ V1B )
% 0.65/1.32 | ( p @ V2C ) ) )
% 0.65/1.32 <=> ( ( ( p @ V0A )
% 0.65/1.32 & ( p @ V1B ) )
% 0.65/1.32 | ( ( p @ V0A )
% 0.65/1.32 & ( p @ V2C ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__AND__OVER__OR,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ! [V2C: $i] :
% 0.65/1.32 ( ( mem @ V2C @ bool )
% 0.65/1.32 => ( ( ( ( p @ V1B )
% 0.65/1.32 | ( p @ V2C ) )
% 0.65/1.32 & ( p @ V0A ) )
% 0.65/1.32 <=> ( ( ( p @ V1B )
% 0.65/1.32 & ( p @ V0A ) )
% 0.65/1.32 | ( ( p @ V2C )
% 0.65/1.32 & ( p @ V0A ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__OR__OVER__AND,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ! [V2C: $i] :
% 0.65/1.32 ( ( mem @ V2C @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 | ( ( p @ V1B )
% 0.65/1.32 & ( p @ V2C ) ) )
% 0.65/1.32 <=> ( ( ( p @ V0A )
% 0.65/1.32 | ( p @ V1B ) )
% 0.65/1.32 & ( ( p @ V0A )
% 0.65/1.32 | ( p @ V2C ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ! [V2C: $i] :
% 0.65/1.32 ( ( mem @ V2C @ bool )
% 0.65/1.32 => ( ( ( ( p @ V1B )
% 0.65/1.32 & ( p @ V2C ) )
% 0.65/1.32 | ( p @ V0A ) )
% 0.65/1.32 <=> ( ( ( p @ V1B )
% 0.65/1.32 | ( p @ V0A ) )
% 0.65/1.32 & ( ( p @ V2C )
% 0.65/1.32 | ( p @ V0A ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__DISJ__THM,axiom,
% 0.65/1.32 ! [V0A: $i] :
% 0.65/1.32 ( ( mem @ V0A @ bool )
% 0.65/1.32 => ! [V1B: $i] :
% 0.65/1.32 ( ( mem @ V1B @ bool )
% 0.65/1.32 => ( ( ( p @ V0A )
% 0.65/1.32 => ( p @ V1B ) )
% 0.65/1.32 <=> ( ~ ( p @ V0A )
% 0.65/1.32 | ( p @ V1B ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EDISJ__IMP__THM,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ! [V2R: $i] :
% 0.65/1.32 ( ( mem @ V2R @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0P )
% 0.65/1.32 | ( p @ V1Q ) )
% 0.65/1.32 => ( p @ V2R ) )
% 0.65/1.32 <=> ( ( ( p @ V0P )
% 0.65/1.32 => ( p @ V2R ) )
% 0.65/1.32 & ( ( p @ V1Q )
% 0.65/1.32 => ( p @ V2R ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__CONJ__THM,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ! [V2R: $i] :
% 0.65/1.32 ( ( mem @ V2R @ bool )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 => ( ( p @ V1Q )
% 0.65/1.32 & ( p @ V2R ) ) )
% 0.65/1.32 <=> ( ( ( p @ V0P )
% 0.65/1.32 => ( p @ V1Q ) )
% 0.65/1.32 & ( ( p @ V0P )
% 0.65/1.32 => ( p @ V2R ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__F__EQ__F,axiom,
% 0.65/1.32 ! [V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( ( p @ V0t )
% 0.65/1.32 => $false )
% 0.65/1.32 <=> ( ( p @ V0t )
% 0.65/1.32 <=> $false ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ! [V2t3: $i] :
% 0.65/1.32 ( ( mem @ V2t3 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 => ( ( p @ V1t2 )
% 0.65/1.32 => ( p @ V2t3 ) ) )
% 0.65/1.32 <=> ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) )
% 0.65/1.32 => ( p @ V2t3 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__IMP__THM,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 <=> ( p @ V1t2 ) )
% 0.65/1.32 <=> ( ( ( p @ V0t1 )
% 0.65/1.32 => ( p @ V1t2 ) )
% 0.65/1.32 & ( ( p @ V1t2 )
% 0.65/1.32 => ( p @ V0t1 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEQ__EXPAND,axiom,
% 0.65/1.32 ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ bool )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ bool )
% 0.65/1.32 => ( ( ( p @ V0t1 )
% 0.65/1.32 <=> ( p @ V1t2 ) )
% 0.65/1.32 <=> ( ( ( p @ V0t1 )
% 0.65/1.32 & ( p @ V1t2 ) )
% 0.65/1.32 | ( ~ ( p @ V0t1 )
% 0.65/1.32 & ~ ( p @ V1t2 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__RATOR,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1f: $i] :
% 0.65/1.32 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V2g: $i] :
% 0.65/1.32 ( ( mem @ V2g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27a @ A_27b ) ) @ V0b ) @ V1f ) @ V2g ) @ V3x )
% 0.65/1.32 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ V0b ) @ ( ap @ V1f @ V3x ) ) @ ( ap @ V2g @ V3x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__RAND,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V1b: $i] :
% 0.65/1.32 ( ( mem @ V1b @ bool )
% 0.65/1.32 => ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ! [V3y: $i] :
% 0.65/1.32 ( ( mem @ V3y @ A_27a )
% 0.65/1.32 => ( ( ap @ V0f @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1b ) @ V2x ) @ V3y ) )
% 0.65/1.32 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ V1b ) @ ( ap @ V0f @ V2x ) ) @ ( ap @ V0f @ V3y ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__ABS,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1f: $i] :
% 0.65/1.32 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V2g: $i] :
% 0.65/1.32 ( ( mem @ V2g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ V0b ) @ ( ap @ V1f @ V3x ) ) @ ( ap @ V2g @ V3x ) ) )
% 0.65/1.32 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27a @ A_27b ) ) @ V0b ) @ V1f ) @ V2g ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__EXPAND,axiom,
% 0.65/1.32 ! [V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1t1: $i] :
% 0.65/1.32 ( ( mem @ V1t1 @ bool )
% 0.65/1.32 => ! [V2t2: $i] :
% 0.65/1.32 ( ( mem @ V2t2 @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0b ) @ V1t1 ) @ V2t2 ) )
% 0.65/1.32 <=> ( ( ~ ( p @ V0b )
% 0.65/1.32 | ( p @ V1t1 ) )
% 0.65/1.32 & ( ( p @ V0b )
% 0.65/1.32 | ( p @ V2t2 ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__EXPAND__IMP,axiom,
% 0.65/1.32 ! [V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1t1: $i] :
% 0.65/1.32 ( ( mem @ V1t1 @ bool )
% 0.65/1.32 => ! [V2t2: $i] :
% 0.65/1.32 ( ( mem @ V2t2 @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0b ) @ V1t1 ) @ V2t2 ) )
% 0.65/1.32 <=> ( ( ( p @ V0b )
% 0.65/1.32 => ( p @ V1t1 ) )
% 0.65/1.32 & ( ~ ( p @ V0b )
% 0.65/1.32 => ( p @ V2t2 ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__EXPAND__OR,axiom,
% 0.65/1.32 ! [V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1t1: $i] :
% 0.65/1.32 ( ( mem @ V1t1 @ bool )
% 0.65/1.32 => ! [V2t2: $i] :
% 0.65/1.32 ( ( mem @ V2t2 @ bool )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0b ) @ V1t1 ) @ V2t2 ) )
% 0.65/1.32 <=> ( ( ( p @ V0b )
% 0.65/1.32 & ( p @ V1t1 ) )
% 0.65/1.32 | ( ~ ( p @ V0b )
% 0.65/1.32 & ( p @ V2t2 ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ETYPE__DEFINITION__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1rep: $i] :
% 0.65/1.32 ( ( mem @ V1rep @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ V0P ) @ V1rep ) )
% 0.65/1.32 <=> ( ! [V2x_27: $i] :
% 0.65/1.32 ( ( mem @ V2x_27 @ A_27b )
% 0.65/1.32 => ! [V3x_27_27: $i] :
% 0.65/1.32 ( ( mem @ V3x_27_27 @ A_27b )
% 0.65/1.32 => ( ( ( ap @ V1rep @ V2x_27 )
% 0.65/1.32 = ( ap @ V1rep @ V3x_27_27 ) )
% 0.65/1.32 => ( V2x_27 = V3x_27_27 ) ) ) )
% 0.65/1.32 & ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V4x ) )
% 0.65/1.32 <=> ? [V5x_27: $i] :
% 0.65/1.32 ( ( mem @ V5x_27 @ A_27b )
% 0.65/1.32 & ( V4x
% 0.65/1.32 = ( ap @ V1rep @ V5x_27 ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EONTO__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( c_2Ebool_2EONTO @ A_27a @ A_27b ) @ V0f ) )
% 0.65/1.32 <=> ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ A_27b )
% 0.65/1.32 => ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( V1y
% 0.65/1.32 = ( ap @ V0f @ V2x ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EONE__ONE__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b ) @ V0f ) )
% 0.65/1.32 <=> ! [V1x1: $i] :
% 0.65/1.32 ( ( mem @ V1x1 @ A_27a )
% 0.65/1.32 => ! [V2x2: $i] :
% 0.65/1.32 ( ( mem @ V2x2 @ A_27a )
% 0.65/1.32 => ( ( ( ap @ V0f @ V1x1 )
% 0.65/1.32 = ( ap @ V0f @ V2x2 ) )
% 0.65/1.32 => ( V1x1 = V2x2 ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EABS__REP__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ? [V1rep: $i] :
% 0.65/1.32 ( ( mem @ V1rep @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.32 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ V0P ) @ V1rep ) ) )
% 0.65/1.32 => ? [V2rep: $i] :
% 0.65/1.32 ( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.32 & ? [V3abs: $i] :
% 0.65/1.32 ( ( mem @ V3abs @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 & ! [V4a: $i] :
% 0.65/1.32 ( ( mem @ V4a @ A_27b )
% 0.65/1.32 => ( ( ap @ V3abs @ ( ap @ V2rep @ V4a ) )
% 0.65/1.32 = V4a ) )
% 0.65/1.32 & ! [V5r: $i] :
% 0.65/1.32 ( ( mem @ V5r @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V5r ) )
% 0.65/1.32 <=> ( ( ap @ V2rep @ ( ap @ V3abs @ V5r ) )
% 0.65/1.32 = V5r ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELET__RAND,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27b @ bool ) )
% 0.65/1.32 => ! [V1N: $i] :
% 0.65/1.32 ( ( mem @ V1N @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V2M: $i] :
% 0.65/1.32 ( ( mem @ V2M @ A_27a )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ V0P
% 0.65/1.32 @ ( ap
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ A_27b )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] : ( ap @ V1N @ V3x ) ) )
% 0.65/1.32 @ V2M ) ) )
% 0.65/1.32 <=> ( p
% 0.65/1.32 @ ( ap
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ bool )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V4x: $i] : ( ap @ V0P @ ( ap @ V1N @ V4x ) ) ) )
% 0.65/1.32 @ V2M ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELET__RATOR,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,A_27c: del,V0N: $i] :
% 0.65/1.32 ( ( mem @ V0N @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 0.65/1.32 => ! [V1M: $i] :
% 0.65/1.32 ( ( mem @ V1M @ A_27a )
% 0.65/1.32 => ! [V2b: $i] :
% 0.65/1.32 ( ( mem @ V2b @ A_27b )
% 0.65/1.32 => ( ( ap
% 0.65/1.32 @ ( ap
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] : ( ap @ V0N @ V3x ) ) )
% 0.65/1.32 @ V1M )
% 0.65/1.32 @ V2b )
% 0.65/1.32 = ( ap
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ A_27c )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V4x: $i] : ( ap @ ( ap @ V0N @ V4x ) @ V2b ) ) )
% 0.65/1.32 @ V1M ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESWAP__FORALL__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 0.65/1.32 => ( ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ! [V2y: $i] :
% 0.65/1.32 ( ( mem @ V2y @ A_27b )
% 0.65/1.32 => ( p @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) )
% 0.65/1.32 <=> ! [V3y: $i] :
% 0.65/1.32 ( ( mem @ V3y @ A_27b )
% 0.65/1.32 => ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ ( ap @ V0P @ V4x ) @ V3y ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESWAP__EXISTS__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 0.65/1.32 => ( ? [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 & ? [V2y: $i] :
% 0.65/1.32 ( ( mem @ V2y @ A_27b )
% 0.65/1.32 & ( p @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) )
% 0.65/1.32 <=> ? [V3y: $i] :
% 0.65/1.32 ( ( mem @ V3y @ A_27b )
% 0.65/1.32 & ? [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ ( ap @ V0P @ V4x ) @ V3y ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXISTS__UNIQUE__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ V0P @ V1x ) ) ) )
% 0.65/1.32 <=> ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.32 & ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ! [V4y: $i] :
% 0.65/1.32 ( ( mem @ V4y @ A_27a )
% 0.65/1.32 => ( ( ( p @ ( ap @ V0P @ V3x ) )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V4y ) ) )
% 0.65/1.32 => ( V3x = V4y ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELET__CONG,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V1g: $i] :
% 0.65/1.32 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V2M: $i] :
% 0.65/1.32 ( ( mem @ V2M @ A_27a )
% 0.65/1.32 => ! [V3N: $i] :
% 0.65/1.32 ( ( mem @ V3N @ A_27a )
% 0.65/1.32 => ( ( ( V2M = V3N )
% 0.65/1.32 & ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( ( V4x = V3N )
% 0.65/1.32 => ( ( ap @ V0f @ V4x )
% 0.65/1.32 = ( ap @ V1g @ V4x ) ) ) ) )
% 0.65/1.32 => ( ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ V0f ) @ V2M )
% 0.65/1.32 = ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ V1g ) @ V3N ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EIMP__CONG,axiom,
% 0.65/1.32 ! [V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ bool )
% 0.65/1.32 => ! [V1x_27: $i] :
% 0.65/1.32 ( ( mem @ V1x_27 @ bool )
% 0.65/1.32 => ! [V2y: $i] :
% 0.65/1.32 ( ( mem @ V2y @ bool )
% 0.65/1.32 => ! [V3y_27: $i] :
% 0.65/1.32 ( ( mem @ V3y_27 @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0x )
% 0.65/1.32 <=> ( p @ V1x_27 ) )
% 0.65/1.32 & ( ( p @ V1x_27 )
% 0.65/1.32 => ( ( p @ V2y )
% 0.65/1.32 <=> ( p @ V3y_27 ) ) ) )
% 0.65/1.32 => ( ( ( p @ V0x )
% 0.65/1.32 => ( p @ V2y ) )
% 0.65/1.32 <=> ( ( p @ V1x_27 )
% 0.65/1.32 => ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EAND__CONG,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1P_27: $i] :
% 0.65/1.32 ( ( mem @ V1P_27 @ bool )
% 0.65/1.32 => ! [V2Q: $i] :
% 0.65/1.32 ( ( mem @ V2Q @ bool )
% 0.65/1.32 => ! [V3Q_27: $i] :
% 0.65/1.32 ( ( mem @ V3Q_27 @ bool )
% 0.65/1.32 => ( ( ( ( p @ V2Q )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 <=> ( p @ V1P_27 ) ) )
% 0.65/1.32 & ( ( p @ V1P_27 )
% 0.65/1.32 => ( ( p @ V2Q )
% 0.65/1.32 <=> ( p @ V3Q_27 ) ) ) )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 & ( p @ V2Q ) )
% 0.65/1.32 <=> ( ( p @ V1P_27 )
% 0.65/1.32 & ( p @ V3Q_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__AND__CONG,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1P_27: $i] :
% 0.65/1.32 ( ( mem @ V1P_27 @ bool )
% 0.65/1.32 => ! [V2Q: $i] :
% 0.65/1.32 ( ( mem @ V2Q @ bool )
% 0.65/1.32 => ! [V3Q_27: $i] :
% 0.65/1.32 ( ( mem @ V3Q_27 @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0P )
% 0.65/1.32 <=> ( p @ V1P_27 ) )
% 0.65/1.32 & ( ( p @ V1P_27 )
% 0.65/1.32 => ( ( p @ V2Q )
% 0.65/1.32 <=> ( p @ V3Q_27 ) ) ) )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 & ( p @ V2Q ) )
% 0.65/1.32 <=> ( ( p @ V1P_27 )
% 0.65/1.32 & ( p @ V3Q_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EOR__CONG,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1P_27: $i] :
% 0.65/1.32 ( ( mem @ V1P_27 @ bool )
% 0.65/1.32 => ! [V2Q: $i] :
% 0.65/1.32 ( ( mem @ V2Q @ bool )
% 0.65/1.32 => ! [V3Q_27: $i] :
% 0.65/1.32 ( ( mem @ V3Q_27 @ bool )
% 0.65/1.32 => ( ( ( ~ ( p @ V2Q )
% 0.65/1.32 => ( ( p @ V0P )
% 0.65/1.32 <=> ( p @ V1P_27 ) ) )
% 0.65/1.32 & ( ~ ( p @ V1P_27 )
% 0.65/1.32 => ( ( p @ V2Q )
% 0.65/1.32 <=> ( p @ V3Q_27 ) ) ) )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 | ( p @ V2Q ) )
% 0.65/1.32 <=> ( ( p @ V1P_27 )
% 0.65/1.32 | ( p @ V3Q_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ELEFT__OR__CONG,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1P_27: $i] :
% 0.65/1.32 ( ( mem @ V1P_27 @ bool )
% 0.65/1.32 => ! [V2Q: $i] :
% 0.65/1.32 ( ( mem @ V2Q @ bool )
% 0.65/1.32 => ! [V3Q_27: $i] :
% 0.65/1.32 ( ( mem @ V3Q_27 @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0P )
% 0.65/1.32 <=> ( p @ V1P_27 ) )
% 0.65/1.32 & ( ~ ( p @ V1P_27 )
% 0.65/1.32 => ( ( p @ V2Q )
% 0.65/1.32 <=> ( p @ V3Q_27 ) ) ) )
% 0.65/1.32 => ( ( ( p @ V0P )
% 0.65/1.32 | ( p @ V2Q ) )
% 0.65/1.32 <=> ( ( p @ V1P_27 )
% 0.65/1.32 | ( p @ V3Q_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ECOND__CONG,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ! [V3x_27: $i] :
% 0.65/1.32 ( ( mem @ V3x_27 @ A_27a )
% 0.65/1.32 => ! [V4y: $i] :
% 0.65/1.32 ( ( mem @ V4y @ A_27a )
% 0.65/1.32 => ! [V5y_27: $i] :
% 0.65/1.32 ( ( mem @ V5y_27 @ A_27a )
% 0.65/1.32 => ( ( ( ( p @ V0P )
% 0.65/1.32 <=> ( p @ V1Q ) )
% 0.65/1.32 & ( ( p @ V1Q )
% 0.65/1.32 => ( V2x = V3x_27 ) )
% 0.65/1.32 & ( ~ ( p @ V1Q )
% 0.65/1.32 => ( V4y = V5y_27 ) ) )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
% 0.65/1.32 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__FORALL__CONG,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V2f: $i] :
% 0.65/1.32 ( ( mem @ V2f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V3g: $i] :
% 0.65/1.32 ( ( mem @ V3g @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( V0P = V1Q )
% 0.65/1.32 => ( ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1Q ) )
% 0.65/1.32 => ( ( p @ ( ap @ V2f @ V4x ) )
% 0.65/1.32 <=> ( p @ ( ap @ V3g @ V4x ) ) ) ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0P ) @ V2f ) )
% 0.65/1.32 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V1Q ) @ V3g ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__EXISTS__CONG,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V2f: $i] :
% 0.65/1.32 ( ( mem @ V2f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V3g: $i] :
% 0.65/1.32 ( ( mem @ V3g @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( V0P = V1Q )
% 0.65/1.32 => ( ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1Q ) )
% 0.65/1.32 => ( ( p @ ( ap @ V2f @ V4x ) )
% 0.65/1.32 <=> ( p @ ( ap @ V3g @ V4x ) ) ) ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0P ) @ V2f ) )
% 0.65/1.32 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V1Q ) @ V3g ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__AND,axiom,
% 0.65/1.32 ! [V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ bool )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ bool )
% 0.65/1.32 => ! [V2z: $i] :
% 0.65/1.32 ( ( mem @ V2z @ bool )
% 0.65/1.32 => ! [V3w: $i] :
% 0.65/1.32 ( ( mem @ V3w @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0x )
% 0.65/1.32 => ( p @ V1y ) )
% 0.65/1.32 & ( ( p @ V2z )
% 0.65/1.32 => ( p @ V3w ) ) )
% 0.65/1.32 => ( ( ( p @ V0x )
% 0.65/1.32 & ( p @ V2z ) )
% 0.65/1.32 => ( ( p @ V1y )
% 0.65/1.32 & ( p @ V3w ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__OR,axiom,
% 0.65/1.32 ! [V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ bool )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ bool )
% 0.65/1.32 => ! [V2z: $i] :
% 0.65/1.32 ( ( mem @ V2z @ bool )
% 0.65/1.32 => ! [V3w: $i] :
% 0.65/1.32 ( ( mem @ V3w @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0x )
% 0.65/1.32 => ( p @ V1y ) )
% 0.65/1.32 & ( ( p @ V2z )
% 0.65/1.32 => ( p @ V3w ) ) )
% 0.65/1.32 => ( ( ( p @ V0x )
% 0.65/1.32 | ( p @ V2z ) )
% 0.65/1.32 => ( ( p @ V1y )
% 0.65/1.32 | ( p @ V3w ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__IMP,axiom,
% 0.65/1.32 ! [V0y: $i] :
% 0.65/1.32 ( ( mem @ V0y @ bool )
% 0.65/1.32 => ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ bool )
% 0.65/1.32 => ! [V2z: $i] :
% 0.65/1.32 ( ( mem @ V2z @ bool )
% 0.65/1.32 => ! [V3w: $i] :
% 0.65/1.32 ( ( mem @ V3w @ bool )
% 0.65/1.32 => ( ( ( ( p @ V0y )
% 0.65/1.32 => ( p @ V1x ) )
% 0.65/1.32 & ( ( p @ V2z )
% 0.65/1.32 => ( p @ V3w ) ) )
% 0.65/1.32 => ( ( ( p @ V1x )
% 0.65/1.32 => ( p @ V2z ) )
% 0.65/1.32 => ( ( p @ V0y )
% 0.65/1.32 => ( p @ V3w ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__NOT,axiom,
% 0.65/1.32 ! [V0y: $i] :
% 0.65/1.32 ( ( mem @ V0y @ bool )
% 0.65/1.32 => ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ bool )
% 0.65/1.32 => ( ( ( p @ V0y )
% 0.65/1.32 => ( p @ V1x ) )
% 0.65/1.32 => ( ~ ( p @ V1x )
% 0.65/1.32 => ~ ( p @ V0y ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__NOT__EQ,axiom,
% 0.65/1.32 ! [V0y: $i] :
% 0.65/1.32 ( ( mem @ V0y @ bool )
% 0.65/1.32 => ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ bool )
% 0.65/1.32 => ( ( ( p @ V0y )
% 0.65/1.32 => ( p @ V1x ) )
% 0.65/1.32 <=> ( ~ ( p @ V1x )
% 0.65/1.32 => ~ ( p @ V0y ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__ALL,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 => ( ! [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 => ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__EXISTS,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.32 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.65/1.32 => ( ? [V3x: $i] :
% 0.65/1.32 ( ( mem @ V3x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V3x ) ) )
% 0.65/1.32 => ? [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EMONO__COND,axiom,
% 0.65/1.32 ! [V0x: $i] :
% 0.65/1.32 ( ( mem @ V0x @ bool )
% 0.65/1.32 => ! [V1y: $i] :
% 0.65/1.32 ( ( mem @ V1y @ bool )
% 0.65/1.32 => ! [V2z: $i] :
% 0.65/1.32 ( ( mem @ V2z @ bool )
% 0.65/1.32 => ! [V3w: $i] :
% 0.65/1.32 ( ( mem @ V3w @ bool )
% 0.65/1.32 => ! [V4b: $i] :
% 0.65/1.32 ( ( mem @ V4b @ bool )
% 0.65/1.32 => ( ( ( p @ V0x )
% 0.65/1.32 => ( p @ V1y ) )
% 0.65/1.32 => ( ( ( p @ V2z )
% 0.65/1.32 => ( p @ V3w ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V4b ) @ V0x ) @ V2z ) )
% 0.65/1.32 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V4b ) @ V1y ) @ V3w ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXISTS__REFL,axiom,
% 0.65/1.32 ! [A_27a: del,V0a: $i] :
% 0.65/1.32 ( ( mem @ V0a @ A_27a )
% 0.65/1.32 => ? [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 & ( V1x = V0a ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EEXISTS__UNIQUE__REFL,axiom,
% 0.65/1.32 ! [A_27a: del,V0a: $i] :
% 0.65/1.32 ( ( mem @ V0a @ A_27a )
% 0.65/1.32 => ( p
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V0a ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EUNWIND__THM1,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1a: $i] :
% 0.65/1.32 ( ( mem @ V1a @ A_27a )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( V1a = V2x )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.32 <=> ( p @ ( ap @ V0P @ V1a ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EUNWIND__THM2,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1a: $i] :
% 0.65/1.32 ( ( mem @ V1a @ A_27a )
% 0.65/1.32 => ( ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( V2x = V1a )
% 0.65/1.32 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.32 <=> ( p @ ( ap @ V0P @ V1a ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EUNWIND__FORALL__THM1,axiom,
% 0.65/1.32 ! [A_27a: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1v: $i] :
% 0.65/1.32 ( ( mem @ V1v @ A_27a )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( V1v = V2x )
% 0.65/1.32 => ( p @ ( ap @ V0f @ V2x ) ) ) )
% 0.65/1.32 <=> ( p @ ( ap @ V0f @ V1v ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EUNWIND__FORALL__THM2,axiom,
% 0.65/1.32 ! [A_27a: del,V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1v: $i] :
% 0.65/1.32 ( ( mem @ V1v @ A_27a )
% 0.65/1.32 => ( ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( V2x = V1v )
% 0.65/1.32 => ( p @ ( ap @ V0f @ V2x ) ) ) )
% 0.65/1.32 <=> ( p @ ( ap @ V0f @ V1v ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ESKOLEM__THM,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 0.65/1.32 => ( ! [V1x: $i] :
% 0.65/1.32 ( ( mem @ V1x @ A_27a )
% 0.65/1.32 => ? [V2y: $i] :
% 0.65/1.32 ( ( mem @ V2y @ A_27b )
% 0.65/1.32 & ( p @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) )
% 0.65/1.32 <=> ? [V3f: $i] :
% 0.65/1.32 ( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 & ! [V4x: $i] :
% 0.65/1.32 ( ( mem @ V4x @ A_27a )
% 0.65/1.32 => ( p @ ( ap @ ( ap @ V0P @ V4x ) @ ( ap @ V3f @ V4x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2Ebool__case__thm,axiom,
% 0.65/1.32 ! [A_27a: del] :
% 0.65/1.32 ( ! [V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ A_27a )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ A_27a )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
% 0.65/1.32 = V0t1 ) ) )
% 0.65/1.32 & ! [V2t1: $i] :
% 0.65/1.32 ( ( mem @ V2t1 @ A_27a )
% 0.65/1.32 => ! [V3t2: $i] :
% 0.65/1.32 ( ( mem @ V3t2 @ A_27a )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
% 0.65/1.32 = V3t2 ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2Ebool__case__ID,axiom,
% 0.65/1.32 ! [A_27a: del,V0b: $i] :
% 0.65/1.32 ( ( mem @ V0b @ bool )
% 0.65/1.32 => ! [V1t: $i] :
% 0.65/1.32 ( ( mem @ V1t @ A_27a )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0b ) @ V1t ) @ V1t )
% 0.65/1.32 = V1t ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EboolAxiom,axiom,
% 0.65/1.32 ! [A_27a: del,V0t1: $i] :
% 0.65/1.32 ( ( mem @ V0t1 @ A_27a )
% 0.65/1.32 => ! [V1t2: $i] :
% 0.65/1.32 ( ( mem @ V1t2 @ A_27a )
% 0.65/1.32 => ? [V2fn: $i] :
% 0.65/1.32 ( ( mem @ V2fn @ ( arr @ bool @ A_27a ) )
% 0.65/1.32 & ( ( ap @ V2fn @ c_2Ebool_2ET )
% 0.65/1.32 = V0t1 )
% 0.65/1.32 & ( ( ap @ V2fn @ c_2Ebool_2EF )
% 0.65/1.32 = V1t2 ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2Ebool__INDUCT,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ bool @ bool ) )
% 0.65/1.32 => ( ( ( p @ ( ap @ V0P @ c_2Ebool_2ET ) )
% 0.65/1.32 & ( p @ ( ap @ V0P @ c_2Ebool_2EF ) ) )
% 0.65/1.32 => ! [V1b: $i] :
% 0.65/1.32 ( ( mem @ V1b @ bool )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V1b ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2Ebool__case__CONG,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ bool )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ bool )
% 0.65/1.32 => ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ! [V3x_27: $i] :
% 0.65/1.32 ( ( mem @ V3x_27 @ A_27a )
% 0.65/1.32 => ! [V4y: $i] :
% 0.65/1.32 ( ( mem @ V4y @ A_27a )
% 0.65/1.32 => ! [V5y_27: $i] :
% 0.65/1.32 ( ( mem @ V5y_27 @ A_27a )
% 0.65/1.32 => ( ( ( ( p @ V0P )
% 0.65/1.32 <=> ( p @ V1Q ) )
% 0.65/1.32 & ( ( p @ V1Q )
% 0.65/1.32 => ( V2x = V3x_27 ) )
% 0.65/1.32 & ( ~ ( p @ V1Q )
% 0.65/1.32 => ( V4y = V5y_27 ) ) )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
% 0.65/1.32 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EFORALL__BOOL,axiom,
% 0.65/1.32 ! [V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ bool @ bool ) )
% 0.65/1.32 => ( ! [V1b: $i] :
% 0.65/1.32 ( ( mem @ V1b @ bool )
% 0.65/1.32 => ( p @ ( ap @ V0P @ V1b ) ) )
% 0.65/1.32 <=> ( ( p @ ( ap @ V0P @ c_2Ebool_2ET ) )
% 0.65/1.32 & ( p @ ( ap @ V0P @ c_2Ebool_2EF ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EUEXISTS__OR__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1Q: $i] :
% 0.65/1.32 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0P @ V2x ) ) @ ( ap @ V1Q @ V2x ) ) ) ) )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] : ( ap @ V0P @ V3x ) ) ) )
% 0.65/1.32 | ( p
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V4x: $i] : ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EUEXISTS__SIMP,axiom,
% 0.65/1.32 ! [A_27a: del,V0t: $i] :
% 0.65/1.32 ( ( mem @ V0t @ bool )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : V0t ) ) )
% 0.65/1.32 <=> ( ( p @ V0t )
% 0.65/1.32 & ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ! [V3y: $i] :
% 0.65/1.32 ( ( mem @ V3y @ A_27a )
% 0.65/1.32 => ( V2x = V3y ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(ax_thm_2Ebool_2ERES__ABSTRACT__DEF,axiom,
% 0.65/1.32 ! [A_27a: del,A_27b: del] :
% 0.65/1.32 ( ! [V0p: $i] :
% 0.65/1.32 ( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1m: $i] :
% 0.65/1.32 ( ( mem @ V1m @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) )
% 0.65/1.32 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ V0p ) @ V1m ) @ V2x )
% 0.65/1.32 = ( ap @ V1m @ V2x ) ) ) ) ) )
% 0.65/1.32 & ! [V3p: $i] :
% 0.65/1.32 ( ( mem @ V3p @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V4m1: $i] :
% 0.65/1.32 ( ( mem @ V4m1 @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ! [V5m2: $i] :
% 0.65/1.32 ( ( mem @ V5m2 @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.32 => ( ! [V6x: $i] :
% 0.65/1.32 ( ( mem @ V6x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V3p ) )
% 0.65/1.32 => ( ( ap @ V4m1 @ V6x )
% 0.65/1.32 = ( ap @ V5m2 @ V6x ) ) ) )
% 0.65/1.32 => ( ( ap @ ( ap @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ V3p ) @ V4m1 )
% 0.65/1.32 = ( ap @ ( ap @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ V3p ) @ V5m2 ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__FORALL__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1f: $i] :
% 0.65/1.32 ( ( mem @ V1f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0P ) @ V1f ) )
% 0.65/1.32 <=> ! [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0P ) )
% 0.65/1.32 => ( p @ ( ap @ V1f @ V2x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__EXISTS__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1f: $i] :
% 0.65/1.32 ( ( mem @ V1f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0P ) @ V1f ) )
% 0.65/1.32 <=> ? [V2x: $i] :
% 0.65/1.32 ( ( mem @ V2x @ A_27a )
% 0.65/1.32 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0P ) )
% 0.65/1.32 & ( p @ ( ap @ V1f @ V2x ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__EXISTS__UNIQUE__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1f: $i] :
% 0.65/1.32 ( ( mem @ V1f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a ) @ V0P ) @ V1f ) )
% 0.65/1.32 <=> ( ( p
% 0.65/1.32 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0P )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ V1f @ V2x ) ) ) )
% 0.65/1.32 & ( p
% 0.65/1.32 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0P )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V3x: $i] :
% 0.65/1.32 ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0P )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V4y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1f @ V3x ) ) @ ( ap @ V1f @ V4y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__SELECT__THM,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ! [V1f: $i] :
% 0.65/1.32 ( ( mem @ V1f @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( ap @ ( ap @ ( c_2Ebool_2ERES__SELECT @ A_27a ) @ V0P ) @ V1f )
% 0.65/1.32 = ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0P ) ) @ ( ap @ V1f @ V2x ) ) ) ) ) ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__FORALL__TRUE,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0P )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : c_2Ebool_2ET ) ) )
% 0.65/1.32 <=> $true ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2ERES__EXISTS__FALSE,axiom,
% 0.65/1.32 ! [A_27a: del,V0P: $i] :
% 0.65/1.32 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.32 => ( ( p
% 0.65/1.32 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0P )
% 0.65/1.32 @ ( lam @ A_27a
% 0.65/1.32 @ ^ [V1x: $i] : c_2Ebool_2EF ) ) )
% 0.65/1.32 <=> $false ) ) ).
% 0.65/1.32
% 0.65/1.32 thf(conj_thm_2Ebool_2EBOOL__FUN__CASES__THM,axiom,
% 0.65/1.32 ! [V0f: $i] :
% 0.65/1.32 ( ( mem @ V0f @ ( arr @ bool @ bool ) )
% 0.65/1.32 => ( ( V0f
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V1b: $i] : c_2Ebool_2ET ) )
% 0.65/1.32 | ( V0f
% 0.65/1.32 = ( lam @ bool
% 0.65/1.32 @ ^ [V2b: $i] : c_2Ebool_2EF ) )
% 0.65/1.33 | ( V0f
% 0.65/1.33 = ( lam @ bool
% 0.65/1.33 @ ^ [V3b: $i] : V3b ) )
% 0.65/1.33 | ( V0f
% 0.65/1.33 = ( lam @ bool
% 0.65/1.33 @ ^ [V4b: $i] : ( ap @ c_2Ebool_2E_7E @ V4b ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EBOOL__FUN__INDUCT,axiom,
% 0.65/1.33 ! [V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( arr @ bool @ bool ) @ bool ) )
% 0.65/1.33 => ( ( ( p
% 0.65/1.33 @ ( ap @ V0P
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V1b: $i] : c_2Ebool_2ET ) ) )
% 0.65/1.33 & ( p
% 0.65/1.33 @ ( ap @ V0P
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V2b: $i] : c_2Ebool_2EF ) ) )
% 0.65/1.33 & ( p
% 0.65/1.33 @ ( ap @ V0P
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V3b: $i] : V3b ) ) )
% 0.65/1.33 & ( p
% 0.65/1.33 @ ( ap @ V0P
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V4b: $i] : ( ap @ c_2Ebool_2E_7E @ V4b ) ) ) ) )
% 0.65/1.33 => ! [V5f: $i] :
% 0.65/1.33 ( ( mem @ V5f @ ( arr @ bool @ bool ) )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V5f ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eliteral__case__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ V0f ) @ V1x )
% 0.65/1.33 = ( ap @ V0f @ V1x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eliteral__case__RAND,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ! [V1N: $i] :
% 0.65/1.33 ( ( mem @ V1N @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V2M: $i] :
% 0.65/1.33 ( ( mem @ V2M @ A_27a )
% 0.65/1.33 => ( ( ap @ V0P
% 0.65/1.33 @ ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ V1N @ V3x ) ) )
% 0.65/1.33 @ V2M ) )
% 0.65/1.33 = ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27c )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V4x: $i] : ( ap @ V0P @ ( ap @ V1N @ V4x ) ) ) )
% 0.65/1.33 @ V2M ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eliteral__case__RATOR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0N: $i] :
% 0.65/1.33 ( ( mem @ V0N @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 0.65/1.33 => ! [V1M: $i] :
% 0.65/1.33 ( ( mem @ V1M @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27b )
% 0.65/1.33 => ( ( ap
% 0.65/1.33 @ ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ V0N @ V3x ) ) )
% 0.65/1.33 @ V1M )
% 0.65/1.33 @ V2b )
% 0.65/1.33 = ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27c )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V4x: $i] : ( ap @ ( ap @ V0N @ V4x ) @ V2b ) ) )
% 0.65/1.33 @ V1M ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eliteral__case__CONG,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V2M: $i] :
% 0.65/1.33 ( ( mem @ V2M @ A_27a )
% 0.65/1.33 => ! [V3N: $i] :
% 0.65/1.33 ( ( mem @ V3N @ A_27a )
% 0.65/1.33 => ( ( ( V2M = V3N )
% 0.65/1.33 & ! [V4x: $i] :
% 0.65/1.33 ( ( mem @ V4x @ A_27a )
% 0.65/1.33 => ( ( V4x = V3N )
% 0.65/1.33 => ( ( ap @ V0f @ V4x )
% 0.65/1.33 = ( ap @ V1g @ V4x ) ) ) ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ V0f ) @ V2M )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ V1g ) @ V3N ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eliteral__case__id,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0a: $i] :
% 0.65/1.33 ( ( mem @ V0a @ A_27a )
% 0.65/1.33 => ! [V1t: $i] :
% 0.65/1.33 ( ( mem @ V1t @ A_27b )
% 0.65/1.33 => ! [V2u: $i] :
% 0.65/1.33 ( ( mem @ V2u @ A_27b )
% 0.65/1.33 => ( ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V0a ) ) @ V1t ) @ V2u ) ) )
% 0.65/1.33 @ V0a )
% 0.65/1.33 = V1t ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EBOUNDED__THM,axiom,
% 0.65/1.33 ! [V0v: $i] :
% 0.65/1.33 ( ( mem @ V0v @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ c_2Ebool_2EBOUNDED @ V0v ) )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2ELCOMM__THM,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
% 0.65/1.33 => ( ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27a )
% 0.65/1.33 => ! [V3z: $i] :
% 0.65/1.33 ( ( mem @ V3z @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V1x ) @ ( ap @ ( ap @ V0f @ V2y ) @ V3z ) )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) @ V3z ) ) ) ) )
% 0.65/1.33 => ( ! [V4x: $i] :
% 0.65/1.33 ( ( mem @ V4x @ A_27a )
% 0.65/1.33 => ! [V5y: $i] :
% 0.65/1.33 ( ( mem @ V5y @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V4x ) @ V5y )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V5y ) @ V4x ) ) ) )
% 0.65/1.33 => ! [V6x: $i] :
% 0.65/1.33 ( ( mem @ V6x @ A_27a )
% 0.65/1.33 => ! [V7y: $i] :
% 0.65/1.33 ( ( mem @ V7y @ A_27a )
% 0.65/1.33 => ! [V8z: $i] :
% 0.65/1.33 ( ( mem @ V8z @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V6x ) @ ( ap @ ( ap @ V0f @ V7y ) @ V8z ) )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V7y ) @ ( ap @ ( ap @ V0f @ V6x ) @ V8z ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EDATATYPE__TAG__THM,axiom,
% 0.65/1.33 ! [A_27a: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ V0x ) )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EDATATYPE__BOOL,axiom,
% 0.65/1.33 ! [V0bool: $i] :
% 0.65/1.33 ( ( mem @ V0bool @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ V0bool @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ebool_2Eitself__TY__DEF,axiom,
% 0.65/1.33 ! [A_27a: del] :
% 0.65/1.33 ? [V0rep: $i] :
% 0.65/1.33 ( ( mem @ V0rep @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ A_27a ) )
% 0.65/1.33 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( c_2Ebool_2EARB @ A_27a ) ) ) @ V0rep ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EITSELF__UNIQUE,axiom,
% 0.65/1.33 ! [A_27a: del,V0i: $i] :
% 0.65/1.33 ( ( mem @ V0i @ ( ty_2Ebool_2Eitself @ A_27a ) )
% 0.65/1.33 => ( V0i
% 0.65/1.33 = ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eitself__Axiom,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0e: $i] :
% 0.65/1.33 ( ( mem @ V0e @ A_27b )
% 0.65/1.33 => ? [V1f: $i] :
% 0.65/1.33 ( ( mem @ V1f @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ A_27b ) )
% 0.65/1.33 & ( ( ap @ V1f @ ( c_2Ebool_2Ethe__value @ A_27a ) )
% 0.65/1.33 = V0e ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2Eitself__induction,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ bool ) )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
% 0.65/1.33 => ! [V1i: $i] :
% 0.65/1.33 ( ( mem @ V1i @ ( ty_2Ebool_2Eitself @ A_27a ) )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V1i ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ebool_2Eitself__case__thm,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0b: $i] :
% 0.65/1.33 ( ( mem @ V0b @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ebool_2Eitself__case @ A_27a @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) @ V0b )
% 0.65/1.33 = V0b ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EFORALL__itself,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ bool ) )
% 0.65/1.33 => ( ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ ( ty_2Ebool_2Eitself @ A_27a ) )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V1x ) ) )
% 0.65/1.33 <=> ( p @ ( ap @ V0P @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EEXISTS__itself,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ bool ) )
% 0.65/1.33 => ( ? [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ ( ty_2Ebool_2Eitself @ A_27a ) )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V1x ) ) )
% 0.65/1.33 <=> ( p @ ( ap @ V0P @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EPULL__EXISTS,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1Q: $i] :
% 0.65/1.33 ( ( mem @ V1Q @ bool )
% 0.65/1.33 => ( ( ( ? [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.65/1.33 => ( p @ V1Q ) )
% 0.65/1.33 <=> ! [V3x: $i] :
% 0.65/1.33 ( ( mem @ V3x @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ V3x ) )
% 0.65/1.33 => ( p @ V1Q ) ) ) )
% 0.65/1.33 & ( ( ? [V4x: $i] :
% 0.65/1.33 ( ( mem @ V4x @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V4x ) ) )
% 0.65/1.33 & ( p @ V1Q ) )
% 0.65/1.33 <=> ? [V5x: $i] :
% 0.65/1.33 ( ( mem @ V5x @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V5x ) )
% 0.65/1.33 & ( p @ V1Q ) ) )
% 0.65/1.33 & ( ( ( p @ V1Q )
% 0.65/1.33 & ? [V6x: $i] :
% 0.65/1.33 ( ( mem @ V6x @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V6x ) ) ) )
% 0.65/1.33 <=> ? [V7x: $i] :
% 0.65/1.33 ( ( mem @ V7x @ A_27a )
% 0.65/1.33 & ( p @ V1Q )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V7x ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EPULL__FORALL,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1Q: $i] :
% 0.65/1.33 ( ( mem @ V1Q @ bool )
% 0.65/1.33 => ( ( ( ( p @ V1Q )
% 0.65/1.33 => ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V2x ) ) ) )
% 0.65/1.33 <=> ! [V3x: $i] :
% 0.65/1.33 ( ( mem @ V3x @ A_27a )
% 0.65/1.33 => ( ( p @ V1Q )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V3x ) ) ) ) )
% 0.65/1.33 & ( ( ! [V4x: $i] :
% 0.65/1.33 ( ( mem @ V4x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V4x ) ) )
% 0.65/1.33 & ( p @ V1Q ) )
% 0.65/1.33 <=> ! [V5x: $i] :
% 0.65/1.33 ( ( mem @ V5x @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ V5x ) )
% 0.65/1.33 & ( p @ V1Q ) ) ) )
% 0.65/1.33 & ( ( ( p @ V1Q )
% 0.65/1.33 & ! [V6x: $i] :
% 0.65/1.33 ( ( mem @ V6x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V6x ) ) ) )
% 0.65/1.33 <=> ! [V7x: $i] :
% 0.65/1.33 ( ( mem @ V7x @ A_27a )
% 0.65/1.33 => ( ( p @ V1Q )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V7x ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EPEIRCE,axiom,
% 0.65/1.33 ! [V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ bool )
% 0.65/1.33 => ! [V1Q: $i] :
% 0.65/1.33 ( ( mem @ V1Q @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0P )
% 0.65/1.33 => ( p @ V1Q ) )
% 0.65/1.33 => ( p @ V0P ) )
% 0.65/1.33 => ( p @ V0P ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EJRH__INDUCT__UTIL,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1t: $i] :
% 0.65/1.33 ( ( mem @ V1t @ A_27a )
% 0.65/1.33 => ( ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 => ( ( V2x = V1t )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V2x ) ) ) )
% 0.65/1.33 => ( p @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0P ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ebool_2EDISJ__EQ__IMP,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ! [V1B: $i] :
% 0.65/1.33 ( ( mem @ V1B @ bool )
% 0.65/1.33 => ( ( ( p @ V0A )
% 0.65/1.33 | ( p @ V1B ) )
% 0.65/1.33 <=> ( ~ ( p @ V0A )
% 0.65/1.33 => ( p @ V1B ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_c_2EConseqConv_2EASM__MARKER,type,
% 0.65/1.33 c_2EConseqConv_2EASM__MARKER: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2EConseqConv_2EASM__MARKER,axiom,
% 0.65/1.33 mem @ c_2EConseqConv_2EASM__MARKER @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2Eforall__eq__thm,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1Q: $i] :
% 0.65/1.33 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ( ! [V2s: $i] :
% 0.65/1.33 ( ( mem @ V2s @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ V2s ) )
% 0.65/1.33 <=> ( p @ ( ap @ V1Q @ V2s ) ) ) )
% 0.65/1.33 => ( ! [V3s: $i] :
% 0.65/1.33 ( ( mem @ V3s @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V3s ) ) )
% 0.65/1.33 <=> ! [V4s: $i] :
% 0.65/1.33 ( ( mem @ V4s @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V1Q @ V4s ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2Eexists__eq__thm,axiom,
% 0.65/1.33 ! [A_27a: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1Q: $i] :
% 0.65/1.33 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ( ! [V2s: $i] :
% 0.65/1.33 ( ( mem @ V2s @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ V2s ) )
% 0.65/1.33 <=> ( p @ ( ap @ V1Q @ V2s ) ) ) )
% 0.65/1.33 => ( ? [V3s: $i] :
% 0.65/1.33 ( ( mem @ V3s @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V3s ) ) )
% 0.65/1.33 <=> ? [V4s: $i] :
% 0.65/1.33 ( ( mem @ V4s @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V1Q @ V4s ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2Etrue__imp,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( p @ V0t )
% 0.65/1.33 => $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2Efalse__imp,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( $false
% 0.65/1.33 => ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ENOT__CLAUSES__X,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ~ ~ ( p @ V0t )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ENOT__CLAUSES__T,axiom,
% 0.65/1.33 ( ~ $true
% 0.65/1.33 <=> $false ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ENOT__CLAUSES__F,axiom,
% 0.65/1.33 ( ~ $false
% 0.65/1.33 <=> $true ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__conj__strengthen,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V2y )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V0x ) ) )
% 0.65/1.33 & ( ( p @ V1x_27 )
% 0.65/1.33 => ( ( p @ V3y_27 )
% 0.65/1.33 => ( p @ V2y ) ) ) )
% 0.65/1.33 => ( ( ( p @ V1x_27 )
% 0.65/1.33 & ( p @ V3y_27 ) )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 & ( p @ V2y ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__conj__weaken,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V2y )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 => ( p @ V1x_27 ) ) )
% 0.65/1.33 & ( ( p @ V1x_27 )
% 0.65/1.33 => ( ( p @ V2y )
% 0.65/1.33 => ( p @ V3y_27 ) ) ) )
% 0.65/1.33 => ( ( ( p @ V0x )
% 0.65/1.33 & ( p @ V2y ) )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 & ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EAND__CLAUSES__TX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( $true
% 0.65/1.33 & ( p @ V0t ) )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EAND__CLAUSES__XT,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 & $true )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EAND__CLAUSES__FX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( $false
% 0.65/1.33 & ( p @ V0t ) )
% 0.65/1.33 <=> $false ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EAND__CLAUSES__XF,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 & $false )
% 0.65/1.33 <=> $false ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EAND__CLAUSES__XX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 & ( p @ V0t ) )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__disj__strengthen,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ~ ( p @ V2y )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V0x ) ) )
% 0.65/1.33 & ( ~ ( p @ V1x_27 )
% 0.65/1.33 => ( ( p @ V3y_27 )
% 0.65/1.33 => ( p @ V2y ) ) ) )
% 0.65/1.33 => ( ( ( p @ V1x_27 )
% 0.65/1.33 | ( p @ V3y_27 ) )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 | ( p @ V2y ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__disj__weaken,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ~ ( p @ V2y )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 => ( p @ V1x_27 ) ) )
% 0.65/1.33 & ( ~ ( p @ V1x_27 )
% 0.65/1.33 => ( ( p @ V2y )
% 0.65/1.33 => ( p @ V3y_27 ) ) ) )
% 0.65/1.33 => ( ( ( p @ V0x )
% 0.65/1.33 | ( p @ V2y ) )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 | ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EOR__CLAUSES__TX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( $true
% 0.65/1.33 | ( p @ V0t ) )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EOR__CLAUSES__XT,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 | $true )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EOR__CLAUSES__FX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( $false
% 0.65/1.33 | ( p @ V0t ) )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EOR__CLAUSES__XF,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 | $false )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EOR__CLAUSES__XX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 | ( p @ V0t ) )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__imp__strengthen,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0x )
% 0.65/1.33 => ( ( p @ V3y_27 )
% 0.65/1.33 => ( p @ V2y ) ) )
% 0.65/1.33 & ( ~ ( p @ V3y_27 )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 => ( p @ V1x_27 ) ) ) )
% 0.65/1.33 => ( ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V3y_27 ) )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 => ( p @ V2y ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__imp__weaken,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0x )
% 0.65/1.33 => ( ( p @ V2y )
% 0.65/1.33 => ( p @ V3y_27 ) ) )
% 0.65/1.33 & ( ~ ( p @ V3y_27 )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V0x ) ) ) )
% 0.65/1.33 => ( ( ( p @ V0x )
% 0.65/1.33 => ( p @ V2y ) )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0x )
% 0.65/1.33 => ( p @ V1x_27 ) )
% 0.65/1.33 & ( ( p @ V1x_27 )
% 0.65/1.33 => ( ( p @ V3y_27 )
% 0.65/1.33 => ( p @ V2y ) ) ) )
% 0.65/1.33 => ( ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V3y_27 ) )
% 0.65/1.33 => ( ( p @ V0x )
% 0.65/1.33 => ( p @ V2y ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ! [V1x_27: $i] :
% 0.65/1.33 ( ( mem @ V1x_27 @ bool )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ bool )
% 0.65/1.33 => ! [V3y_27: $i] :
% 0.65/1.33 ( ( mem @ V3y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V0x ) )
% 0.65/1.33 & ( ( p @ V1x_27 )
% 0.65/1.33 => ( ( p @ V2y )
% 0.65/1.33 => ( p @ V3y_27 ) ) ) )
% 0.65/1.33 => ( ( ( p @ V0x )
% 0.65/1.33 => ( p @ V2y ) )
% 0.65/1.33 => ( ( p @ V1x_27 )
% 0.65/1.33 => ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CLAUSES__TX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( $true
% 0.65/1.33 => ( p @ V0t ) )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CLAUSES__XT,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 => $true )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CLAUSES__FX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( $false
% 0.65/1.33 => ( p @ V0t ) )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CLAUSES__XX,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 => ( p @ V0t ) )
% 0.65/1.33 <=> $true ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CLAUSES__XF,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ( ( p @ V0t )
% 0.65/1.33 => $false )
% 0.65/1.33 <=> ~ ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__cond__simple,axiom,
% 0.65/1.33 ! [V0c: $i] :
% 0.65/1.33 ( ( mem @ V0c @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ! [V2x_27: $i] :
% 0.65/1.33 ( ( mem @ V2x_27 @ bool )
% 0.65/1.33 => ! [V3y: $i] :
% 0.65/1.33 ( ( mem @ V3y @ bool )
% 0.65/1.33 => ! [V4y_27: $i] :
% 0.65/1.33 ( ( mem @ V4y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V2x_27 )
% 0.65/1.33 => ( p @ V1x ) )
% 0.65/1.33 & ( ( p @ V4y_27 )
% 0.65/1.33 => ( p @ V3y ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ V2x_27 ) @ V4y_27 ) )
% 0.65/1.33 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ V1x ) @ V3y ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EIMP__CONG__cond,axiom,
% 0.65/1.33 ! [V0c: $i] :
% 0.65/1.33 ( ( mem @ V0c @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ! [V2x_27: $i] :
% 0.65/1.33 ( ( mem @ V2x_27 @ bool )
% 0.65/1.33 => ! [V3y: $i] :
% 0.65/1.33 ( ( mem @ V3y @ bool )
% 0.65/1.33 => ! [V4y_27: $i] :
% 0.65/1.33 ( ( mem @ V4y_27 @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0c )
% 0.65/1.33 => ( ( p @ V2x_27 )
% 0.65/1.33 => ( p @ V1x ) ) )
% 0.65/1.33 & ( ~ ( p @ V0c )
% 0.65/1.33 => ( ( p @ V4y_27 )
% 0.65/1.33 => ( p @ V3y ) ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ V2x_27 ) @ V4y_27 ) )
% 0.65/1.33 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ V1x ) @ V3y ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__CT,axiom,
% 0.65/1.33 ! [A_27a: del,V0t1: $i] :
% 0.65/1.33 ( ( mem @ V0t1 @ A_27a )
% 0.65/1.33 => ! [V1t2: $i] :
% 0.65/1.33 ( ( mem @ V1t2 @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
% 0.65/1.33 = V0t1 ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__CF,axiom,
% 0.65/1.33 ! [A_27a: del,V0t1: $i] :
% 0.65/1.33 ( ( mem @ V0t1 @ A_27a )
% 0.65/1.33 => ! [V1t2: $i] :
% 0.65/1.33 ( ( mem @ V1t2 @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V0t1 ) @ V1t2 )
% 0.65/1.33 = V1t2 ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__ID,axiom,
% 0.65/1.33 ! [A_27a: del,V0b: $i] :
% 0.65/1.33 ( ( mem @ V0b @ bool )
% 0.65/1.33 => ! [V1t: $i] :
% 0.65/1.33 ( ( mem @ V1t @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0b ) @ V1t ) @ V1t )
% 0.65/1.33 = V1t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__TT,axiom,
% 0.65/1.33 ! [V0c: $i] :
% 0.65/1.33 ( ( mem @ V0c @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ c_2Ebool_2ET ) @ V1x ) )
% 0.65/1.33 <=> ( ~ ( p @ V0c )
% 0.65/1.33 => ( p @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__FT,axiom,
% 0.65/1.33 ! [V0c: $i] :
% 0.65/1.33 ( ( mem @ V0c @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ V1x ) @ c_2Ebool_2ET ) )
% 0.65/1.33 <=> ( ( p @ V0c )
% 0.65/1.33 => ( p @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__TF,axiom,
% 0.65/1.33 ! [V0c: $i] :
% 0.65/1.33 ( ( mem @ V0c @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ c_2Ebool_2EF ) @ V1x ) )
% 0.65/1.33 <=> ( ~ ( p @ V0c )
% 0.65/1.33 & ( p @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2ECOND__CLAUSES__FF,axiom,
% 0.65/1.33 ! [V0c: $i] :
% 0.65/1.33 ( ( mem @ V0c @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V0c ) @ V1x ) @ c_2Ebool_2EF ) )
% 0.65/1.33 <=> ( ( p @ V0c )
% 0.65/1.33 & ( p @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2EConseqConv_2EASM__MARKER__DEF,axiom,
% 0.65/1.33 ( c_2EConseqConv_2EASM__MARKER
% 0.65/1.33 = ( lam @ bool
% 0.65/1.33 @ ^ [V0y: $i] :
% 0.65/1.33 ( lam @ bool
% 0.65/1.33 @ ^ [V1x: $i] : V1x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EConseqConv_2EASM__MARKER__THM,axiom,
% 0.65/1.33 ! [V0y: $i] :
% 0.65/1.33 ( ( mem @ V0y @ bool )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ c_2EConseqConv_2EASM__MARKER @ V0y ) @ V1x ) )
% 0.65/1.33 <=> ( p @ V1x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(conj_thm_2Esat_2EAND__IMP,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ! [V1B: $i] :
% 0.65/1.33 ( ( mem @ V1B @ bool )
% 0.65/1.33 => ! [V2C: $i] :
% 0.65/1.33 ( ( mem @ V2C @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0A )
% 0.65/1.33 & ( p @ V1B ) )
% 0.65/1.33 => ( p @ V2C ) )
% 0.65/1.33 <=> ( ( p @ V0A )
% 0.65/1.33 => ( ( p @ V1B )
% 0.65/1.33 => ( p @ V2C ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2ENOT__NOT,axiom,
% 0.65/1.33 ! [V0t: $i] :
% 0.65/1.33 ( ( mem @ V0t @ bool )
% 0.65/1.33 => ( ~ ~ ( p @ V0t )
% 0.65/1.33 <=> ( p @ V0t ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EAND__INV,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ( ( ~ ( p @ V0A )
% 0.65/1.33 & ( p @ V0A ) )
% 0.65/1.33 <=> $false ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EAND__INV__IMP,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ( ( p @ V0A )
% 0.65/1.33 => ( ~ ( p @ V0A )
% 0.65/1.33 => $false ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EOR__DUAL,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ! [V1B: $i] :
% 0.65/1.33 ( ( mem @ V1B @ bool )
% 0.65/1.33 => ( ( ~ ( ( p @ V0A )
% 0.65/1.33 | ( p @ V1B ) )
% 0.65/1.33 => $false )
% 0.65/1.33 <=> ( ~ ( p @ V0A )
% 0.65/1.33 => ( ~ ( p @ V1B )
% 0.65/1.33 => $false ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EOR__DUAL2,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ! [V1B: $i] :
% 0.65/1.33 ( ( mem @ V1B @ bool )
% 0.65/1.33 => ( ( ~ ( ( p @ V0A )
% 0.65/1.33 | ( p @ V1B ) )
% 0.65/1.33 => $false )
% 0.65/1.33 <=> ( ( ( p @ V0A )
% 0.65/1.33 => $false )
% 0.65/1.33 => ( ~ ( p @ V1B )
% 0.65/1.33 => $false ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EOR__DUAL3,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ! [V1B: $i] :
% 0.65/1.33 ( ( mem @ V1B @ bool )
% 0.65/1.33 => ( ( ~ ( ~ ( p @ V0A )
% 0.65/1.33 | ( p @ V1B ) )
% 0.65/1.33 => $false )
% 0.65/1.33 <=> ( ( p @ V0A )
% 0.65/1.33 => ( ~ ( p @ V1B )
% 0.65/1.33 => $false ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EAND__INV2,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ( ( ~ ( p @ V0A )
% 0.65/1.33 => $false )
% 0.65/1.33 => ( ( ( p @ V0A )
% 0.65/1.33 => $false )
% 0.65/1.33 => $false ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2ENOT__ELIM2,axiom,
% 0.65/1.33 ! [V0A: $i] :
% 0.65/1.33 ( ( mem @ V0A @ bool )
% 0.65/1.33 => ( ( ~ ( p @ V0A )
% 0.65/1.33 => $false )
% 0.65/1.33 <=> ( p @ V0A ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EEQT__Imp1,axiom,
% 0.65/1.33 ! [V0b: $i] :
% 0.65/1.33 ( ( mem @ V0b @ bool )
% 0.65/1.33 => ( ( p @ V0b )
% 0.65/1.33 => ( ( p @ V0b )
% 0.65/1.33 <=> $true ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2EEQF__Imp1,axiom,
% 0.65/1.33 ! [V0b: $i] :
% 0.65/1.33 ( ( mem @ V0b @ bool )
% 0.65/1.33 => ( ~ ( p @ V0b )
% 0.65/1.33 => ( ( p @ V0b )
% 0.65/1.33 <=> $false ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Edc__eq,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2r: $i] :
% 0.65/1.33 ( ( mem @ V2r @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 <=> ( ( p @ V1q )
% 0.65/1.33 <=> ( p @ V2r ) ) )
% 0.65/1.33 <=> ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q )
% 0.65/1.33 | ( p @ V2r ) )
% 0.65/1.33 & ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V1q ) )
% 0.65/1.33 & ( ( p @ V1q )
% 0.65/1.33 | ~ ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V0p ) )
% 0.65/1.33 & ( ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V1q )
% 0.65/1.33 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Edc__conj,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2r: $i] :
% 0.65/1.33 ( ( mem @ V2r @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 <=> ( ( p @ V1q )
% 0.65/1.33 & ( p @ V2r ) ) )
% 0.65/1.33 <=> ( ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V1q )
% 0.65/1.33 | ~ ( p @ V2r ) )
% 0.65/1.33 & ( ( p @ V1q )
% 0.65/1.33 | ~ ( p @ V0p ) )
% 0.65/1.33 & ( ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Edc__disj,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2r: $i] :
% 0.65/1.33 ( ( mem @ V2r @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 <=> ( ( p @ V1q )
% 0.65/1.33 | ( p @ V2r ) ) )
% 0.65/1.33 <=> ( ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V1q ) )
% 0.65/1.33 & ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V2r ) )
% 0.65/1.33 & ( ( p @ V1q )
% 0.65/1.33 | ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Edc__imp,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2r: $i] :
% 0.65/1.33 ( ( mem @ V2r @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 <=> ( ( p @ V1q )
% 0.65/1.33 => ( p @ V2r ) ) )
% 0.65/1.33 <=> ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 & ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V2r ) )
% 0.65/1.33 & ( ~ ( p @ V1q )
% 0.65/1.33 | ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Edc__neg,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 <=> ~ ( p @ V1q ) )
% 0.65/1.33 <=> ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 & ( ~ ( p @ V1q )
% 0.65/1.33 | ~ ( p @ V0p ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Edc__cond,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2r: $i] :
% 0.65/1.33 ( ( mem @ V2r @ bool )
% 0.65/1.33 => ! [V3s: $i] :
% 0.65/1.33 ( ( mem @ V3s @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ V1q ) @ V2r ) @ V3s ) ) )
% 0.65/1.33 <=> ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q )
% 0.65/1.33 | ~ ( p @ V3s ) )
% 0.65/1.33 & ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V1q ) )
% 0.65/1.33 & ( ( p @ V0p )
% 0.65/1.33 | ~ ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V3s ) )
% 0.65/1.33 & ( ~ ( p @ V1q )
% 0.65/1.33 | ( p @ V2r )
% 0.65/1.33 | ~ ( p @ V0p ) )
% 0.65/1.33 & ( ( p @ V1q )
% 0.65/1.33 | ( p @ V3s )
% 0.65/1.33 | ~ ( p @ V0p ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__ni1,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ~ ( ( p @ V0p )
% 0.65/1.33 => ( p @ V1q ) )
% 0.65/1.33 => ( p @ V0p ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__ni2,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ~ ( ( p @ V0p )
% 0.65/1.33 => ( p @ V1q ) )
% 0.65/1.33 => ~ ( p @ V1q ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__no1,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ~ ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 => ~ ( p @ V0p ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__no2,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ~ ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 => ~ ( p @ V1q ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__an1,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 & ( p @ V1q ) )
% 0.65/1.33 => ( p @ V0p ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__an2,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ( ( ( p @ V0p )
% 0.65/1.33 & ( p @ V1q ) )
% 0.65/1.33 => ( p @ V1q ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esat_2Epth__nn,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ( ~ ~ ( p @ V0p )
% 0.65/1.33 => ( p @ V0p ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_c_2EnormalForms_2EEXT__POINT,type,
% 0.65/1.33 c_2EnormalForms_2EEXT__POINT: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2EnormalForms_2EEXT__POINT,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2EnormalForms_2EUNIV__POINT,type,
% 0.65/1.33 c_2EnormalForms_2EUNIV__POINT: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2EnormalForms_2EUNIV__POINT,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2EnormalForms_2EUNIV__POINT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2EnormalForms_2EEXT__POINT__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ( ap @ V0f @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
% 0.65/1.33 = ( ap @ V1g @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) ) )
% 0.65/1.33 => ( V0f = V1g ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EnormalForms_2EEXT__POINT,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ( ap @ V0f @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
% 0.65/1.33 = ( ap @ V1g @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) ) )
% 0.65/1.33 <=> ( V0f = V1g ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2EnormalForms_2EUNIV__POINT__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ( ( p @ ( ap @ V0p @ ( ap @ ( c_2EnormalForms_2EUNIV__POINT @ A_27a ) @ V0p ) ) )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0p @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2EnormalForms_2EUNIV__POINT,axiom,
% 0.65/1.33 ! [A_27a: del,V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ( ( p @ ( ap @ V0p @ ( ap @ ( c_2EnormalForms_2EUNIV__POINT @ A_27a ) @ V0p ) ) )
% 0.65/1.33 <=> ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0p @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_c_2Emarker_2E_3A_2D,type,
% 0.65/1.33 c_2Emarker_2E_3A_2D: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2E_3A_2D,axiom,
% 0.65/1.33 mem @ c_2Emarker_2E_3A_2D @ ( arr @ ind @ ( arr @ bool @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Emarker_2EAC,type,
% 0.65/1.33 c_2Emarker_2EAC: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2EAC,axiom,
% 0.65/1.33 mem @ c_2Emarker_2EAC @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Emarker_2EAbbrev,type,
% 0.65/1.33 c_2Emarker_2EAbbrev: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2EAbbrev,axiom,
% 0.65/1.33 mem @ c_2Emarker_2EAbbrev @ ( arr @ bool @ bool ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Emarker_2ECong,type,
% 0.65/1.33 c_2Emarker_2ECong: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2ECong,axiom,
% 0.65/1.33 mem @ c_2Emarker_2ECong @ ( arr @ bool @ bool ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Emarker_2EIfCases,type,
% 0.65/1.33 c_2Emarker_2EIfCases: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2EIfCases,axiom,
% 0.65/1.33 mem @ c_2Emarker_2EIfCases @ bool ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Emarker_2Estmarker,type,
% 0.65/1.33 c_2Emarker_2Estmarker: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2Estmarker,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Emarker_2Estmarker @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Emarker_2Eunint,type,
% 0.65/1.33 c_2Emarker_2Eunint: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Emarker_2Eunint,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Emarker_2Eunint @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2Estmarker__def,axiom,
% 0.65/1.33 ! [A_27a: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( c_2Emarker_2Estmarker @ A_27a ) @ V0x )
% 0.65/1.33 = V0x ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Emarker_2Emove__left__conj,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2m: $i] :
% 0.65/1.33 ( ( mem @ V2m @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0p )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V0p ) ) )
% 0.65/1.33 & ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V0p )
% 0.65/1.33 & ( p @ V1q ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V0p )
% 0.65/1.33 & ( p @ V1q ) ) )
% 0.65/1.33 & ( ( ( p @ V0p )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V1q ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V0p )
% 0.65/1.33 & ( p @ V1q ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Emarker_2Emove__right__conj,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2m: $i] :
% 0.65/1.33 ( ( mem @ V2m @ bool )
% 0.65/1.33 => ( ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V0p ) )
% 0.65/1.33 <=> ( ( p @ V0p )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
% 0.65/1.33 & ( ( ( p @ V0p )
% 0.65/1.33 & ( p @ V1q )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
% 0.65/1.33 <=> ( ( p @ V0p )
% 0.65/1.33 & ( p @ V1q )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
% 0.65/1.33 & ( ( ( p @ V0p )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 & ( p @ V1q ) )
% 0.65/1.33 <=> ( ( p @ V0p )
% 0.65/1.33 & ( p @ V1q )
% 0.65/1.33 & ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Emarker_2Emove__left__disj,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2m: $i] :
% 0.65/1.33 ( ( mem @ V2m @ bool )
% 0.65/1.33 => ( ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V0p ) ) )
% 0.65/1.33 & ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) ) )
% 0.65/1.33 & ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V0p )
% 0.65/1.33 | ( p @ V1q ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Emarker_2Emove__right__disj,axiom,
% 0.65/1.33 ! [V0p: $i] :
% 0.65/1.33 ( ( mem @ V0p @ bool )
% 0.65/1.33 => ! [V1q: $i] :
% 0.65/1.33 ( ( mem @ V1q @ bool )
% 0.65/1.33 => ! [V2m: $i] :
% 0.65/1.33 ( ( mem @ V2m @ bool )
% 0.65/1.33 => ( ( ( ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V0p ) )
% 0.65/1.33 <=> ( ( p @ V0p )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
% 0.65/1.33 & ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) )
% 0.65/1.33 <=> ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) )
% 0.65/1.33 & ( ( ( p @ V0p )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) )
% 0.65/1.33 | ( p @ V1q ) )
% 0.65/1.33 <=> ( ( p @ V0p )
% 0.65/1.33 | ( p @ V1q )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Emarker_2Estmarker @ bool ) @ V2m ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2Eunint__def,axiom,
% 0.65/1.33 ! [A_27a: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( c_2Emarker_2Eunint @ A_27a ) @ V0x )
% 0.65/1.33 = V0x ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2EAbbrev__def,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ c_2Emarker_2EAbbrev @ V0x ) )
% 0.65/1.33 <=> ( p @ V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2EIfCases__def,axiom,
% 0.65/1.33 ( ( p @ c_2Emarker_2EIfCases )
% 0.65/1.33 <=> $true ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2EAC__DEF,axiom,
% 0.65/1.33 ! [V0b1: $i] :
% 0.65/1.33 ( ( mem @ V0b1 @ bool )
% 0.65/1.33 => ! [V1b2: $i] :
% 0.65/1.33 ( ( mem @ V1b2 @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ c_2Emarker_2EAC @ V0b1 ) @ V1b2 ) )
% 0.65/1.33 <=> ( ( p @ V0b1 )
% 0.65/1.33 & ( p @ V1b2 ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2ECong__def,axiom,
% 0.65/1.33 ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ c_2Emarker_2ECong @ V0x ) )
% 0.65/1.33 <=> ( p @ V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Emarker_2Elabel__def,axiom,
% 0.65/1.33 ! [V0lab: tp__i,V1argument: $i] :
% 0.65/1.33 ( ( mem @ V1argument @ bool )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ c_2Emarker_2E_3A_2D @ ( inj__i @ V0lab ) ) @ V1argument ) )
% 0.65/1.33 <=> ( p @ V1argument ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_c_2Ecombin_2E_3A_3E,type,
% 0.65/1.33 c_2Ecombin_2E_3A_3E: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2E_3A_3E,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2E_3A_3E @ A_27a @ A_27b ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27b @ A_27a ) @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EASSOC,type,
% 0.65/1.33 c_2Ecombin_2EASSOC: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EASSOC,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Ecombin_2EASSOC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EC,type,
% 0.65/1.33 c_2Ecombin_2EC: del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EC,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Ecombin_2EC @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) @ ( arr @ A_27b @ ( arr @ A_27a @ A_27c ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2ECOMM,type,
% 0.65/1.33 c_2Ecombin_2ECOMM: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2ECOMM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2ECOMM @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EFAIL,type,
% 0.65/1.33 c_2Ecombin_2EFAIL: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EFAIL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2EFAIL @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EFCOMM,type,
% 0.65/1.33 c_2Ecombin_2EFCOMM: del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EFCOMM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) @ ( arr @ ( arr @ A_27c @ ( arr @ A_27a @ A_27a ) ) @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EI,type,
% 0.65/1.33 c_2Ecombin_2EI: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EI,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Ecombin_2EI @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EK,type,
% 0.65/1.33 c_2Ecombin_2EK: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EK,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2EK @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2ELEFT__ID,type,
% 0.65/1.33 c_2Ecombin_2ELEFT__ID: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2ELEFT__ID,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EMONOID,type,
% 0.65/1.33 c_2Ecombin_2EMONOID: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EMONOID,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Ecombin_2EMONOID @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2ERIGHT__ID,type,
% 0.65/1.33 c_2Ecombin_2ERIGHT__ID: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2ERIGHT__ID,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) @ ( arr @ A_27b @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2ES,type,
% 0.65/1.33 c_2Ecombin_2ES: del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2ES,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Ecombin_2ES @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EUPDATE,type,
% 0.65/1.33 c_2Ecombin_2EUPDATE: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EUPDATE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2EW,type,
% 0.65/1.33 c_2Ecombin_2EW: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2EW,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ecombin_2EW @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ A_27b ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Ecombin_2Eo,type,
% 0.65/1.33 c_2Ecombin_2Eo: del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Ecombin_2Eo,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27c @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27c ) @ ( arr @ A_27a @ A_27b ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EK__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ( c_2Ecombin_2EK @ A_27a @ A_27b )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V0x: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V1y: $i] : V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2ES__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] :
% 0.65/1.33 ( ( c_2Ecombin_2ES @ A_27a @ A_27b @ A_27c )
% 0.65/1.33 = ( lam @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 @ ^ [V0f: $i] :
% 0.65/1.33 ( lam @ ( arr @ A_27a @ A_27b )
% 0.65/1.33 @ ^ [V1g: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EI__DEF,axiom,
% 0.65/1.33 ! [A_27a: del] :
% 0.65/1.33 ( ( c_2Ecombin_2EI @ A_27a )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ ( arr @ A_27a @ A_27a ) @ A_27a ) @ ( c_2Ecombin_2EK @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK @ A_27a @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EC__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] :
% 0.65/1.33 ( ( c_2Ecombin_2EC @ A_27a @ A_27b @ A_27c )
% 0.65/1.33 = ( lam @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 @ ^ [V0f: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V1x: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V2y: $i] : ( ap @ ( ap @ V0f @ V2y ) @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EW__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ( c_2Ecombin_2EW @ A_27a @ A_27b )
% 0.65/1.33 = ( lam @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 @ ^ [V0f: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V1x: $i] : ( ap @ ( ap @ V0f @ V1x ) @ V1x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2Eo__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27c @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1g )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ V0f @ ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EAPP__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27b )
% 0.65/1.33 => ! [V1f: $i] :
% 0.65/1.33 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2E_3A_3E @ A_27a @ A_27b ) @ V0x ) @ V1f )
% 0.65/1.33 = ( ap @ V1f @ V0x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EUPDATE__def,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0a: $i] :
% 0.65/1.33 ( ( mem @ V0a @ A_27a )
% 0.65/1.33 => ! [V1b: $i] :
% 0.65/1.33 ( ( mem @ V1b @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V0a ) @ V1b )
% 0.65/1.33 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.65/1.33 @ ^ [V2f: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V3c: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0a ) @ V3c ) ) @ V1b ) @ ( ap @ V2f @ V3c ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2Eo__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27c @ A_27a ) )
% 0.65/1.33 => ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27c )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ A_27b @ A_27a ) @ V0f ) @ V1g ) @ V2x )
% 0.65/1.33 = ( ap @ V0f @ ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2Eo__ASSOC,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27c @ A_27a ) )
% 0.65/1.33 => ! [V2h: $i] :
% 0.65/1.33 ( ( mem @ V2h @ ( arr @ A_27d @ A_27c ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27d @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27d @ A_27a @ A_27c ) @ V1g ) @ V2h ) )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27d @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ A_27b @ A_27a ) @ V0f ) @ V1g ) ) @ V2h ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2Eo__ABS__L,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.33 => ( ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ A_27c @ A_27a )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ V0f @ V2x ) ) )
% 0.65/1.33 @ V1g )
% 0.65/1.33 = ( lam @ A_27b
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ V0f @ ( ap @ V1g @ V3x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2Eo__ABS__R,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27c @ A_27b ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27c ) @ V0f )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ V1g @ V2x ) ) )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ V0f @ ( ap @ V1g @ V3x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EK__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2EK @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 0.65/1.33 = V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2ES__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1g ) @ V2x )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2ES__ABS__L,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27c @ A_27b ) ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ( ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ A_27c @ A_27b )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ V0f @ V2x ) ) )
% 0.65/1.33 @ V1g )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ ( ap @ V0f @ V3x ) @ ( ap @ V1g @ V3x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2ES__ABS__R,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27c @ A_27b ) ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ A_27c @ A_27b ) @ V0f )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ V1g @ V2x ) ) )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ ( ap @ V0f @ V3x ) @ ( ap @ V1g @ V3x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EC__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27b )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1x ) @ V2y )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V2y ) @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EC__ABS__L,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27c @ A_27b ) ) )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27c )
% 0.65/1.33 => ( ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ecombin_2EC @ A_27a @ A_27c @ A_27b )
% 0.65/1.33 @ ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] : ( ap @ V0f @ V2x ) ) )
% 0.65/1.33 @ V1y )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V3x: $i] : ( ap @ ( ap @ V0f @ V3x ) @ V1y ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EW__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2EW @ A_27a @ A_27b ) @ V0f ) @ V1x )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V1x ) @ V1x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EI__THM,axiom,
% 0.65/1.33 ! [A_27a: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( c_2Ecombin_2EI @ A_27a ) @ V0x )
% 0.65/1.33 = V0x ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EI__o__ID,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27b ) @ ( c_2Ecombin_2EI @ A_27b ) ) @ V0f )
% 0.65/1.33 = V0f )
% 0.65/1.33 & ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27a ) @ V0f ) @ ( c_2Ecombin_2EI @ A_27a ) )
% 0.65/1.33 = V0f ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EK__o__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del] :
% 0.65/1.33 ( ! [V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1v: $i] :
% 0.65/1.33 ( ( mem @ V1v @ A_27c )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ ( ap @ ( c_2Ecombin_2EK @ A_27c @ A_27b ) @ V1v ) ) @ V0f )
% 0.65/1.33 = ( ap @ ( c_2Ecombin_2EK @ A_27c @ A_27a ) @ V1v ) ) ) )
% 0.65/1.33 & ! [V2f: $i] :
% 0.65/1.33 ( ( mem @ V2f @ ( arr @ A_27d @ A_27e ) )
% 0.65/1.33 => ! [V3v: $i] :
% 0.65/1.33 ( ( mem @ V3v @ A_27d )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27f @ A_27e @ A_27d ) @ V2f ) @ ( ap @ ( c_2Ecombin_2EK @ A_27d @ A_27f ) @ V3v ) )
% 0.65/1.33 = ( ap @ ( c_2Ecombin_2EK @ A_27e @ A_27f ) @ ( ap @ V2f @ V3v ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPDATE__APPLY,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
% 0.65/1.33 ( ! [V0a: $i] :
% 0.65/1.33 ( ( mem @ V0a @ A_27a )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27b )
% 0.65/1.33 => ! [V2f: $i] :
% 0.65/1.33 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V0a ) @ V1x ) @ V2f ) @ V0a )
% 0.65/1.33 = V1x ) ) ) )
% 0.65/1.33 & ! [V3a: $i] :
% 0.65/1.33 ( ( mem @ V3a @ A_27c )
% 0.65/1.33 => ! [V4b: $i] :
% 0.65/1.33 ( ( mem @ V4b @ A_27c )
% 0.65/1.33 => ! [V5x: $i] :
% 0.65/1.33 ( ( mem @ V5x @ A_27d )
% 0.65/1.33 => ! [V6f: $i] :
% 0.65/1.33 ( ( mem @ V6f @ ( arr @ A_27c @ A_27d ) )
% 0.65/1.33 => ( ( V3a != V4b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27c @ A_27d ) @ V3a ) @ V5x ) @ V6f ) @ V4b )
% 0.65/1.33 = ( ap @ V6f @ V4b ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EAPPLY__UPDATE__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27b )
% 0.65/1.33 => ! [V3c: $i] :
% 0.65/1.33 ( ( mem @ V3c @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V2b ) @ V0f ) @ V3c )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1a ) @ V3c ) ) @ V2b ) @ ( ap @ V0f @ V3c ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPDATE__COMMUTES,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27a )
% 0.65/1.33 => ! [V3c: $i] :
% 0.65/1.33 ( ( mem @ V3c @ A_27b )
% 0.65/1.33 => ! [V4d: $i] :
% 0.65/1.33 ( ( mem @ V4d @ A_27b )
% 0.65/1.33 => ( ( V1a != V2b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2b ) @ V4d ) @ V0f ) )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2b ) @ V4d ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ V0f ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPDATE__EQ,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27b )
% 0.65/1.33 => ! [V3c: $i] :
% 0.65/1.33 ( ( mem @ V3c @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V2b ) @ V0f ) )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ V0f ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPDATE__APPLY__ID,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27b )
% 0.65/1.33 => ( ( ( ap @ V0f @ V1a )
% 0.65/1.33 = V2b )
% 0.65/1.33 <=> ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V2b ) @ V0f )
% 0.65/1.33 = V0f ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPDATE__APPLY__IMP__ID,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1b: $i] :
% 0.65/1.33 ( ( mem @ V1b @ A_27b )
% 0.65/1.33 => ! [V2a: $i] :
% 0.65/1.33 ( ( mem @ V2a @ A_27a )
% 0.65/1.33 => ( ( ( ap @ V0f @ V2a )
% 0.65/1.33 = V1b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2a ) @ V1b ) @ V0f )
% 0.65/1.33 = V0f ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EAPPLY__UPDATE__ID,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ ( ap @ V0f @ V1a ) ) @ V0f )
% 0.65/1.33 = V0f ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPD11__SAME__BASE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27a )
% 0.65/1.33 => ! [V3c: $i] :
% 0.65/1.33 ( ( mem @ V3c @ A_27b )
% 0.65/1.33 => ! [V4d: $i] :
% 0.65/1.33 ( ( mem @ V4d @ A_27b )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ V0f )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2b ) @ V4d ) @ V0f ) )
% 0.65/1.33 <=> ( ( ( V1a = V2b )
% 0.65/1.33 & ( V3c = V4d ) )
% 0.65/1.33 | ( ( V1a != V2b )
% 0.65/1.33 & ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ V0f )
% 0.65/1.33 = V0f )
% 0.65/1.33 & ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2b ) @ V4d ) @ V0f )
% 0.65/1.33 = V0f ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27c @ A_27d ) )
% 0.65/1.33 => ! [V1f1: $i] :
% 0.65/1.33 ( ( mem @ V1f1 @ A_27a )
% 0.65/1.33 => ! [V2f2: $i] :
% 0.65/1.33 ( ( mem @ V2f2 @ A_27b )
% 0.65/1.33 => ! [V3a: $i] :
% 0.65/1.33 ( ( mem @ V3a @ A_27c )
% 0.65/1.33 => ! [V4b: $i] :
% 0.65/1.33 ( ( mem @ V4b @ A_27d )
% 0.65/1.33 => ! [V5c: $i] :
% 0.65/1.33 ( ( mem @ V5c @ A_27d )
% 0.65/1.33 => ( ( V4b != V5c )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27c @ A_27d ) @ V3a ) @ V4b ) @ V0f )
% 0.65/1.33 != ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27c @ A_27d ) @ V3a ) @ V5c ) @ V0f ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1a: $i] :
% 0.65/1.33 ( ( mem @ V1a @ A_27a )
% 0.65/1.33 => ! [V2b: $i] :
% 0.65/1.33 ( ( mem @ V2b @ A_27b )
% 0.65/1.33 => ! [V3c: $i] :
% 0.65/1.33 ( ( mem @ V3c @ A_27b )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V2b ) @ V0f )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V1a ) @ V3c ) @ V0f ) )
% 0.65/1.33 <=> ( V2b = V3c ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EUPD__SAME__KEY__UNWIND,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f1: $i] :
% 0.65/1.33 ( ( mem @ V0f1 @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1f2: $i] :
% 0.65/1.33 ( ( mem @ V1f2 @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V2a: $i] :
% 0.65/1.33 ( ( mem @ V2a @ A_27a )
% 0.65/1.33 => ! [V3b: $i] :
% 0.65/1.33 ( ( mem @ V3b @ A_27b )
% 0.65/1.33 => ! [V4c: $i] :
% 0.65/1.33 ( ( mem @ V4c @ A_27b )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2a ) @ V3b ) @ V0f1 )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2a ) @ V4c ) @ V1f2 ) )
% 0.65/1.33 => ( ( V3b = V4c )
% 0.65/1.33 & ! [V5v: $i] :
% 0.65/1.33 ( ( mem @ V5v @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2a ) @ V5v ) @ V0f1 )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V2a ) @ V5v ) @ V1f2 ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EGEN__LET__RAND,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.33 => ! [V1f: $i] :
% 0.65/1.33 ( ( mem @ V1f @ ( arr @ A_27c @ A_27b ) )
% 0.65/1.33 => ! [V2v: $i] :
% 0.65/1.33 ( ( mem @ V2v @ A_27c )
% 0.65/1.33 => ( ( ap @ V0P @ ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27c @ A_27b ) @ V1f ) @ V2v ) )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27c @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ A_27a @ A_27b ) @ V0P ) @ V1f ) ) @ V2v ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EGEN__LET__RATOR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 0.65/1.33 => ! [V1v: $i] :
% 0.65/1.33 ( ( mem @ V1v @ A_27b )
% 0.65/1.33 => ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27c )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27b @ ( arr @ A_27c @ A_27a ) ) @ V0f ) @ V1v ) @ V2x )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ A_27b @ A_27c @ A_27a ) @ V0f ) @ V2x ) ) @ V1v ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2ELET__FORALL__ELIM,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1v: $i] :
% 0.65/1.33 ( ( mem @ V1v @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2ELET @ A_27a @ bool ) @ V0f ) @ V1v ) )
% 0.65/1.33 <=> ( p @ ( ap @ ( c_2Ebool_2E_21 @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ bool @ bool ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( arr @ bool @ bool ) @ bool ) @ c_2Emin_2E_3D_3D_3E ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Emarker_2EAbbrev ) @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ A_27a @ A_27a @ bool ) @ ( c_2Emin_2E_3D @ A_27a ) ) @ V1v ) ) ) ) @ V0f ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EGEN__literal__case__RAND,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27b @ A_27a ) )
% 0.65/1.33 => ! [V1f: $i] :
% 0.65/1.33 ( ( mem @ V1f @ ( arr @ A_27c @ A_27b ) )
% 0.65/1.33 => ! [V2v: $i] :
% 0.65/1.33 ( ( mem @ V2v @ A_27c )
% 0.65/1.33 => ( ( ap @ V0P @ ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27c @ A_27b ) @ V1f ) @ V2v ) )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27c @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ A_27a @ A_27b ) @ V0P ) @ V1f ) ) @ V2v ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EGEN__literal__case__RATOR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 0.65/1.33 => ! [V1v: $i] :
% 0.65/1.33 ( ( mem @ V1v @ A_27b )
% 0.65/1.33 => ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27c )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27b @ ( arr @ A_27c @ A_27a ) ) @ V0f ) @ V1v ) @ V2x )
% 0.65/1.33 = ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ A_27b @ A_27c @ A_27a ) @ V0f ) @ V2x ) ) @ V1v ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2Eliteral__case__FORALL__ELIM,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1v: $i] :
% 0.65/1.33 ( ( mem @ V1v @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2Eliteral__case @ A_27a @ bool ) @ V0f ) @ V1v ) )
% 0.65/1.33 <=> ( p @ ( ap @ ( c_2Ebool_2E_21 @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ bool @ bool ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( arr @ bool @ bool ) @ bool ) @ c_2Emin_2E_3D_3D_3E ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Emarker_2EAbbrev ) @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ A_27a @ A_27a @ bool ) @ ( c_2Emin_2E_3D @ A_27a ) ) @ V1v ) ) ) ) @ V0f ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EASSOC__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
% 0.65/1.33 <=> ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27a )
% 0.65/1.33 => ! [V3z: $i] :
% 0.65/1.33 ( ( mem @ V3z @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V1x ) @ ( ap @ ( ap @ V0f @ V2y ) @ V3z ) )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) @ V3z ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2ECOMM__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Ecombin_2ECOMM @ A_27a @ A_27b ) @ V0f ) )
% 0.65/1.33 <=> ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V1x ) @ V2y )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V2y ) @ V1x ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EFCOMM__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27c @ ( arr @ A_27a @ A_27a ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1g ) )
% 0.65/1.33 <=> ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27c )
% 0.65/1.33 => ! [V3y: $i] :
% 0.65/1.33 ( ( mem @ V3y @ A_27a )
% 0.65/1.33 => ! [V4z: $i] :
% 0.65/1.33 ( ( mem @ V4z @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ V1g @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4z ) )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ ( ap @ ( ap @ V1g @ V2x ) @ V3y ) ) @ V4z ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2ERIGHT__ID__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
% 0.65/1.33 => ! [V1e: $i] :
% 0.65/1.33 ( ( mem @ V1e @ A_27b )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27b ) @ V0f ) @ V1e ) )
% 0.65/1.33 <=> ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V2x ) @ V1e )
% 0.65/1.33 = V2x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2ELEFT__ID__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 0.65/1.33 => ! [V1e: $i] :
% 0.65/1.33 ( ( mem @ V1e @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27b ) @ V0f ) @ V1e ) )
% 0.65/1.33 <=> ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ V1e ) @ V2x )
% 0.65/1.33 = V2x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EMONOID__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
% 0.65/1.33 => ! [V1e: $i] :
% 0.65/1.33 ( ( mem @ V1e @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ A_27a ) @ V0f ) @ V1e ) )
% 0.65/1.33 <=> ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
% 0.65/1.33 & ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a ) @ V0f ) @ V1e ) )
% 0.65/1.33 & ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a ) @ V0f ) @ V1e ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EASSOC__CONJ,axiom,
% 0.65/1.33 p @ ( ap @ ( c_2Ecombin_2EASSOC @ bool ) @ c_2Ebool_2E_2F_5C ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EASSOC__SYM,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
% 0.65/1.33 <=> ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27a )
% 0.65/1.33 => ! [V3z: $i] :
% 0.65/1.33 ( ( mem @ V3z @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ V0f @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) @ V3z )
% 0.65/1.33 = ( ap @ ( ap @ V0f @ V1x ) @ ( ap @ ( ap @ V0f @ V2y ) @ V3z ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EASSOC__DISJ,axiom,
% 0.65/1.33 p @ ( ap @ ( c_2Ecombin_2EASSOC @ bool ) @ c_2Ebool_2E_5C_2F ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EFCOMM__ASSOC,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27a @ A_27a ) @ V0f ) @ V0f ) )
% 0.65/1.33 <=> ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EMONOID__CONJ__T,axiom,
% 0.65/1.33 p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ bool ) @ c_2Ebool_2E_2F_5C ) @ c_2Ebool_2ET ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EMONOID__DISJ__F,axiom,
% 0.65/1.33 p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Ecombin_2EFAIL__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ( c_2Ecombin_2EFAIL @ A_27a @ A_27b )
% 0.65/1.33 = ( lam @ A_27a
% 0.65/1.33 @ ^ [V0x: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V1y: $i] : V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Ecombin_2EFAIL__THM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 0.65/1.33 = V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_ty_2Enum_2Enum,type,
% 0.65/1.33 ty_2Enum_2Enum: del ).
% 0.65/1.33
% 0.65/1.33 thf(stp_ty_2Enum_2Enum,type,
% 0.65/1.33 tp__ty_2Enum_2Enum: $tType ).
% 0.65/1.33
% 0.65/1.33 thf(stp_inj_ty_2Enum_2Enum,type,
% 0.65/1.33 inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
% 0.65/1.33
% 0.65/1.33 thf(stp_surj_ty_2Enum_2Enum,type,
% 0.65/1.33 surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
% 0.65/1.33
% 0.65/1.33 thf(stp_inj_surj_ty_2Enum_2Enum,axiom,
% 0.65/1.33 ! [X: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
% 0.65/1.33 = X ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_inj_mem_ty_2Enum_2Enum,axiom,
% 0.65/1.33 ! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_iso_mem_ty_2Enum_2Enum,axiom,
% 0.65/1.33 ! [X: $i] :
% 0.65/1.33 ( ( mem @ X @ ty_2Enum_2Enum )
% 0.65/1.33 => ( X
% 0.65/1.33 = ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2E0,type,
% 0.65/1.33 c_2Enum_2E0: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2E0,axiom,
% 0.65/1.33 mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Enum_2E0,type,
% 0.65/1.33 fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Enum_2E0,axiom,
% 0.65/1.33 ( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
% 0.65/1.33 = c_2Enum_2E0 ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2EABS__num,type,
% 0.65/1.33 c_2Enum_2EABS__num: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2EABS__num,axiom,
% 0.65/1.33 mem @ c_2Enum_2EABS__num @ ( arr @ ind @ ty_2Enum_2Enum ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Enum_2EABS__num,type,
% 0.65/1.33 fo__c_2Enum_2EABS__num: tp__i > tp__ty_2Enum_2Enum ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Enum_2EABS__num,axiom,
% 0.65/1.33 ! [X0: tp__i] :
% 0.65/1.33 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enum_2EABS__num @ X0 ) )
% 0.65/1.33 = ( ap @ c_2Enum_2EABS__num @ ( inj__i @ X0 ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2EIS__NUM__REP,type,
% 0.65/1.33 c_2Enum_2EIS__NUM__REP: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2EIS__NUM__REP,axiom,
% 0.65/1.33 mem @ c_2Enum_2EIS__NUM__REP @ ( arr @ ind @ bool ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2EREP__num,type,
% 0.65/1.33 c_2Enum_2EREP__num: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2EREP__num,axiom,
% 0.65/1.33 mem @ c_2Enum_2EREP__num @ ( arr @ ty_2Enum_2Enum @ ind ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Enum_2EREP__num,type,
% 0.65/1.33 fo__c_2Enum_2EREP__num: tp__ty_2Enum_2Enum > tp__i ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Enum_2EREP__num,axiom,
% 0.65/1.33 ! [X0: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( inj__i @ ( fo__c_2Enum_2EREP__num @ X0 ) )
% 0.65/1.33 = ( ap @ c_2Enum_2EREP__num @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2ESUC,type,
% 0.65/1.33 c_2Enum_2ESUC: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2ESUC,axiom,
% 0.65/1.33 mem @ c_2Enum_2ESUC @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Enum_2ESUC,type,
% 0.65/1.33 fo__c_2Enum_2ESUC: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Enum_2ESUC,axiom,
% 0.65/1.33 ! [X0: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enum_2ESUC @ X0 ) )
% 0.65/1.33 = ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2ESUC__REP,type,
% 0.65/1.33 c_2Enum_2ESUC__REP: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2ESUC__REP,axiom,
% 0.65/1.33 mem @ c_2Enum_2ESUC__REP @ ( arr @ ind @ ind ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Enum_2ESUC__REP,type,
% 0.65/1.33 fo__c_2Enum_2ESUC__REP: tp__i > tp__i ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Enum_2ESUC__REP,axiom,
% 0.65/1.33 ! [X0: tp__i] :
% 0.65/1.33 ( ( inj__i @ ( fo__c_2Enum_2ESUC__REP @ X0 ) )
% 0.65/1.33 = ( ap @ c_2Enum_2ESUC__REP @ ( inj__i @ X0 ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Enum_2EZERO__REP,type,
% 0.65/1.33 c_2Enum_2EZERO__REP: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Enum_2EZERO__REP,axiom,
% 0.65/1.33 mem @ c_2Enum_2EZERO__REP @ ind ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Enum_2EZERO__REP,type,
% 0.65/1.33 fo__c_2Enum_2EZERO__REP: tp__i ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Enum_2EZERO__REP,axiom,
% 0.65/1.33 ( ( inj__i @ fo__c_2Enum_2EZERO__REP )
% 0.65/1.33 = c_2Enum_2EZERO__REP ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2ESUC__REP__DEF,axiom,
% 0.65/1.33 ( ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ c_2Enum_2ESUC__REP ) )
% 0.65/1.33 & ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ c_2Enum_2ESUC__REP ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2EZERO__REP__DEF,axiom,
% 0.65/1.33 ! [V0y: tp__i] :
% 0.65/1.33 ( fo__c_2Enum_2EZERO__REP
% 0.65/1.33 != ( surj__i @ ( ap @ c_2Enum_2ESUC__REP @ ( inj__i @ V0y ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2EIS__NUM__REP,axiom,
% 0.65/1.33 ! [V0m: tp__i] :
% 0.65/1.33 ( ( p @ ( ap @ c_2Enum_2EIS__NUM__REP @ ( inj__i @ V0m ) ) )
% 0.65/1.33 <=> ! [V1P: $i] :
% 0.65/1.33 ( ( mem @ V1P @ ( arr @ ind @ bool ) )
% 0.65/1.33 => ( ( ( p @ ( ap @ V1P @ ( inj__i @ fo__c_2Enum_2EZERO__REP ) ) )
% 0.65/1.33 & ! [V2n: tp__i] :
% 0.65/1.33 ( ( p @ ( ap @ V1P @ ( inj__i @ V2n ) ) )
% 0.65/1.33 => ( p @ ( ap @ V1P @ ( ap @ c_2Enum_2ESUC__REP @ ( inj__i @ V2n ) ) ) ) ) )
% 0.65/1.33 => ( p @ ( ap @ V1P @ ( inj__i @ V0m ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2Enum__TY__DEF,axiom,
% 0.65/1.33 ? [V0rep: $i] :
% 0.65/1.33 ( ( mem @ V0rep @ ( arr @ ty_2Enum_2Enum @ ind ) )
% 0.65/1.33 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ind @ ty_2Enum_2Enum ) @ c_2Enum_2EIS__NUM__REP ) @ V0rep ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2Enum__ISO__DEF,axiom,
% 0.65/1.33 ( ! [V0a: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2EABS__num @ ( ap @ c_2Enum_2EREP__num @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) )
% 0.65/1.33 = V0a )
% 0.65/1.33 & ! [V1r: tp__i] :
% 0.65/1.33 ( ( p @ ( ap @ c_2Enum_2EIS__NUM__REP @ ( inj__i @ V1r ) ) )
% 0.65/1.33 <=> ( ( surj__i @ ( ap @ c_2Enum_2EREP__num @ ( ap @ c_2Enum_2EABS__num @ ( inj__i @ V1r ) ) ) )
% 0.65/1.33 = V1r ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2EZERO__DEF,axiom,
% 0.65/1.33 ( fo__c_2Enum_2E0
% 0.65/1.33 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2EABS__num @ ( inj__i @ fo__c_2Enum_2EZERO__REP ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Enum_2ESUC__DEF,axiom,
% 0.65/1.33 ! [V0m: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 0.65/1.33 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2EABS__num @ ( ap @ c_2Enum_2ESUC__REP @ ( ap @ c_2Enum_2EREP__num @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Enum_2ENOT__SUC,axiom,
% 0.65/1.33 ! [V0n: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 0.65/1.33 != fo__c_2Enum_2E0 ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Enum_2EINV__SUC,axiom,
% 0.65/1.33 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 0.65/1.33 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 0.65/1.33 => ( V0m = V1n ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Enum_2EINDUCTION,axiom,
% 0.65/1.33 ! [V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 0.65/1.33 => ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 0.65/1.33 & ! [V1n: tp__ty_2Enum_2Enum] :
% 0.65/1.33 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 0.65/1.33 => ( p @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) )
% 0.65/1.33 => ! [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_ty_2Eone_2Eone,type,
% 0.65/1.33 ty_2Eone_2Eone: del ).
% 0.65/1.33
% 0.65/1.33 thf(stp_ty_2Eone_2Eone,type,
% 0.65/1.33 tp__ty_2Eone_2Eone: $tType ).
% 0.65/1.33
% 0.65/1.33 thf(stp_inj_ty_2Eone_2Eone,type,
% 0.65/1.33 inj__ty_2Eone_2Eone: tp__ty_2Eone_2Eone > $i ).
% 0.65/1.33
% 0.65/1.33 thf(stp_surj_ty_2Eone_2Eone,type,
% 0.65/1.33 surj__ty_2Eone_2Eone: $i > tp__ty_2Eone_2Eone ).
% 0.65/1.33
% 0.65/1.33 thf(stp_inj_surj_ty_2Eone_2Eone,axiom,
% 0.65/1.33 ! [X: tp__ty_2Eone_2Eone] :
% 0.65/1.33 ( ( surj__ty_2Eone_2Eone @ ( inj__ty_2Eone_2Eone @ X ) )
% 0.65/1.33 = X ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_inj_mem_ty_2Eone_2Eone,axiom,
% 0.65/1.33 ! [X: tp__ty_2Eone_2Eone] : ( mem @ ( inj__ty_2Eone_2Eone @ X ) @ ty_2Eone_2Eone ) ).
% 0.65/1.33
% 0.65/1.33 thf(stp_iso_mem_ty_2Eone_2Eone,axiom,
% 0.65/1.33 ! [X: $i] :
% 0.65/1.33 ( ( mem @ X @ ty_2Eone_2Eone )
% 0.65/1.33 => ( X
% 0.65/1.33 = ( inj__ty_2Eone_2Eone @ ( surj__ty_2Eone_2Eone @ X ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Eone_2Eone,type,
% 0.65/1.33 c_2Eone_2Eone: $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Eone_2Eone,axiom,
% 0.65/1.33 mem @ c_2Eone_2Eone @ ty_2Eone_2Eone ).
% 0.65/1.33
% 0.65/1.33 thf(stp_fo_c_2Eone_2Eone,type,
% 0.65/1.33 fo__c_2Eone_2Eone: tp__ty_2Eone_2Eone ).
% 0.65/1.33
% 0.65/1.33 thf(stp_eq_fo_c_2Eone_2Eone,axiom,
% 0.65/1.33 ( ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone )
% 0.65/1.33 = c_2Eone_2Eone ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Eone_2Eone__CASE,type,
% 0.65/1.33 c_2Eone_2Eone__CASE: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Eone_2Eone__CASE,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Eone_2Eone__CASE @ A_27a ) @ ( arr @ ty_2Eone_2Eone @ ( arr @ A_27a @ A_27a ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Eone_2Eone__TY__DEF,axiom,
% 0.65/1.33 ? [V0rep: $i] :
% 0.65/1.33 ( ( mem @ V0rep @ ( arr @ ty_2Eone_2Eone @ bool ) )
% 0.65/1.33 & ( p
% 0.65/1.33 @ ( ap
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ bool @ ty_2Eone_2Eone )
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V1b: $i] : V1b ) )
% 0.65/1.33 @ V0rep ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2Eone__axiom,axiom,
% 0.65/1.33 ! [A_27a: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
% 0.65/1.33 => ( V0f = V1g ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Eone_2Eone__DEF,axiom,
% 0.65/1.33 ( fo__c_2Eone_2Eone
% 0.65/1.33 = ( surj__ty_2Eone_2Eone
% 0.65/1.33 @ ( ap @ ( c_2Emin_2E_40 @ ty_2Eone_2Eone )
% 0.65/1.33 @ ( lam @ ty_2Eone_2Eone
% 0.65/1.33 @ ^ [V0x: $i] : c_2Ebool_2ET ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2Eone,axiom,
% 0.65/1.33 ! [V0v: tp__ty_2Eone_2Eone] : ( V0v = fo__c_2Eone_2Eone ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2Eone__Axiom,axiom,
% 0.65/1.33 ! [A_27a: del,V0e: $i] :
% 0.65/1.33 ( ( mem @ V0e @ A_27a )
% 0.65/1.33 => ( p
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ ty_2Eone_2Eone @ A_27a ) )
% 0.65/1.33 @ ( lam @ ( arr @ ty_2Eone_2Eone @ A_27a )
% 0.65/1.33 @ ^ [V1fn: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1fn @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) @ V0e ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2Eone__prim__rec,axiom,
% 0.65/1.33 ! [A_27a: del,V0e: $i] :
% 0.65/1.33 ( ( mem @ V0e @ A_27a )
% 0.65/1.33 => ? [V1fn: $i] :
% 0.65/1.33 ( ( mem @ V1fn @ ( arr @ ty_2Eone_2Eone @ A_27a ) )
% 0.65/1.33 & ( ( ap @ V1fn @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) )
% 0.65/1.33 = V0e ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2Eone__induction,axiom,
% 0.65/1.33 ! [V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ty_2Eone_2Eone @ bool ) )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) )
% 0.65/1.33 => ! [V1x: tp__ty_2Eone_2Eone] : ( p @ ( ap @ V0P @ ( inj__ty_2Eone_2Eone @ V1x ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2EFORALL__ONE,axiom,
% 0.65/1.33 ! [V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ty_2Eone_2Eone @ bool ) )
% 0.65/1.33 => ( ! [V1x: tp__ty_2Eone_2Eone] : ( p @ ( ap @ V0P @ ( inj__ty_2Eone_2Eone @ V1x ) ) )
% 0.65/1.33 <=> ( p @ ( ap @ V0P @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Eone_2Eone__case__def,axiom,
% 0.65/1.33 ! [A_27a: del,V0u: tp__ty_2Eone_2Eone,V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Eone_2Eone__CASE @ A_27a ) @ ( inj__ty_2Eone_2Eone @ V0u ) ) @ V1x )
% 0.65/1.33 = V1x ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Eone_2Eone__case__thm,axiom,
% 0.65/1.33 ! [A_27a: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( c_2Eone_2Eone__CASE @ A_27a ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) @ V0x )
% 0.65/1.33 = V0x ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_ty_2Esum_2Esum,type,
% 0.65/1.33 ty_2Esum_2Esum: del > del > del ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2E_2B_2B,type,
% 0.65/1.33 c_2Esum_2E_2B_2B: del > del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2E_2B_2B,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] : ( mem @ ( c_2Esum_2E_2B_2B @ A_27a @ A_27b @ A_27c @ A_27d ) @ ( arr @ ( arr @ A_27a @ A_27c ) @ ( arr @ ( arr @ A_27b @ A_27d ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EABS__sum,type,
% 0.65/1.33 c_2Esum_2EABS__sum: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EABS__sum,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EABS__sum @ A_27a @ A_27b ) @ ( arr @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EINL,type,
% 0.65/1.33 c_2Esum_2EINL: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EINL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EINR,type,
% 0.65/1.33 c_2Esum_2EINR: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EINR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ ( arr @ A_27b @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EISL,type,
% 0.65/1.33 c_2Esum_2EISL: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EISL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EISR,type,
% 0.65/1.33 c_2Esum_2EISR: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EISR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EIS__SUM__REP,type,
% 0.65/1.33 c_2Esum_2EIS__SUM__REP: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EIS__SUM__REP,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EIS__SUM__REP @ A_27a @ A_27b ) @ ( arr @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EOUTL,type,
% 0.65/1.33 c_2Esum_2EOUTL: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EOUTL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EOUTL @ A_27a @ A_27b ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27a ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EOUTR,type,
% 0.65/1.33 c_2Esum_2EOUTR: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EOUTR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EOUTR @ A_27a @ A_27b ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27b ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2EREP__sum,type,
% 0.65/1.33 c_2Esum_2EREP__sum: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2EREP__sum,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2EREP__sum @ A_27a @ A_27b ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2ESUM__ALL,type,
% 0.65/1.33 c_2Esum_2ESUM__ALL: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2ESUM__ALL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Esum_2Esum__CASE,type,
% 0.65/1.33 c_2Esum_2Esum__CASE: del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Esum_2Esum__CASE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Esum_2Esum__CASE @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27c ) @ ( arr @ ( arr @ A_27b @ A_27c ) @ A_27c ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EIS__SUM__REP,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Esum_2EIS__SUM__REP @ A_27a @ A_27b ) @ V0f ) )
% 0.65/1.33 <=> ? [V1v1: $i] :
% 0.65/1.33 ( ( mem @ V1v1 @ A_27a )
% 0.65/1.33 & ? [V2v2: $i] :
% 0.65/1.33 ( ( mem @ V2v2 @ A_27b )
% 0.65/1.33 & ( ( V0f
% 0.65/1.33 = ( lam @ bool
% 0.65/1.33 @ ^ [V3b: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V4x: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V5y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ V1v1 ) ) @ V3b ) ) ) ) )
% 0.65/1.33 | ( V0f
% 0.65/1.33 = ( lam @ bool
% 0.65/1.33 @ ^ [V6b: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V7x: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V8y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V8y ) @ V2v2 ) ) @ ( ap @ c_2Ebool_2E_7E @ V6b ) ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2Esum__TY__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ? [V0rep: $i] :
% 0.65/1.33 ( ( mem @ V0rep @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) )
% 0.65/1.33 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2EIS__SUM__REP @ A_27a @ A_27b ) ) @ V0rep ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2Esum__ISO__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ! [V0a: $i] :
% 0.65/1.33 ( ( mem @ V0a @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EABS__sum @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EREP__sum @ A_27a @ A_27b ) @ V0a ) )
% 0.65/1.33 = V0a ) )
% 0.65/1.33 & ! [V1r: $i] :
% 0.65/1.33 ( ( mem @ V1r @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Esum_2EIS__SUM__REP @ A_27a @ A_27b ) @ V1r ) )
% 0.65/1.33 <=> ( ( ap @ ( c_2Esum_2EREP__sum @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EABS__sum @ A_27a @ A_27b ) @ V1r ) )
% 0.65/1.33 = V1r ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EINL__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0e: $i] :
% 0.65/1.33 ( ( mem @ V0e @ A_27a )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0e )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EABS__sum @ A_27a @ A_27b )
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V1b: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V3y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2x ) @ V0e ) ) @ V1b ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EINR__DEF,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0e: $i] :
% 0.65/1.33 ( ( mem @ V0e @ A_27b )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V0e )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EABS__sum @ A_27a @ A_27b )
% 0.65/1.33 @ ( lam @ bool
% 0.65/1.33 @ ^ [V1b: $i] :
% 0.65/1.33 ( lam @ A_27a
% 0.65/1.33 @ ^ [V2x: $i] :
% 0.65/1.33 ( lam @ A_27b
% 0.65/1.33 @ ^ [V3y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V3y ) @ V0e ) ) @ ( ap @ c_2Ebool_2E_7E @ V1b ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EINL__11,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27a )
% 0.65/1.33 => ( ( ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0x )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V1y ) )
% 0.65/1.33 <=> ( V0x = V1y ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EINR__11,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27b )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27b )
% 0.65/1.33 => ( ( ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V0x )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V1y ) )
% 0.65/1.33 <=> ( V0x = V1y ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EINR__INL__11,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ! [V0y: $i] :
% 0.65/1.33 ( ( mem @ V0y @ A_27a )
% 0.65/1.33 => ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( ( ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V1x )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0y ) )
% 0.65/1.33 <=> ( V1x = V0y ) ) ) )
% 0.65/1.33 & ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27b )
% 0.65/1.33 => ! [V3x: $i] :
% 0.65/1.33 ( ( mem @ V3x @ A_27b )
% 0.65/1.33 => ( ( ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V3x )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V2y ) )
% 0.65/1.33 <=> ( V3x = V2y ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EINR__neq__INL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0v1: $i] :
% 0.65/1.33 ( ( mem @ V0v1 @ A_27a )
% 0.65/1.33 => ! [V1v2: $i] :
% 0.65/1.33 ( ( mem @ V1v2 @ A_27b )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V1v2 )
% 0.65/1.33 != ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0v1 ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__axiom,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ( p
% 0.65/1.33 @ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) )
% 0.65/1.33 @ ( lam @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c )
% 0.65/1.33 @ ^ [V2h: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ V2h ) @ ( c_2Esum_2EINL @ A_27a @ A_27b ) ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27b @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ A_27c @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ V2h ) @ ( c_2Esum_2EINR @ A_27a @ A_27b ) ) ) @ V1g ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__INDUCT,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) )
% 0.65/1.33 => ( ( ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V1x ) ) ) )
% 0.65/1.33 & ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27b )
% 0.65/1.33 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V2y ) ) ) ) )
% 0.65/1.33 => ! [V3s: $i] :
% 0.65/1.33 ( ( mem @ V3s @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V3s ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EFORALL__SUM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) )
% 0.65/1.33 => ( ! [V1s: $i] :
% 0.65/1.33 ( ( mem @ V1s @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( p @ ( ap @ V0P @ V1s ) ) )
% 0.65/1.33 <=> ( ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V2x ) ) ) )
% 0.65/1.33 & ! [V3y: $i] :
% 0.65/1.33 ( ( mem @ V3y @ A_27b )
% 0.65/1.33 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V3y ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EEXISTS__SUM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) )
% 0.65/1.33 => ( ? [V1s: $i] :
% 0.65/1.33 ( ( mem @ V1s @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 & ( p @ ( ap @ V0P @ V1s ) ) )
% 0.65/1.33 <=> ( ? [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 & ( p @ ( ap @ V0P @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V2x ) ) ) )
% 0.65/1.33 | ? [V3y: $i] :
% 0.65/1.33 ( ( mem @ V3y @ A_27b )
% 0.65/1.33 & ( p @ ( ap @ V0P @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V3y ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__Axiom,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ? [V2h: $i] :
% 0.65/1.33 ( ( mem @ V2h @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) )
% 0.65/1.33 & ! [V3x: $i] :
% 0.65/1.33 ( ( mem @ V3x @ A_27a )
% 0.65/1.33 => ( ( ap @ V2h @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V3x ) )
% 0.65/1.33 = ( ap @ V0f @ V3x ) ) )
% 0.65/1.33 & ! [V4y: $i] :
% 0.65/1.33 ( ( mem @ V4y @ A_27b )
% 0.65/1.33 => ( ( ap @ V2h @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V4y ) )
% 0.65/1.33 = ( ap @ V1g @ V4y ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__CASES,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0ss: $i] :
% 0.65/1.33 ( ( mem @ V0ss @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ? [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 & ( V0ss
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V1x ) ) )
% 0.65/1.33 | ? [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27b )
% 0.65/1.33 & ( V0ss
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V2y ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__distinct,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27b )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0x )
% 0.65/1.33 != ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V1y ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__distinct1,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27b )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V1y )
% 0.65/1.33 != ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EISL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( p @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0x ) ) ) )
% 0.65/1.33 & ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27b )
% 0.65/1.33 => ~ ( p @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V1y ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EISR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27b )
% 0.65/1.33 => ( p @ ( ap @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V0x ) ) ) )
% 0.65/1.33 & ! [V1y: $i] :
% 0.65/1.33 ( ( mem @ V1y @ A_27a )
% 0.65/1.33 => ~ ( p @ ( ap @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V1y ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EOUTL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EOUTL @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 = V0x ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2EOUTR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27b )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EOUTR @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 = V0x ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EISL__OR__ISR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 | ( p @ ( ap @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ V0x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EINL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EOUTL @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 = V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2EINR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 => ( ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ ( ap @ ( c_2Esum_2EOUTR @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 = V0x ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2Esum__case__def,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del] :
% 0.65/1.33 ( ! [V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ A_27a )
% 0.65/1.33 => ! [V1f: $i] :
% 0.65/1.33 ( ( mem @ V1f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V2f1: $i] :
% 0.65/1.33 ( ( mem @ V2f1 @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2Esum__CASE @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V0x ) ) @ V1f ) @ V2f1 )
% 0.65/1.33 = ( ap @ V1f @ V0x ) ) ) ) )
% 0.65/1.33 & ! [V3y: $i] :
% 0.65/1.33 ( ( mem @ V3y @ A_27b )
% 0.65/1.33 => ! [V4f: $i] :
% 0.65/1.33 ( ( mem @ V4f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V5f1: $i] :
% 0.65/1.33 ( ( mem @ V5f1 @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2Esum__CASE @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V3y ) ) @ V4f ) @ V5f1 )
% 0.65/1.33 = ( ap @ V5f1 @ V3y ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Esum__case__cong,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0f_27: $i] :
% 0.65/1.33 ( ( mem @ V0f_27 @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1f1_27: $i] :
% 0.65/1.33 ( ( mem @ V1f1_27 @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ! [V2M: $i] :
% 0.65/1.33 ( ( mem @ V2M @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V3M_27: $i] :
% 0.65/1.33 ( ( mem @ V3M_27 @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V4f: $i] :
% 0.65/1.33 ( ( mem @ V4f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V5f1: $i] :
% 0.65/1.33 ( ( mem @ V5f1 @ ( arr @ A_27b @ A_27c ) )
% 0.65/1.33 => ( ( ( V2M = V3M_27 )
% 0.65/1.33 & ! [V6x: $i] :
% 0.65/1.33 ( ( mem @ V6x @ A_27a )
% 0.65/1.33 => ( ( V3M_27
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V6x ) )
% 0.65/1.33 => ( ( ap @ V4f @ V6x )
% 0.65/1.33 = ( ap @ V0f_27 @ V6x ) ) ) )
% 0.65/1.33 & ! [V7y: $i] :
% 0.65/1.33 ( ( mem @ V7y @ A_27b )
% 0.65/1.33 => ( ( V3M_27
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V7y ) )
% 0.65/1.33 => ( ( ap @ V5f1 @ V7y )
% 0.65/1.33 = ( ap @ V1f1_27 @ V7y ) ) ) ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2Esum__CASE @ A_27a @ A_27b @ A_27c ) @ V2M ) @ V4f ) @ V5f1 )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Esum_2Esum__CASE @ A_27a @ A_27b @ A_27c ) @ V3M_27 ) @ V0f_27 ) @ V1f1_27 ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2ESUM__MAP__def,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
% 0.65/1.33 ( ! [V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27b @ A_27d ) )
% 0.65/1.33 => ! [V2a: $i] :
% 0.65/1.33 ( ( mem @ V2a @ A_27a )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2E_2B_2B @ A_27a @ A_27b @ A_27c @ A_27d ) @ V0f ) @ V1g ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V2a ) )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27c @ A_27d ) @ ( ap @ V0f @ V2a ) ) ) ) ) )
% 0.65/1.33 & ! [V3f: $i] :
% 0.65/1.33 ( ( mem @ V3f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V4g: $i] :
% 0.65/1.33 ( ( mem @ V4g @ ( arr @ A_27b @ A_27d ) )
% 0.65/1.33 => ! [V5b: $i] :
% 0.65/1.33 ( ( mem @ V5b @ A_27b )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2E_2B_2B @ A_27a @ A_27b @ A_27c @ A_27d ) @ V3f ) @ V4g ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V5b ) )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27c @ A_27d ) @ ( ap @ V4g @ V5b ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ESUM__MAP,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27b @ A_27d ) )
% 0.65/1.33 => ! [V2z: $i] :
% 0.65/1.33 ( ( mem @ V2z @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2E_2B_2B @ A_27a @ A_27b @ A_27c @ A_27d ) @ V0f ) @ V1g ) @ V2z )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ V2z ) ) @ ( ap @ ( c_2Esum_2EINL @ A_27c @ A_27d ) @ ( ap @ V0f @ ( ap @ ( c_2Esum_2EOUTL @ A_27a @ A_27b ) @ V2z ) ) ) ) @ ( ap @ ( c_2Esum_2EINR @ A_27c @ A_27d ) @ ( ap @ V1g @ ( ap @ ( c_2Esum_2EOUTR @ A_27a @ A_27b ) @ V2z ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ESUM__MAP__CASE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 0.65/1.33 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 0.65/1.33 => ! [V1g: $i] :
% 0.65/1.33 ( ( mem @ V1g @ ( arr @ A_27b @ A_27d ) )
% 0.65/1.33 => ! [V2z: $i] :
% 0.65/1.33 ( ( mem @ V2z @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ap @ ( ap @ ( ap @ ( c_2Esum_2E_2B_2B @ A_27a @ A_27b @ A_27c @ A_27d ) @ V0f ) @ V1g ) @ V2z )
% 0.65/1.33 = ( ap @ ( ap @ ( ap @ ( c_2Esum_2Esum__CASE @ A_27a @ A_27b @ ( ty_2Esum_2Esum @ A_27c @ A_27d ) ) @ V2z ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( ty_2Esum_2Esum @ A_27c @ A_27d ) @ A_27c ) @ ( c_2Esum_2EINL @ A_27c @ A_27d ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ ( ty_2Esum_2Esum @ A_27c @ A_27d ) @ A_27d ) @ ( c_2Esum_2EINR @ A_27c @ A_27d ) ) @ V1g ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ESUM__MAP__I,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ( ap @ ( ap @ ( c_2Esum_2E_2B_2B @ A_27a @ A_27b @ A_27a @ A_27b ) @ ( c_2Ecombin_2EI @ A_27a ) ) @ ( c_2Ecombin_2EI @ A_27b ) )
% 0.65/1.33 = ( c_2Ecombin_2EI @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Econd__sum__expand,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,A_27g: del,A_27h: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ bool )
% 0.65/1.33 => ( ! [V1x: $i] :
% 0.65/1.33 ( ( mem @ V1x @ A_27a )
% 0.65/1.33 => ! [V2y: $i] :
% 0.65/1.33 ( ( mem @ V2y @ A_27b )
% 0.65/1.33 => ! [V3z: $i] :
% 0.65/1.33 ( ( mem @ V3z @ A_27a )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Esum_2Esum @ A_27b @ A_27a ) ) @ V0P ) @ ( ap @ ( c_2Esum_2EINR @ A_27b @ A_27a ) @ V1x ) ) @ ( ap @ ( c_2Esum_2EINL @ A_27b @ A_27a ) @ V2y ) )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27b @ A_27a ) @ V3z ) )
% 0.65/1.33 <=> ( ( p @ V0P )
% 0.65/1.33 & ( V3z = V1x ) ) ) ) ) )
% 0.65/1.33 & ! [V4x: $i] :
% 0.65/1.33 ( ( mem @ V4x @ A_27c )
% 0.65/1.33 => ! [V5y: $i] :
% 0.65/1.33 ( ( mem @ V5y @ A_27d )
% 0.65/1.33 => ! [V6z: $i] :
% 0.65/1.33 ( ( mem @ V6z @ A_27d )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Esum_2Esum @ A_27d @ A_27c ) ) @ V0P ) @ ( ap @ ( c_2Esum_2EINR @ A_27d @ A_27c ) @ V4x ) ) @ ( ap @ ( c_2Esum_2EINL @ A_27d @ A_27c ) @ V5y ) )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27d @ A_27c ) @ V6z ) )
% 0.65/1.33 <=> ( ~ ( p @ V0P )
% 0.65/1.33 & ( V6z = V5y ) ) ) ) ) )
% 0.65/1.33 & ! [V7x: $i] :
% 0.65/1.33 ( ( mem @ V7x @ A_27e )
% 0.65/1.33 => ! [V8y: $i] :
% 0.65/1.33 ( ( mem @ V8y @ A_27f )
% 0.65/1.33 => ! [V9z: $i] :
% 0.65/1.33 ( ( mem @ V9z @ A_27e )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Esum_2Esum @ A_27e @ A_27f ) ) @ V0P ) @ ( ap @ ( c_2Esum_2EINL @ A_27e @ A_27f ) @ V7x ) ) @ ( ap @ ( c_2Esum_2EINR @ A_27e @ A_27f ) @ V8y ) )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27e @ A_27f ) @ V9z ) )
% 0.65/1.33 <=> ( ( p @ V0P )
% 0.65/1.33 & ( V9z = V7x ) ) ) ) ) )
% 0.65/1.33 & ! [V10x: $i] :
% 0.65/1.33 ( ( mem @ V10x @ A_27g )
% 0.65/1.33 => ! [V11y: $i] :
% 0.65/1.33 ( ( mem @ V11y @ A_27h )
% 0.65/1.33 => ! [V12z: $i] :
% 0.65/1.33 ( ( mem @ V12z @ A_27h )
% 0.65/1.33 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Esum_2Esum @ A_27g @ A_27h ) ) @ V0P ) @ ( ap @ ( c_2Esum_2EINL @ A_27g @ A_27h ) @ V10x ) ) @ ( ap @ ( c_2Esum_2EINR @ A_27g @ A_27h ) @ V11y ) )
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27g @ A_27h ) @ V12z ) )
% 0.65/1.33 <=> ( ~ ( p @ V0P )
% 0.65/1.33 & ( V12z = V11y ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ENOT__ISL__ISR,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ~ ( p @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 <=> ( p @ ( ap @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ V0x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ENOT__ISR__ISL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.65/1.33 ( ( mem @ V0x @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ~ ( p @ ( ap @ ( c_2Esum_2EISR @ A_27a @ A_27b ) @ V0x ) )
% 0.65/1.33 <=> ( p @ ( ap @ ( c_2Esum_2EISL @ A_27a @ A_27b ) @ V0x ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(ax_thm_2Esum_2ESUM__ALL__def,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] :
% 0.65/1.33 ( ! [V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1Q: $i] :
% 0.65/1.33 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 0.65/1.33 => ! [V2x: $i] :
% 0.65/1.33 ( ( mem @ V2x @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ V0P ) @ V1Q ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V2x ) ) )
% 0.65/1.33 <=> ( p @ ( ap @ V0P @ V2x ) ) ) ) ) )
% 0.65/1.33 & ! [V3P: $i] :
% 0.65/1.33 ( ( mem @ V3P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V4Q: $i] :
% 0.65/1.33 ( ( mem @ V4Q @ ( arr @ A_27b @ bool ) )
% 0.65/1.33 => ! [V5y: $i] :
% 0.65/1.33 ( ( mem @ V5y @ A_27b )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ V3P ) @ V4Q ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V5y ) ) )
% 0.65/1.33 <=> ( p @ ( ap @ V4Q @ V5y ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ESUM__ALL__MONO,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0P: $i] :
% 0.65/1.33 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V1P_27: $i] :
% 0.65/1.33 ( ( mem @ V1P_27 @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V2Q: $i] :
% 0.65/1.33 ( ( mem @ V2Q @ ( arr @ A_27b @ bool ) )
% 0.65/1.33 => ! [V3Q_27: $i] :
% 0.65/1.33 ( ( mem @ V3Q_27 @ ( arr @ A_27b @ bool ) )
% 0.65/1.33 => ! [V4s: $i] :
% 0.65/1.33 ( ( mem @ V4s @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ( ( ! [V5x: $i] :
% 0.65/1.33 ( ( mem @ V5x @ A_27a )
% 0.65/1.33 => ( ( p @ ( ap @ V0P @ V5x ) )
% 0.65/1.33 => ( p @ ( ap @ V1P_27 @ V5x ) ) ) )
% 0.65/1.33 & ! [V6y: $i] :
% 0.65/1.33 ( ( mem @ V6y @ A_27b )
% 0.65/1.33 => ( ( p @ ( ap @ V2Q @ V6y ) )
% 0.65/1.33 => ( p @ ( ap @ V3Q_27 @ V6y ) ) ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ V0P ) @ V2Q ) @ V4s ) )
% 0.65/1.33 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ V1P_27 ) @ V3Q_27 ) @ V4s ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2ESUM__ALL__CONG,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,V0s: $i] :
% 0.65/1.33 ( ( mem @ V0s @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V1s_27: $i] :
% 0.65/1.33 ( ( mem @ V1s_27 @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 0.65/1.33 => ! [V2P: $i] :
% 0.65/1.33 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V3P_27: $i] :
% 0.65/1.33 ( ( mem @ V3P_27 @ ( arr @ A_27a @ bool ) )
% 0.65/1.33 => ! [V4Q: $i] :
% 0.65/1.33 ( ( mem @ V4Q @ ( arr @ A_27b @ bool ) )
% 0.65/1.33 => ! [V5Q_27: $i] :
% 0.65/1.33 ( ( mem @ V5Q_27 @ ( arr @ A_27b @ bool ) )
% 0.65/1.33 => ( ( ( V0s = V1s_27 )
% 0.65/1.33 & ! [V6a: $i] :
% 0.65/1.33 ( ( mem @ V6a @ A_27a )
% 0.65/1.33 => ( ( V1s_27
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V6a ) )
% 0.65/1.33 => ( ( p @ ( ap @ V2P @ V6a ) )
% 0.65/1.33 <=> ( p @ ( ap @ V3P_27 @ V6a ) ) ) ) )
% 0.65/1.33 & ! [V7b: $i] :
% 0.65/1.33 ( ( mem @ V7b @ A_27b )
% 0.65/1.33 => ( ( V1s_27
% 0.65/1.33 = ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V7b ) )
% 0.65/1.33 => ( ( p @ ( ap @ V4Q @ V7b ) )
% 0.65/1.33 <=> ( p @ ( ap @ V5Q_27 @ V7b ) ) ) ) ) )
% 0.65/1.33 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ V2P ) @ V4Q ) @ V0s ) )
% 0.65/1.33 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Esum_2ESUM__ALL @ A_27a @ A_27b ) @ V3P_27 ) @ V5Q_27 ) @ V1s_27 ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(conj_thm_2Esum_2Edatatype__sum,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del,A_27c: del,V0sum: $i] :
% 0.65/1.33 ( ( mem @ V0sum @ ( arr @ ( arr @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( arr @ ( arr @ A_27b @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ A_27c ) ) )
% 0.65/1.33 => ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ A_27c ) @ ( ap @ ( ap @ V0sum @ ( c_2Esum_2EINL @ A_27a @ A_27b ) ) @ ( c_2Esum_2EINR @ A_27a @ A_27b ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 %------------------------------------------------------------------------------
% 0.65/1.33 thf(tp_c_2Erelation_2ECR,type,
% 0.65/1.33 c_2Erelation_2ECR: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ECR,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ECR @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EEMPTY__REL,type,
% 0.65/1.33 c_2Erelation_2EEMPTY__REL: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EEMPTY__REL,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EEMPTY__REL @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EEQC,type,
% 0.65/1.33 c_2Erelation_2EEQC: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EEQC,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EEQC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EIDEM,type,
% 0.65/1.33 c_2Erelation_2EIDEM: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EIDEM,axiom,
% 0.65/1.33 ! [A_27z: del] : ( mem @ ( c_2Erelation_2EIDEM @ A_27z ) @ ( arr @ ( arr @ A_27z @ A_27z ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EINDUCTIVE__INVARIANT,type,
% 0.65/1.33 c_2Erelation_2EINDUCTIVE__INVARIANT: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EINDUCTIVE__INVARIANT,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2EINDUCTIVE__INVARIANT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EINDUCTIVE__INVARIANT__ON,type,
% 0.65/1.33 c_2Erelation_2EINDUCTIVE__INVARIANT__ON: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EINDUCTIVE__INVARIANT__ON,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2EINDUCTIVE__INVARIANT__ON @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EINVOL,type,
% 0.65/1.33 c_2Erelation_2EINVOL: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EINVOL,axiom,
% 0.65/1.33 ! [A_27z: del] : ( mem @ ( c_2Erelation_2EINVOL @ A_27z ) @ ( arr @ ( arr @ A_27z @ A_27z ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ELinearOrder,type,
% 0.65/1.33 c_2Erelation_2ELinearOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ELinearOrder,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ELinearOrder @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EO,type,
% 0.65/1.33 c_2Erelation_2EO: del > del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EO,axiom,
% 0.65/1.33 ! [A_27g: del,A_27h: del,A_27k: del] : ( mem @ ( c_2Erelation_2EO @ A_27g @ A_27h @ A_27k ) @ ( arr @ ( arr @ A_27h @ ( arr @ A_27k @ bool ) ) @ ( arr @ ( arr @ A_27g @ ( arr @ A_27h @ bool ) ) @ ( arr @ A_27g @ ( arr @ A_27k @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EOrder,type,
% 0.65/1.33 c_2Erelation_2EOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EOrder,axiom,
% 0.65/1.33 ! [A_27g: del] : ( mem @ ( c_2Erelation_2EOrder @ A_27g ) @ ( arr @ ( arr @ A_27g @ ( arr @ A_27g @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EPreOrder,type,
% 0.65/1.33 c_2Erelation_2EPreOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EPreOrder,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EPreOrder @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERC,type,
% 0.65/1.33 c_2Erelation_2ERC: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERC,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ERC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERCOMPL,type,
% 0.65/1.33 c_2Erelation_2ERCOMPL: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERCOMPL,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERCOMPL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERDOM,type,
% 0.65/1.33 c_2Erelation_2ERDOM: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERDOM,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERDOM__DELETE,type,
% 0.65/1.33 c_2Erelation_2ERDOM__DELETE: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERDOM__DELETE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERDOM__DELETE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERESTRICT,type,
% 0.65/1.33 c_2Erelation_2ERESTRICT: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERESTRICT,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERINTER,type,
% 0.65/1.33 c_2Erelation_2ERINTER: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERINTER,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERRANGE,type,
% 0.65/1.33 c_2Erelation_2ERRANGE: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERRANGE,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERRANGE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27b @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERRESTRICT,type,
% 0.65/1.33 c_2Erelation_2ERRESTRICT: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERRESTRICT,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERRESTRICT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERSUBSET,type,
% 0.65/1.33 c_2Erelation_2ERSUBSET: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERSUBSET,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERTC,type,
% 0.65/1.33 c_2Erelation_2ERTC: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERTC,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ERTC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERUNION,type,
% 0.65/1.33 c_2Erelation_2ERUNION: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERUNION,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ERUNIV,type,
% 0.65/1.33 c_2Erelation_2ERUNIV: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ERUNIV,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2ERUNIV @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ESC,type,
% 0.65/1.33 c_2Erelation_2ESC: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ESC,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ESC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ESN,type,
% 0.65/1.33 c_2Erelation_2ESN: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ESN,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ESN @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ESTRORD,type,
% 0.65/1.33 c_2Erelation_2ESTRORD: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ESTRORD,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ESTRORD @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EStrongLinearOrder,type,
% 0.65/1.33 c_2Erelation_2EStrongLinearOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EStrongLinearOrder,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EStrongLinearOrder @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EStrongOrder,type,
% 0.65/1.33 c_2Erelation_2EStrongOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EStrongOrder,axiom,
% 0.65/1.33 ! [A_27g: del] : ( mem @ ( c_2Erelation_2EStrongOrder @ A_27g ) @ ( arr @ ( arr @ A_27g @ ( arr @ A_27g @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2ETC,type,
% 0.65/1.33 c_2Erelation_2ETC: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2ETC,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2ETC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EWCR,type,
% 0.65/1.33 c_2Erelation_2EWCR: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EWCR,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EWCR @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EWF,type,
% 0.65/1.33 c_2Erelation_2EWF: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EWF,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EWF @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EWFP,type,
% 0.65/1.33 c_2Erelation_2EWFP: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EWFP,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EWFP @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EWFREC,type,
% 0.65/1.33 c_2Erelation_2EWFREC: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EWFREC,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ A_27b ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EWeakLinearOrder,type,
% 0.65/1.33 c_2Erelation_2EWeakLinearOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EWeakLinearOrder,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2EWeakLinearOrder @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2EWeakOrder,type,
% 0.65/1.33 c_2Erelation_2EWeakOrder: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2EWeakOrder,axiom,
% 0.65/1.33 ! [A_27g: del] : ( mem @ ( c_2Erelation_2EWeakOrder @ A_27g ) @ ( arr @ ( arr @ A_27g @ ( arr @ A_27g @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Eantisymmetric,type,
% 0.65/1.33 c_2Erelation_2Eantisymmetric: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Eantisymmetric,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Eapprox,type,
% 0.65/1.33 c_2Erelation_2Eapprox: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Eapprox,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2Eapprox @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Ediag,type,
% 0.65/1.33 c_2Erelation_2Ediag: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Ediag,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Ediag @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Ediamond,type,
% 0.65/1.33 c_2Erelation_2Ediamond: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Ediamond,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Ediamond @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Eequivalence,type,
% 0.65/1.33 c_2Erelation_2Eequivalence: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Eequivalence,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Eequivalence @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Einv,type,
% 0.65/1.33 c_2Erelation_2Einv: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Einv,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2Einv @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Einv__image,type,
% 0.65/1.33 c_2Erelation_2Einv__image: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Einv__image,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2Einv__image @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Eirreflexive,type,
% 0.65/1.33 c_2Erelation_2Eirreflexive: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Eirreflexive,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Enf,type,
% 0.65/1.33 c_2Erelation_2Enf: del > del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Enf,axiom,
% 0.65/1.33 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2Enf @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Ercdiamond,type,
% 0.65/1.33 c_2Erelation_2Ercdiamond: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Ercdiamond,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Ercdiamond @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Ereflexive,type,
% 0.65/1.33 c_2Erelation_2Ereflexive: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Ereflexive,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Esymmetric,type,
% 0.65/1.33 c_2Erelation_2Esymmetric: del > $i ).
% 0.65/1.33
% 0.65/1.33 thf(mem_c_2Erelation_2Esymmetric,axiom,
% 0.65/1.33 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Esymmetric @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.33
% 0.65/1.33 thf(tp_c_2Erelation_2Ethe__fun,type,
% 0.65/1.33 c_2Erelation_2Ethe__fun: del > del > $i ).
% 0.65/1.34
% 0.65/1.34 thf(mem_c_2Erelation_2Ethe__fun,axiom,
% 0.65/1.34 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erelation_2Ethe__fun @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(tp_c_2Erelation_2Etotal,type,
% 0.65/1.34 c_2Erelation_2Etotal: del > $i ).
% 0.65/1.34
% 0.65/1.34 thf(mem_c_2Erelation_2Etotal,axiom,
% 0.65/1.34 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Etotal @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(tp_c_2Erelation_2Etransitive,type,
% 0.65/1.34 c_2Erelation_2Etransitive: del > $i ).
% 0.65/1.34
% 0.65/1.34 thf(mem_c_2Erelation_2Etransitive,axiom,
% 0.65/1.34 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(tp_c_2Erelation_2Etrichotomous,type,
% 0.65/1.34 c_2Erelation_2Etrichotomous: del > $i ).
% 0.65/1.34
% 0.65/1.34 thf(mem_c_2Erelation_2Etrichotomous,axiom,
% 0.65/1.34 ! [A_27a: del] : ( mem @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Etransitive__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ! [V3z: $i] :
% 0.65/1.34 ( ( mem @ V3z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V3z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3z ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Ereflexive__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V1x ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Eirreflexive__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ~ ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V1x ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Esymmetric__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 <=> ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Eantisymmetric__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) ) )
% 0.65/1.34 => ( V1x = V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Eequivalence__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eequivalence @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 0.65/1.34 & ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 0.65/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Etotal__def,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etotal @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 | ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2Etrichotomous,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ V0R ) )
% 0.65/1.34 <=> ! [V1a: $i] :
% 0.65/1.34 ( ( mem @ V1a @ A_27a )
% 0.65/1.34 => ! [V2b: $i] :
% 0.65/1.34 ( ( mem @ V2b @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1a ) @ V2b ) )
% 0.65/1.34 | ( p @ ( ap @ ( ap @ V0R @ V2b ) @ V1a ) )
% 0.65/1.34 | ( V1a = V2b ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2ETC__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1a: $i] :
% 0.65/1.34 ( ( mem @ V1a @ A_27a )
% 0.65/1.34 => ! [V2b: $i] :
% 0.65/1.34 ( ( mem @ V2b @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1a ) @ V2b ) )
% 0.65/1.34 <=> ! [V3P: $i] :
% 0.65/1.34 ( ( mem @ V3P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V3P @ V4x ) @ V5y ) ) ) ) )
% 0.65/1.34 & ! [V6x: $i] :
% 0.65/1.34 ( ( mem @ V6x @ A_27a )
% 0.65/1.34 => ! [V7y: $i] :
% 0.65/1.34 ( ( mem @ V7y @ A_27a )
% 0.65/1.34 => ! [V8z: $i] :
% 0.65/1.34 ( ( mem @ V8z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V3P @ V6x ) @ V7y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V3P @ V7y ) @ V8z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V3P @ V6x ) @ V8z ) ) ) ) ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V3P @ V1a ) @ V2b ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2ERTC__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1a: $i] :
% 0.65/1.34 ( ( mem @ V1a @ A_27a )
% 0.65/1.34 => ! [V2b: $i] :
% 0.65/1.34 ( ( mem @ V2b @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1a ) @ V2b ) )
% 0.65/1.34 <=> ! [V3P: $i] :
% 0.65/1.34 ( ( mem @ V3P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V3P @ V4x ) @ V4x ) ) )
% 0.65/1.34 & ! [V5x: $i] :
% 0.65/1.34 ( ( mem @ V5x @ A_27a )
% 0.65/1.34 => ! [V6y: $i] :
% 0.65/1.34 ( ( mem @ V6y @ A_27a )
% 0.65/1.34 => ! [V7z: $i] :
% 0.65/1.34 ( ( mem @ V7z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V5x ) @ V6y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V3P @ V6y ) @ V7z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V3P @ V5x ) @ V7z ) ) ) ) ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V3P @ V1a ) @ V2b ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2ERC__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 <=> ( ( V1x = V2y )
% 0.65/1.34 | ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2ESC__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 | ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(ax_thm_2Erelation_2EEQC__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R )
% 0.65/1.34 = ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ESC__SYMMETRIC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__TRANSITIVE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__INDUCT,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V2x ) ) )
% 0.65/1.34 & ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1P @ V4y ) @ V5z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V3x ) @ V5z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V6x: $i] :
% 0.65/1.34 ( ( mem @ V6x @ A_27a )
% 0.65/1.34 => ! [V7y: $i] :
% 0.65/1.34 ( ( mem @ V7y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V6x ) @ V7y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V6x ) @ V7y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__RULES,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) )
% 0.65/1.34 & ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V4y ) @ V5z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V3x ) @ V5z ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__RULES,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V1x ) ) )
% 0.65/1.34 & ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ! [V4z: $i] :
% 0.65/1.34 ( ( mem @ V4z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3y ) @ V4z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2x ) @ V4z ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__REFL,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V1x ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__SINGLE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__STRONG__INDUCT,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V2x ) ) )
% 0.65/1.34 & ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V4y ) @ V5z ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1P @ V4y ) @ V5z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V3x ) @ V5z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V6x: $i] :
% 0.65/1.34 ( ( mem @ V6x @ A_27a )
% 0.65/1.34 => ! [V7y: $i] :
% 0.65/1.34 ( ( mem @ V7y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V6x ) @ V7y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V6x ) @ V7y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__RTC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 => ! [V3z: $i] :
% 0.65/1.34 ( ( mem @ V3z @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2y ) @ V3z ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V3z ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__TRANSITIVE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Etransitive__RTC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__REFLEXIVE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Ereflexive__RTC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__REFLEXIVE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Ereflexive__RC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__lifts__monotonicities,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1f: $i] :
% 0.65/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ V2x ) ) @ ( ap @ V1f @ V3y ) ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ ( ap @ V1f @ V4x ) ) @ ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__MONOTONE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1Q: $i] :
% 0.65/1.34 ( ( mem @ V1Q @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1Q @ V4x ) @ V5y ) ) ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V1Q ) @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__lifts__invariants,axiom,
% 0.65/1.34 ! [A_27a: del,V0P: $i] :
% 0.65/1.34 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ! [V1R: $i] :
% 0.65/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1R @ V2x ) @ V3y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V0P @ V3y ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V0P @ V4x ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V1R ) @ V4x ) @ V5y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V0P @ V5y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__lifts__equalities,axiom,
% 0.65/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1f: $i] :
% 0.65/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( ( ap @ V1f @ V2x )
% 0.65/1.34 = ( ap @ V1f @ V3y ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 => ( ( ap @ V1f @ V4x )
% 0.65/1.34 = ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ESC__lifts__monotonicities,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1f: $i] :
% 0.65/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ V2x ) ) @ ( ap @ V1f @ V3y ) ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) @ ( ap @ V1f @ V4x ) ) @ ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ESC__lifts__equalities,axiom,
% 0.65/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1f: $i] :
% 0.65/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( ( ap @ V1f @ V2x )
% 0.65/1.34 = ( ap @ V1f @ V3y ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 => ( ( ap @ V1f @ V4x )
% 0.65/1.34 = ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ESC__MONOTONE,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1Q: $i] :
% 0.65/1.34 ( ( mem @ V1Q @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1Q @ V4x ) @ V5y ) ) ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V1Q ) @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Esymmetric__RC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) )
% 0.65/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Eantisymmetric__RC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) )
% 0.65/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Etransitive__RC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) )
% 0.65/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__SUBSET,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__SUBSET,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__SUBSET,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERC__RTC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__INDUCT,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ! [V6z: $i] :
% 0.65/1.34 ( ( mem @ V6z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1P @ V5y ) @ V6z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V6z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V7u: $i] :
% 0.65/1.34 ( ( mem @ V7u @ A_27a )
% 0.65/1.34 => ! [V8v: $i] :
% 0.65/1.34 ( ( mem @ V8v @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V7u ) @ V8v ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7u ) @ V8v ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__INDUCT__LEFT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ! [V6z: $i] :
% 0.65/1.34 ( ( mem @ V6z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1P @ V5y ) @ V6z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V6z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V7x: $i] :
% 0.65/1.34 ( ( mem @ V7x @ A_27a )
% 0.65/1.34 => ! [V8y: $i] :
% 0.65/1.34 ( ( mem @ V8y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V7x ) @ V8y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__INDUCT__RIGHT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ! [V6z: $i] :
% 0.65/1.34 ( ( mem @ V6z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V5y ) @ V6z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V6z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V7x: $i] :
% 0.65/1.34 ( ( mem @ V7x @ A_27a )
% 0.65/1.34 => ! [V8y: $i] :
% 0.65/1.34 ( ( mem @ V8y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V7x ) @ V8y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__STRONG__INDUCT,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ! [V6z: $i] :
% 0.65/1.34 ( ( mem @ V6z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1P @ V5y ) @ V6z ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V5y ) @ V6z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V6z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V7u: $i] :
% 0.65/1.34 ( ( mem @ V7u @ A_27a )
% 0.65/1.34 => ! [V8v: $i] :
% 0.65/1.34 ( ( mem @ V8v @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V7u ) @ V8v ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7u ) @ V8v ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ! [V6z: $i] :
% 0.65/1.34 ( ( mem @ V6z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1P @ V5y ) @ V6z ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V5y ) @ V6z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V6z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V7u: $i] :
% 0.65/1.34 ( ( mem @ V7u @ A_27a )
% 0.65/1.34 => ! [V8v: $i] :
% 0.65/1.34 ( ( mem @ V8v @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V7u ) @ V8v ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7u ) @ V8v ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ! [V6z: $i] :
% 0.65/1.34 ( ( mem @ V6z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V5y ) @ V6z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V6z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V7u: $i] :
% 0.65/1.34 ( ( mem @ V7u @ A_27a )
% 0.65/1.34 => ! [V8v: $i] :
% 0.65/1.34 ( ( mem @ V8v @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V7u ) @ V8v ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7u ) @ V8v ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__INDUCT__ALT__LEFT,axiom,
% 0.65/1.34 ! [A_27a: del,V0b: $i] :
% 0.65/1.34 ( ( mem @ V0b @ A_27a )
% 0.65/1.34 => ! [V1R: $i] :
% 0.65/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V2Q: $i] :
% 0.65/1.34 ( ( mem @ V2Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ( ( ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V1R @ V3x ) @ V0b ) )
% 0.65/1.34 => ( p @ ( ap @ V2Q @ V3x ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1R @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ V2Q @ V5y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V2Q @ V4x ) ) ) ) ) )
% 0.65/1.34 => ! [V6a: $i] :
% 0.65/1.34 ( ( mem @ V6a @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V1R ) @ V6a ) @ V0b ) )
% 0.65/1.34 => ( p @ ( ap @ V2Q @ V6a ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__INDUCT__ALT__RIGHT,axiom,
% 0.65/1.34 ! [A_27a: del,V0a: $i] :
% 0.65/1.34 ( ( mem @ V0a @ A_27a )
% 0.65/1.34 => ! [V1R: $i] :
% 0.65/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V2Q: $i] :
% 0.65/1.34 ( ( mem @ V2Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ( ( ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V1R @ V0a ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ V2Q @ V3y ) ) ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V2Q @ V4x ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1R @ V4x ) @ V5y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V2Q @ V5y ) ) ) ) ) )
% 0.65/1.34 => ! [V6b: $i] :
% 0.65/1.34 ( ( mem @ V6b @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V1R ) @ V0a ) @ V6b ) )
% 0.65/1.34 => ( p @ ( ap @ V2Q @ V6b ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__lifts__monotonicities,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1f: $i] :
% 0.65/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ V2x ) ) @ ( ap @ V1f @ V3y ) ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ ( ap @ V1f @ V4x ) ) @ ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__lifts__invariants,axiom,
% 0.65/1.34 ! [A_27a: del,V0P: $i] :
% 0.65/1.34 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ! [V1R: $i] :
% 0.65/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V0P @ V2x ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V1R @ V2x ) @ V3y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V0P @ V3y ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V0P @ V4x ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V1R ) @ V4x ) @ V5y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V0P @ V5y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__lifts__equalities,axiom,
% 0.65/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1f: $i] :
% 0.65/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.34 => ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 0.65/1.34 => ( ( ap @ V1f @ V2x )
% 0.65/1.34 = ( ap @ V1f @ V3y ) ) ) ) )
% 0.65/1.34 => ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 0.65/1.34 => ( ( ap @ V1f @ V4x )
% 0.65/1.34 = ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__lifts__transitive__relations,axiom,
% 0.65/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1Q: $i] :
% 0.65/1.34 ( ( mem @ V1Q @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 0.65/1.34 => ! [V2f: $i] :
% 0.65/1.34 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 0.65/1.34 => ( ( ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1Q @ ( ap @ V2f @ V3x ) ) @ ( ap @ V2f @ V4y ) ) ) ) ) )
% 0.65/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27b ) @ V1Q ) ) )
% 0.65/1.34 => ! [V5x: $i] :
% 0.65/1.34 ( ( mem @ V5x @ A_27a )
% 0.65/1.34 => ! [V6y: $i] :
% 0.65/1.34 ( ( mem @ V6y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V5x ) @ V6y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1Q @ ( ap @ V2f @ V5x ) ) @ ( ap @ V2f @ V6y ) ) ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__implies__one__step,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 & ( V1x != V2y ) )
% 0.65/1.34 => ? [V3z: $i] :
% 0.65/1.34 ( ( mem @ V3z @ A_27a )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3z ) )
% 0.65/1.34 & ( V1x != V3z ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__RTC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__TC__RC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 0.65/1.34 | ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ETC__RC__EQNS,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) )
% 0.65/1.34 = ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) )
% 0.65/1.34 & ( ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 0.65/1.34 = ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__ALT__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1a: $i] :
% 0.65/1.34 ( ( mem @ V1a @ A_27a )
% 0.65/1.34 => ! [V2b: $i] :
% 0.65/1.34 ( ( mem @ V2b @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1a ) @ V2b ) )
% 0.65/1.34 <=> ! [V3Q: $i] :
% 0.65/1.34 ( ( mem @ V3Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ( ( ( p @ ( ap @ V3Q @ V2b ) )
% 0.65/1.34 & ! [V4x: $i] :
% 0.65/1.34 ( ( mem @ V4x @ A_27a )
% 0.65/1.34 => ! [V5y: $i] :
% 0.65/1.34 ( ( mem @ V5y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 0.65/1.34 & ( p @ ( ap @ V3Q @ V5y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V3Q @ V4x ) ) ) ) ) )
% 0.65/1.34 => ( p @ ( ap @ V3Q @ V1a ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__ALT__INDUCT,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1Q: $i] :
% 0.65/1.34 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ! [V2b: $i] :
% 0.65/1.34 ( ( mem @ V2b @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V1Q @ V2b ) )
% 0.65/1.34 & ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ V1Q @ V4y ) ) )
% 0.65/1.34 => ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) )
% 0.65/1.34 => ! [V5x: $i] :
% 0.65/1.34 ( ( mem @ V5x @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V5x ) @ V2b ) )
% 0.65/1.34 => ( p @ ( ap @ V1Q @ V5x ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__ALT__RIGHT__DEF,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1a: $i] :
% 0.65/1.34 ( ( mem @ V1a @ A_27a )
% 0.65/1.34 => ! [V2b: $i] :
% 0.65/1.34 ( ( mem @ V2b @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1a ) @ V2b ) )
% 0.65/1.34 <=> ! [V3Q: $i] :
% 0.65/1.34 ( ( mem @ V3Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ( ( ( p @ ( ap @ V3Q @ V1a ) )
% 0.65/1.34 & ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V3Q @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V4y ) @ V5z ) ) )
% 0.65/1.34 => ( p @ ( ap @ V3Q @ V5z ) ) ) ) ) )
% 0.65/1.34 => ( p @ ( ap @ V3Q @ V2b ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1Q: $i] :
% 0.65/1.34 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.65/1.34 => ! [V2a: $i] :
% 0.65/1.34 ( ( mem @ V2a @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V1Q @ V2a ) )
% 0.65/1.34 & ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ! [V4z: $i] :
% 0.65/1.34 ( ( mem @ V4z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ V1Q @ V3y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V4z ) ) )
% 0.65/1.34 => ( p @ ( ap @ V1Q @ V4z ) ) ) ) ) )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2a ) @ V5z ) )
% 0.65/1.34 => ( p @ ( ap @ V1Q @ V5z ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__INDUCT__RIGHT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V2x ) ) )
% 0.65/1.34 & ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V4y ) @ V5z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V3x ) @ V5z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V6x: $i] :
% 0.65/1.34 ( ( mem @ V6x @ A_27a )
% 0.65/1.34 => ! [V7y: $i] :
% 0.65/1.34 ( ( mem @ V7y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V6x ) @ V7y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V6x ) @ V7y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__RULES__RIGHT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V1x ) ) )
% 0.65/1.34 & ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ! [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 => ! [V4z: $i] :
% 0.65/1.34 ( ( mem @ V4z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V4z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2x ) @ V4z ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1P: $i] :
% 0.65/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( ! [V2x: $i] :
% 0.65/1.34 ( ( mem @ V2x @ A_27a )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V2x ) ) )
% 0.65/1.34 & ! [V3x: $i] :
% 0.65/1.34 ( ( mem @ V3x @ A_27a )
% 0.65/1.34 => ! [V4y: $i] :
% 0.65/1.34 ( ( mem @ V4y @ A_27a )
% 0.65/1.34 => ! [V5z: $i] :
% 0.65/1.34 ( ( mem @ V5z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3x ) @ V4y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V4y ) @ V5z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V3x ) @ V5z ) ) ) ) ) ) )
% 0.65/1.34 => ! [V6x: $i] :
% 0.65/1.34 ( ( mem @ V6x @ A_27a )
% 0.65/1.34 => ! [V7y: $i] :
% 0.65/1.34 ( ( mem @ V7y @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V6x ) @ V7y ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ V1P @ V6x ) @ V7y ) ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2EEXTEND__RTC__TC,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2y: $i] :
% 0.65/1.34 ( ( mem @ V2y @ A_27a )
% 0.65/1.34 => ! [V3z: $i] :
% 0.65/1.34 ( ( mem @ V3z @ A_27a )
% 0.65/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2y ) @ V3z ) ) )
% 0.65/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V3z ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2EEXTEND__RTC__TC__EQN,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ! [V1x: $i] :
% 0.65/1.34 ( ( mem @ V1x @ A_27a )
% 0.65/1.34 => ! [V2z: $i] :
% 0.65/1.34 ( ( mem @ V2z @ A_27a )
% 0.65/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2z ) )
% 0.65/1.34 <=> ? [V3y: $i] :
% 0.65/1.34 ( ( mem @ V3y @ A_27a )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3y ) )
% 0.65/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3y ) @ V2z ) ) ) ) ) ) ) ).
% 0.65/1.34
% 0.65/1.34 thf(conj_thm_2Erelation_2Ereflexive__RC__identity,axiom,
% 0.65/1.34 ! [A_27a: del,V0R: $i] :
% 0.65/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 0.65/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 0.65/1.34 => ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__SC__identity,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etransitive__TC__identity,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERC__IDEM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ESC__IDEM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETC__IDEM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERC__MOVES__OUT,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__TC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ereflexive__TC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__EQUIVALENCE,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eequivalence @ A_27a ) @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__IDEM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__IDEM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__CASES1,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ( ( V1x = V2y )
% 1.17/1.34 | ? [V3u: $i] :
% 1.17/1.34 ( ( mem @ V3u @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3u ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3u ) @ V2y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__CASES__TC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ( ( V1x = V2y )
% 1.17/1.34 | ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__CASES2,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ( ( V1x = V2y )
% 1.17/1.34 | ? [V3u: $i] :
% 1.17/1.34 ( ( mem @ V3u @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V3u ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V3u ) @ V2y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__CASES__RTC__TWICE,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ? [V3u: $i] :
% 1.17/1.34 ( ( mem @ V3u @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V3u ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3u ) @ V2y ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETC__CASES1__E,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2z: $i] :
% 1.17/1.34 ( ( mem @ V2z @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2z ) )
% 1.17/1.34 | ? [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V3y ) @ V2z ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETC__CASES1,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2z: $i] :
% 1.17/1.34 ( ( mem @ V2z @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2z ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2z ) )
% 1.17/1.34 | ? [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V3y ) @ V2z ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETC__CASES2__E,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2z: $i] :
% 1.17/1.34 ( ( mem @ V2z @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2z ) )
% 1.17/1.34 | ? [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V3y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V2z ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETC__CASES2,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2z: $i] :
% 1.17/1.34 ( ( mem @ V2z @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2z ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2z ) )
% 1.17/1.34 | ? [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V3y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V2z ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETC__MONOTONE,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1Q: $i] :
% 1.17/1.34 ( ( mem @ V1Q @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1Q @ V4x ) @ V5y ) ) ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V1Q ) @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__MONOTONE,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1Q: $i] :
% 1.17/1.34 ( ( mem @ V1Q @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1Q @ V4x ) @ V5y ) ) ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V1Q ) @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__INDUCTION,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.34 & ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V4x ) ) )
% 1.17/1.34 & ! [V5x: $i] :
% 1.17/1.34 ( ( mem @ V5x @ A_27a )
% 1.17/1.34 => ! [V6y: $i] :
% 1.17/1.34 ( ( mem @ V6y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V1P @ V5x ) @ V6y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V6y ) @ V5x ) ) ) ) )
% 1.17/1.34 & ! [V7x: $i] :
% 1.17/1.34 ( ( mem @ V7x @ A_27a )
% 1.17/1.34 => ! [V8y: $i] :
% 1.17/1.34 ( ( mem @ V8y @ A_27a )
% 1.17/1.34 => ! [V9z: $i] :
% 1.17/1.34 ( ( mem @ V9z @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V7x ) @ V8y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1P @ V8y ) @ V9z ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7x ) @ V9z ) ) ) ) ) ) )
% 1.17/1.34 => ! [V10x: $i] :
% 1.17/1.34 ( ( mem @ V10x @ A_27a )
% 1.17/1.34 => ! [V11y: $i] :
% 1.17/1.34 ( ( mem @ V11y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V10x ) @ V11y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V10x ) @ V11y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__REFL,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V1x ) @ V1x ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__R,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__SYM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V2y ) @ V1x ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__TRANS,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ! [V3z: $i] :
% 1.17/1.34 ( ( mem @ V3z @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V2y ) @ V3z ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V1x ) @ V3z ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etransitive__EQC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__EQC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ereflexive__EQC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__MOVES__IN,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ESTRONG__EQC__INDUCTION,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.34 & ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ V4x ) ) )
% 1.17/1.34 & ! [V5x: $i] :
% 1.17/1.34 ( ( mem @ V5x @ A_27a )
% 1.17/1.34 => ! [V6y: $i] :
% 1.17/1.34 ( ( mem @ V6y @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V5x ) @ V6y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1P @ V5x ) @ V6y ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V6y ) @ V5x ) ) ) ) )
% 1.17/1.34 & ! [V7x: $i] :
% 1.17/1.34 ( ( mem @ V7x @ A_27a )
% 1.17/1.34 => ! [V8y: $i] :
% 1.17/1.34 ( ( mem @ V8y @ A_27a )
% 1.17/1.34 => ! [V9z: $i] :
% 1.17/1.34 ( ( mem @ V9z @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ V1P @ V7x ) @ V8y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1P @ V8y ) @ V9z ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V7x ) @ V8y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V8y ) @ V9z ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V7x ) @ V9z ) ) ) ) ) ) )
% 1.17/1.34 => ! [V10x: $i] :
% 1.17/1.34 ( ( mem @ V10x @ A_27a )
% 1.17/1.34 => ! [V11y: $i] :
% 1.17/1.34 ( ( mem @ V11y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V10x ) @ V11y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V10x ) @ V11y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EALT__equivalence,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eequivalence @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ( ( ap @ V0R @ V1x )
% 1.17/1.34 = ( ap @ V0R @ V2y ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEQC__MONOTONE,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1R_27: $i] :
% 1.17/1.34 ( ( mem @ V1R_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4x ) @ V5y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1R_27 @ V4x ) @ V5y ) ) ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V1R_27 ) @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__EQC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__lifts__monotonicities,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ V2x ) ) @ ( ap @ V1f @ V3y ) ) ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ ( ap @ V1f @ V4x ) ) @ ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1Q: $i] :
% 1.17/1.34 ( ( mem @ V1Q @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2f: $i] :
% 1.17/1.34 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ( ( ! [V3x: $i] :
% 1.17/1.34 ( ( mem @ V3x @ A_27a )
% 1.17/1.34 => ! [V4y: $i] :
% 1.17/1.34 ( ( mem @ V4y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1Q @ ( ap @ V2f @ V3x ) ) @ ( ap @ V2f @ V4y ) ) ) ) ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27b ) @ V1Q ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27b ) @ V1Q ) ) )
% 1.17/1.34 => ! [V5x: $i] :
% 1.17/1.34 ( ( mem @ V5x @ A_27a )
% 1.17/1.34 => ! [V6y: $i] :
% 1.17/1.34 ( ( mem @ V6y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V5x ) @ V6y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1Q @ ( ap @ V2f @ V5x ) ) @ ( ap @ V2f @ V6y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__lifts__equalities,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 1.17/1.34 => ( ( ap @ V1f @ V2x )
% 1.17/1.34 = ( ap @ V1f @ V3y ) ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V4x ) @ V5y ) )
% 1.17/1.34 => ( ( ap @ V1f @ V4x )
% 1.17/1.34 = ( ap @ V1f @ V5y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERTC__lifts__invariants,axiom,
% 1.17/1.34 ! [A_27a: del,V0P: $i] :
% 1.17/1.34 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ V0P @ V2x ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1R @ V2x ) @ V3y ) ) )
% 1.17/1.34 => ( p @ ( ap @ V0P @ V3y ) ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ V0P @ V4x ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V1R ) @ V4x ) @ V5y ) ) )
% 1.17/1.34 => ( p @ ( ap @ V0P @ V5y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EWF__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1B: $i] :
% 1.17/1.34 ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ? [V2w: $i] :
% 1.17/1.34 ( ( mem @ V2w @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ V1B @ V2w ) ) )
% 1.17/1.34 => ? [V3min: $i] :
% 1.17/1.34 ( ( mem @ V3min @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ V1B @ V3min ) )
% 1.17/1.34 & ! [V4b: $i] :
% 1.17/1.34 ( ( mem @ V4b @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4b ) @ V3min ) )
% 1.17/1.34 => ~ ( p @ ( ap @ V1B @ V4b ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__INDUCTION__THM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V2x ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V3y ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V2x ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V4x ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EINDUCTION__WF__THM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V2x ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V3y ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V2x ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V4x ) ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__EQ__INDUCTION__THM,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V2x ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V3y ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V2x ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V4x ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__NOT__REFL,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 1.17/1.34 => ( V1x != V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__irreflexive,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EEMPTY__REL__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,V0x: $i] :
% 1.17/1.34 ( ( mem @ V0x @ A_27a )
% 1.17/1.34 => ! [V1y: $i] :
% 1.17/1.34 ( ( mem @ V1y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2EEMPTY__REL @ A_27a ) @ V0x ) @ V1y ) )
% 1.17/1.34 <=> $false ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__EMPTY__REL,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( c_2Erelation_2EEMPTY__REL @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__SUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 & ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V1P @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) ) ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V1P ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__TC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__TC__EQN,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__noloops,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 => ( V1x != V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__antisymmetric,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Einv__image__def,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27a @ A_27b ) @ V0R ) @ V1f )
% 1.17/1.34 = ( lam @ A_27a
% 1.17/1.34 @ ^ [V2x: $i] :
% 1.17/1.34 ( lam @ A_27a
% 1.17/1.34 @ ^ [V3y: $i] : ( ap @ ( ap @ V0R @ ( ap @ V1f @ V2x ) ) @ ( ap @ V1f @ V3y ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__image__thm,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27a @ A_27b ) @ V0R ) @ V1f ) @ V2x ) @ V3y ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ V2x ) ) @ ( ap @ V1f @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__inv__image,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27b ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27a @ A_27b ) @ V0R ) @ V1f ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etotal__inv__image,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etotal @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etotal @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27b @ A_27a ) @ V0R ) @ V1f ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ereflexive__inv__image,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27b @ A_27a ) @ V0R ) @ V1f ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__inv__image,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27b @ A_27a ) @ V0R ) @ V1f ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etransitive__inv__image,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1f: $i] :
% 1.17/1.34 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2Einv__image @ A_27b @ A_27a ) @ V0R ) @ V1f ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERESTRICT__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ V0f ) @ V1R ) @ V2x )
% 1.17/1.34 = ( lam @ A_27a
% 1.17/1.34 @ ^ [V3y: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ V1R @ V3y ) @ V2x ) ) @ ( ap @ V0f @ V3y ) ) @ ( c_2Ebool_2EARB @ A_27b ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERESTRICT__LEMMA,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ! [V3z: $i] :
% 1.17/1.34 ( ( mem @ V3z @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V1R @ V2y ) @ V3z ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ V0f ) @ V1R ) @ V3z ) @ V2y )
% 1.17/1.34 = ( ap @ V0f @ V2y ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Eapprox__def,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1M: $i] :
% 1.17/1.34 ( ( mem @ V1M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3f: $i] :
% 1.17/1.34 ( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2Eapprox @ A_27a @ A_27b ) @ V0R ) @ V1M ) @ V2x ) @ V3f ) )
% 1.17/1.34 <=> ( V3f
% 1.17/1.34 = ( ap
% 1.17/1.34 @ ( ap
% 1.17/1.34 @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b )
% 1.17/1.34 @ ( lam @ A_27a
% 1.17/1.34 @ ^ [V4y: $i] : ( ap @ ( ap @ V1M @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ V3f ) @ V0R ) @ V4y ) ) @ V4y ) ) )
% 1.17/1.34 @ V0R )
% 1.17/1.34 @ V2x ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Ethe__fun__def,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1M: $i] :
% 1.17/1.34 ( ( mem @ V1M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ( ap @ ( ap @ ( ap @ ( c_2Erelation_2Ethe__fun @ A_27a @ A_27b ) @ V0R ) @ V1M ) @ V2x )
% 1.17/1.34 = ( ap @ ( c_2Emin_2E_40 @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 @ ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.34 @ ^ [V3f: $i] : ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2Eapprox @ A_27a @ A_27b ) @ V0R ) @ V1M ) @ V2x ) @ V3f ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EWFREC__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1M: $i] :
% 1.17/1.34 ( ( mem @ V1M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V0R ) @ V1M )
% 1.17/1.34 = ( lam @ A_27a
% 1.17/1.34 @ ^ [V2x: $i] :
% 1.17/1.34 ( ap
% 1.17/1.34 @ ( ap @ V1M
% 1.17/1.34 @ ( ap
% 1.17/1.34 @ ( ap
% 1.17/1.34 @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b )
% 1.17/1.34 @ ( ap
% 1.17/1.34 @ ( ap @ ( ap @ ( c_2Erelation_2Ethe__fun @ A_27a @ A_27b ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) )
% 1.17/1.34 @ ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.34 @ ^ [V3f: $i] :
% 1.17/1.34 ( lam @ A_27a
% 1.17/1.34 @ ^ [V4v: $i] : ( ap @ ( ap @ V1M @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ V3f ) @ V0R ) @ V4v ) ) @ V4v ) ) ) )
% 1.17/1.34 @ V2x ) )
% 1.17/1.34 @ V0R )
% 1.17/1.34 @ V2x ) )
% 1.17/1.34 @ V2x ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWFREC__THM,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1M: $i] :
% 1.17/1.34 ( ( mem @ V1M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V0R ) @ V1M ) @ V2x )
% 1.17/1.34 = ( ap @ ( ap @ V1M @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V0R ) @ V1M ) ) @ V0R ) @ V2x ) ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWFREC__COROLLARY,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0M: $i] :
% 1.17/1.34 ( ( mem @ V0M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2f: $i] :
% 1.17/1.34 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ( ( V2f
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V1R ) @ V0M ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V1R ) )
% 1.17/1.34 => ! [V3x: $i] :
% 1.17/1.34 ( ( mem @ V3x @ A_27a )
% 1.17/1.34 => ( ( ap @ V2f @ V3x )
% 1.17/1.34 = ( ap @ ( ap @ V0M @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ V2f ) @ V1R ) @ V3x ) ) @ V3x ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__RECURSION__THM,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 => ! [V1M: $i] :
% 1.17/1.34 ( ( mem @ V1M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ( p
% 1.17/1.34 @ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 @ ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.34 @ ^ [V2f: $i] :
% 1.17/1.34 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 1.17/1.34 @ ( lam @ A_27a
% 1.17/1.34 @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ ( ap @ ( ap @ V1M @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERESTRICT @ A_27a @ A_27b ) @ V2f ) @ V0R ) @ V3x ) ) @ V3x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EWFP__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1a: $i] :
% 1.17/1.34 ( ( mem @ V1a @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V1a ) )
% 1.17/1.34 <=> ! [V2P: $i] :
% 1.17/1.34 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ! [V3x: $i] :
% 1.17/1.34 ( ( mem @ V3x @ A_27a )
% 1.17/1.34 => ( ! [V4y: $i] :
% 1.17/1.34 ( ( mem @ V4y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V4y ) @ V3x ) )
% 1.17/1.34 => ( p @ ( ap @ V2P @ V4y ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V2P @ V3x ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V2P @ V1a ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWFP__RULES,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ( ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V2y ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V1x ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWFP__INDUCT,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V3y ) @ V2x ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V3y ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V2x ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V4x ) )
% 1.17/1.34 => ( p @ ( ap @ V1P @ V4x ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWFP__CASES,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V1x ) )
% 1.17/1.34 <=> ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V2y ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWFP__STRONG__INDUCT,axiom,
% 1.17/1.34 ! [A_27a: del,V0P: $i] :
% 1.17/1.34 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V1R ) @ V2x ) )
% 1.17/1.34 & ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V1R @ V3y ) @ V2x ) )
% 1.17/1.34 => ( p @ ( ap @ V0P @ V3y ) ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ V0P @ V2x ) ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V1R ) @ V4x ) )
% 1.17/1.34 => ( p @ ( ap @ V0P @ V4x ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWF__EQ__WFP,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2EWFP @ A_27a ) @ V0R ) @ V1x ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2M: $i] :
% 1.17/1.34 ( ( mem @ V2M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EINDUCTIVE__INVARIANT @ A_27a @ A_27b ) @ V0R ) @ V1P ) @ V2M ) )
% 1.17/1.34 <=> ! [V3f: $i] :
% 1.17/1.34 ( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( ! [V5y: $i] :
% 1.17/1.34 ( ( mem @ V5y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V5y ) @ V4x ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V5y ) @ ( ap @ V3f @ V5y ) ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ ( ap @ ( ap @ V2M @ V3f ) @ V4x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1D: $i] :
% 1.17/1.34 ( ( mem @ V1D @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V2P: $i] :
% 1.17/1.34 ( ( mem @ V2P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V3M: $i] :
% 1.17/1.34 ( ( mem @ V3M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EINDUCTIVE__INVARIANT__ON @ A_27a @ A_27b ) @ V0R ) @ V1D ) @ V2P ) @ V3M ) )
% 1.17/1.34 <=> ! [V4f: $i] :
% 1.17/1.34 ( ( mem @ V4f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V5x: $i] :
% 1.17/1.34 ( ( mem @ V5x @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ V1D @ V5x ) )
% 1.17/1.34 & ! [V6y: $i] :
% 1.17/1.34 ( ( mem @ V6y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ V1D @ V6y ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V6y ) @ V5x ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V2P @ V6y ) @ ( ap @ V4f @ V6y ) ) ) ) ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V2P @ V5x ) @ ( ap @ ( ap @ V3M @ V4f ) @ V5x ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2M: $i] :
% 1.17/1.34 ( ( mem @ V2M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EINDUCTIVE__INVARIANT @ A_27a @ A_27b ) @ V0R ) @ V1P ) @ V2M ) ) )
% 1.17/1.34 => ! [V3x: $i] :
% 1.17/1.34 ( ( mem @ V3x @ A_27a )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V3x ) @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V0R ) @ V2M ) @ V3x ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2P: $i] :
% 1.17/1.34 ( ( mem @ V2P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V3M: $i] :
% 1.17/1.34 ( ( mem @ V3M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( ( ( V0f
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V1R ) @ V3M ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V1R ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EINDUCTIVE__INVARIANT @ A_27a @ A_27b ) @ V1R ) @ V2P ) @ V3M ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V2P @ V4x ) @ ( ap @ V0f @ V4x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1P: $i] :
% 1.17/1.34 ( ( mem @ V1P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2M: $i] :
% 1.17/1.34 ( ( mem @ V2M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ! [V3D: $i] :
% 1.17/1.34 ( ( mem @ V3D @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V4x: $i] :
% 1.17/1.34 ( ( mem @ V4x @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EINDUCTIVE__INVARIANT__ON @ A_27a @ A_27b ) @ V0R ) @ V3D ) @ V1P ) @ V2M ) )
% 1.17/1.34 & ( p @ ( ap @ V3D @ V4x ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1P @ V4x ) @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V0R ) @ V2M ) @ V4x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V2D: $i] :
% 1.17/1.34 ( ( mem @ V2D @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V3P: $i] :
% 1.17/1.34 ( ( mem @ V3P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V4M: $i] :
% 1.17/1.34 ( ( mem @ V4M @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.34 => ! [V5x: $i] :
% 1.17/1.34 ( ( mem @ V5x @ A_27a )
% 1.17/1.34 => ( ( ( V0f
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ A_27a @ A_27b ) @ V1R ) @ V4M ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V1R ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EINDUCTIVE__INVARIANT__ON @ A_27a @ A_27b ) @ V1R ) @ V2D ) @ V3P ) @ V4M ) )
% 1.17/1.34 & ( p @ ( ap @ V2D @ V5x ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V3P @ V5x ) @ ( ap @ V0f @ V5x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Einv__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27b )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27b ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V1x ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__inv,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27b @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27b ) @ V0R ) )
% 1.17/1.34 = V0R ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__RC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__SC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__TC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__EQC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__MOVES__OUT,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = V0R )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2ESC @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) )
% 1.17/1.34 & ( ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2EEQC @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ereflexive__inv,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eirreflexive__inv,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__inv,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eantisymmetric__inv,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etransitive__inv,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__inv__identity,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eequivalence__inv__identity,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Eequivalence @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EINVOL__DEF,axiom,
% 1.17/1.34 ! [A_27z: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27z @ A_27z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EINVOL @ A_27z ) @ V0f ) )
% 1.17/1.34 <=> ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27z @ A_27z @ A_27z ) @ V0f ) @ V0f )
% 1.17/1.34 = ( c_2Ecombin_2EI @ A_27z ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EINVOL,axiom,
% 1.17/1.34 ! [A_27z: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27z @ A_27z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EINVOL @ A_27z ) @ V0f ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27z )
% 1.17/1.34 => ( ( ap @ V0f @ ( ap @ V0f @ V1x ) )
% 1.17/1.34 = V1x ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EINVOL__ONE__ONE,axiom,
% 1.17/1.34 ! [A_27z: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27z @ A_27z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EINVOL @ A_27z ) @ V0f ) )
% 1.17/1.34 => ! [V1a: $i] :
% 1.17/1.34 ( ( mem @ V1a @ A_27z )
% 1.17/1.34 => ! [V2b: $i] :
% 1.17/1.34 ( ( mem @ V2b @ A_27z )
% 1.17/1.34 => ( ( ( ap @ V0f @ V1a )
% 1.17/1.34 = ( ap @ V0f @ V2b ) )
% 1.17/1.34 <=> ( V1a = V2b ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EINVOL__ONE__ENO,axiom,
% 1.17/1.34 ! [A_27z: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27z @ A_27z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EINVOL @ A_27z ) @ V0f ) )
% 1.17/1.34 => ! [V1a: $i] :
% 1.17/1.34 ( ( mem @ V1a @ A_27z )
% 1.17/1.34 => ! [V2b: $i] :
% 1.17/1.34 ( ( mem @ V2b @ A_27z )
% 1.17/1.34 => ( ( ( ap @ V0f @ V1a )
% 1.17/1.34 = V2b )
% 1.17/1.34 <=> ( V1a
% 1.17/1.34 = ( ap @ V0f @ V2b ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ENOT__INVOL,axiom,
% 1.17/1.34 p @ ( ap @ ( c_2Erelation_2EINVOL @ bool ) @ c_2Ebool_2E_7E ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EIDEM__DEF,axiom,
% 1.17/1.34 ! [A_27z: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27z @ A_27z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EIDEM @ A_27z ) @ V0f ) )
% 1.17/1.34 <=> ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27z @ A_27z @ A_27z ) @ V0f ) @ V0f )
% 1.17/1.34 = V0f ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIDEM,axiom,
% 1.17/1.34 ! [A_27z: del,V0f: $i] :
% 1.17/1.34 ( ( mem @ V0f @ ( arr @ A_27z @ A_27z ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EIDEM @ A_27z ) @ V0f ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27z )
% 1.17/1.34 => ( ( ap @ V0f @ ( ap @ V0f @ V1x ) )
% 1.17/1.34 = ( ap @ V0f @ V1x ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__INVOL,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EINVOL @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EO__DEF,axiom,
% 1.17/1.34 ! [A_27g: del,A_27h: del,A_27k: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27h @ ( arr @ A_27k @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27g @ ( arr @ A_27h @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27g )
% 1.17/1.34 => ! [V3z: $i] :
% 1.17/1.34 ( ( mem @ V3z @ A_27k )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27g @ A_27h @ A_27k ) @ V0R1 ) @ V1R2 ) @ V2x ) @ V3z ) )
% 1.17/1.34 <=> ? [V4y: $i] :
% 1.17/1.34 ( ( mem @ V4y @ A_27h )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1R2 @ V2x ) @ V4y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R1 @ V4y ) @ V3z ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__O,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,A_27c: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R_27: $i] :
% 1.17/1.34 ( ( mem @ V1R_27 @ ( arr @ A_27c @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27c @ A_27a @ A_27b ) @ V0R ) @ V1R_27 ) )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27b @ A_27a @ A_27c ) @ ( ap @ ( c_2Erelation_2Einv @ A_27c @ A_27a ) @ V1R_27 ) ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27b ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERSUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) )
% 1.17/1.34 <=> ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R1 @ V2x ) @ V3y ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ V1R2 @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eirreflexive__RSUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ V1R2 ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ V0R1 ) @ V1R2 ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ V0R1 ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERUNION,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) @ V2x ) @ V3y ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R1 @ V2x ) @ V3y ) )
% 1.17/1.34 | ( p @ ( ap @ ( ap @ V1R2 @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERUNION__COMM,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V1R2 ) @ V0R1 ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERUNION__ASSOC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2R3: $i] :
% 1.17/1.34 ( ( mem @ V2R3 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V0R1 ) @ ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V1R2 ) @ V2R3 ) )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) ) @ V2R3 ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERINTER,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) @ V2x ) @ V3y ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R1 @ V2x ) @ V3y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1R2 @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERINTER__COMM,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ V1R2 ) @ V0R1 ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERINTER__ASSOC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2R3: $i] :
% 1.17/1.34 ( ( mem @ V2R3 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ V0R1 ) @ ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ V1R2 ) @ V2R3 ) )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) ) @ V2R3 ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eantisymmetric__RINTER,axiom,
% 1.17/1.34 ! [A_27a: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V0R1 ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27a ) @ V0R1 ) @ V1R2 ) ) ) )
% 1.17/1.34 & ( ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V1R2 ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27a ) @ V0R1 ) @ V1R2 ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etransitive__RINTER,axiom,
% 1.17/1.34 ! [A_27a: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R1 ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V1R2 ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27a ) @ V0R1 ) @ V1R2 ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERCOMPL,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERCOMPL @ A_27a @ A_27b ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ~ ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ereflexive__Id__RSUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ ( c_2Emin_2E_3D @ A_27a ) ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Esymmetric__inv__RSUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etransitive__O__RSUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27a @ A_27a @ A_27a ) @ V0R ) @ V0R ) ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EPreOrder,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EPreOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EOrder,axiom,
% 1.17/1.34 ! [A_27g: del,V0Z: $i] :
% 1.17/1.34 ( ( mem @ V0Z @ ( arr @ A_27g @ ( arr @ A_27g @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EOrder @ A_27g ) @ V0Z ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27g ) @ V0Z ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27g ) @ V0Z ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EWeakOrder,axiom,
% 1.17/1.34 ! [A_27g: del,V0Z: $i] :
% 1.17/1.34 ( ( mem @ V0Z @ ( arr @ A_27g @ ( arr @ A_27g @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27g ) @ V0Z ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27g ) @ V0Z ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27g ) @ V0Z ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27g ) @ V0Z ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EStrongOrder,axiom,
% 1.17/1.34 ! [A_27g: del,V0Z: $i] :
% 1.17/1.34 ( ( mem @ V0Z @ ( arr @ A_27g @ ( arr @ A_27g @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EStrongOrder @ A_27g ) @ V0Z ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27g ) @ V0Z ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27g ) @ V0Z ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eirrefl__trans__implies__antisym,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EStrongOrd__Ord,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EStrongOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2EOrder @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWeakOrd__Ord,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2EOrder @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWeakOrder__EQ,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 => ! [V1y: $i] :
% 1.17/1.34 ( ( mem @ V1y @ A_27a )
% 1.17/1.34 => ! [V2z: $i] :
% 1.17/1.34 ( ( mem @ V2z @ A_27a )
% 1.17/1.34 => ( ( V1y = V2z )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V1y ) @ V2z ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V2z ) @ V1y ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERSUBSET__ANTISYM,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V1R2 ) @ V0R1 ) ) )
% 1.17/1.34 => ( V0R1 = V1R2 ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERSUBSET__antisymmetric,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( p @ ( ap @ ( c_2Erelation_2Eantisymmetric @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERSUBSET__WeakOrder,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EEqIsBothRSUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0y: $i] :
% 1.17/1.34 ( ( mem @ V0y @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1z: $i] :
% 1.17/1.34 ( ( mem @ V1z @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( V0y = V1z )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V0y ) @ V1z ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V1z ) @ V0y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ESTRORD,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V1a: $i] :
% 1.17/1.34 ( ( mem @ V1a @ A_27a )
% 1.17/1.34 => ! [V2b: $i] :
% 1.17/1.34 ( ( mem @ V2b @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ESTRORD @ A_27a ) @ V0R ) @ V1a ) @ V2b ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V1a ) @ V2b ) )
% 1.17/1.34 & ( V1a != V2b ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ESTRORD__AND__NOT__Id,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ESTRORD @ A_27a ) @ V0R )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2ERINTER @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Erelation_2ERCOMPL @ A_27a @ A_27a ) @ ( c_2Emin_2E_3D @ A_27a ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERC__OR__Id,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27a ) @ V0R ) @ ( c_2Emin_2E_3D @ A_27a ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERC__Weak,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ESTRORD__Strong,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2EStrongOrder @ A_27a ) @ ( ap @ ( c_2Erelation_2ESTRORD @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ESTRORD__RC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EStrongOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ESTRORD @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERC__STRORD,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ ( ap @ ( c_2Erelation_2ESTRORD @ A_27a ) @ V0R ) )
% 1.17/1.34 = V0R ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIDEM__STRORD,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EIDEM @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( c_2Erelation_2ESTRORD @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIDEM__RC,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EIDEM @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( c_2Erelation_2ERC @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIDEM__SC,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EIDEM @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( c_2Erelation_2ESC @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIDEM__TC,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EIDEM @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( c_2Erelation_2ETC @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIDEM__RTC,axiom,
% 1.17/1.34 ! [A_27a: del] : ( p @ ( ap @ ( c_2Erelation_2EIDEM @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( c_2Erelation_2ERTC @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etrichotomous__STRORD,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ ( ap @ ( c_2Erelation_2ESTRORD @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Etrichotomous__RC,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ELinearOrder,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2ELinearOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2EOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EStrongLinearOrder,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EStrongLinearOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2EStrongOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EWeakLinearOrder,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWeakLinearOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2Etrichotomous @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EWeakLinearOrder__dichotomy,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWeakLinearOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( c_2Erelation_2EWeakOrder @ A_27a ) @ V0R ) )
% 1.17/1.34 & ! [V1a: $i] :
% 1.17/1.34 ( ( mem @ V1a @ A_27a )
% 1.17/1.34 => ! [V2b: $i] :
% 1.17/1.34 ( ( mem @ V2b @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ V0R @ V1a ) @ V2b ) )
% 1.17/1.34 | ( p @ ( ap @ ( ap @ V0R @ V2b ) @ V1a ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Ediag__def,axiom,
% 1.17/1.34 ! [A_27a: del,V0A: $i] :
% 1.17/1.34 ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2Ediag @ A_27a ) @ V0A ) @ V1x ) @ V2y ) )
% 1.17/1.34 <=> ( ( V1x = V2y )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0A ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EO__ASSOC,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27c @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27d @ ( arr @ A_27c @ bool ) ) )
% 1.17/1.34 => ! [V2R3: $i] :
% 1.17/1.34 ( ( mem @ V2R3 @ ( arr @ A_27a @ ( arr @ A_27d @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27a @ A_27c @ A_27b ) @ V0R1 ) @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27a @ A_27d @ A_27c ) @ V1R2 ) @ V2R3 ) )
% 1.17/1.34 = ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27a @ A_27d @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27d @ A_27c @ A_27b ) @ V0R1 ) @ V1R2 ) ) @ V2R3 ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EId__O,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27a @ A_27b @ A_27b ) @ ( c_2Emin_2E_3D @ A_27b ) ) @ V0R )
% 1.17/1.34 = V0R ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EO__Id,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27a @ A_27a @ A_27b ) @ V0R ) @ ( c_2Emin_2E_3D @ A_27a ) )
% 1.17/1.34 = V0R ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EO__MONO,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,A_27c: del,V0R1: $i] :
% 1.17/1.34 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1R2: $i] :
% 1.17/1.34 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2S1: $i] :
% 1.17/1.34 ( ( mem @ V2S1 @ ( arr @ A_27c @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ! [V3S2: $i] :
% 1.17/1.34 ( ( mem @ V3S2 @ ( arr @ A_27c @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27c @ A_27a ) @ V2S1 ) @ V3S2 ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27c @ A_27a @ A_27b ) @ V0R1 ) @ V2S1 ) ) @ ( ap @ ( ap @ ( c_2Erelation_2EO @ A_27c @ A_27a @ A_27b ) @ V1R2 ) @ V3S2 ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__Id,axiom,
% 1.17/1.34 ! [A_27a: del] :
% 1.17/1.34 ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( c_2Emin_2E_3D @ A_27a ) )
% 1.17/1.34 = ( c_2Emin_2E_3D @ A_27a ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Einv__diag,axiom,
% 1.17/1.34 ! [A_27a: del,V0A: $i] :
% 1.17/1.34 ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ ( ap @ ( c_2Erelation_2Ediag @ A_27a ) @ V0A ) )
% 1.17/1.34 = ( ap @ ( c_2Erelation_2Ediag @ A_27a ) @ V0A ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERDOM__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ V0R ) @ V1x ) )
% 1.17/1.34 <=> ? [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27b )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIN__RDOM,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.34 ( ( mem @ V0x @ A_27a )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ V1R ) ) )
% 1.17/1.34 <=> ? [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27b )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1R @ V0x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERRANGE,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1y: $i] :
% 1.17/1.34 ( ( mem @ V1y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERRANGE @ A_27a @ A_27b ) @ V0R ) @ V1y ) )
% 1.17/1.34 <=> ? [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V1y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIN__RRANGE,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0y: $i] :
% 1.17/1.34 ( ( mem @ V0y @ A_27a )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0y ) @ ( ap @ ( c_2Erelation_2ERRANGE @ A_27b @ A_27a ) @ V1R ) ) )
% 1.17/1.34 <=> ? [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27b )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V1R @ V2x ) @ V0y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIN__RDOM__RUNION,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.34 ( ( mem @ V0x @ A_27a )
% 1.17/1.34 => ! [V1R1: $i] :
% 1.17/1.34 ( ( mem @ V1R1 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2R2: $i] :
% 1.17/1.34 ( ( mem @ V2R2 @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27b ) @ V1R1 ) @ V2R2 ) ) ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ V1R1 ) ) )
% 1.17/1.34 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ V2R2 ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERUNIV,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.34 ( ( mem @ V0x @ A_27a )
% 1.17/1.34 => ! [V1y: $i] :
% 1.17/1.34 ( ( mem @ V1y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERUNIV @ A_27a @ A_27b ) @ V0x ) @ V1y ) )
% 1.17/1.34 <=> $true ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ERUNIV__SUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ ( c_2Erelation_2ERUNIV @ A_27a @ A_27b ) ) @ V0R ) )
% 1.17/1.34 <=> ( V0R
% 1.17/1.34 = ( c_2Erelation_2ERUNIV @ A_27a @ A_27b ) ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27b ) @ V0R ) @ ( c_2Erelation_2ERUNIV @ A_27a @ A_27b ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EREMPTY__SUBSET,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ ( c_2Erelation_2EEMPTY__REL @ A_27a ) ) @ V0R ) )
% 1.17/1.34 & ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ V0R ) @ ( c_2Erelation_2EEMPTY__REL @ A_27a ) ) )
% 1.17/1.34 <=> ( V0R
% 1.17/1.34 = ( c_2Erelation_2EEMPTY__REL @ A_27a ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERRESTRICT__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1s: $i] :
% 1.17/1.34 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ! [V2x: $i] :
% 1.17/1.34 ( ( mem @ V2x @ A_27a )
% 1.17/1.34 => ! [V3y: $i] :
% 1.17/1.34 ( ( mem @ V3y @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERRESTRICT @ A_27a @ A_27b ) @ V0R ) @ V1s ) @ V2x ) @ V3y ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIN__RDOM__RRESTRICT,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.34 ( ( mem @ V0x @ A_27a )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2s: $i] :
% 1.17/1.34 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2ERRESTRICT @ A_27a @ A_27b ) @ V1R ) @ V2s ) ) ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ V1R ) ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ERDOM__DELETE__DEF,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2u: $i] :
% 1.17/1.34 ( ( mem @ V2u @ A_27a )
% 1.17/1.34 => ! [V3v: $i] :
% 1.17/1.34 ( ( mem @ V3v @ A_27b )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERDOM__DELETE @ A_27a @ A_27b ) @ V0R ) @ V1x ) @ V2u ) @ V3v ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ V0R @ V2u ) @ V3v ) )
% 1.17/1.34 & ( V2u != V1x ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2EIN__RDOM__DELETE,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.34 ( ( mem @ V0x @ A_27a )
% 1.17/1.34 => ! [V1R: $i] :
% 1.17/1.34 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V2k: $i] :
% 1.17/1.34 ( ( mem @ V2k @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Erelation_2ERDOM__DELETE @ A_27a @ A_27b ) @ V1R ) @ V2k ) ) ) )
% 1.17/1.34 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Erelation_2ERDOM @ A_27a @ A_27b ) @ V1R ) ) )
% 1.17/1.34 & ( V0x != V2k ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Ediamond__def,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ! [V3z: $i] :
% 1.17/1.34 ( ( mem @ V3z @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3z ) ) )
% 1.17/1.34 => ? [V4u: $i] :
% 1.17/1.34 ( ( mem @ V4u @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V2y ) @ V4u ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V3z ) @ V4u ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Ercdiamond__def,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ercdiamond @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ! [V3z: $i] :
% 1.17/1.34 ( ( mem @ V3z @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3z ) ) )
% 1.17/1.34 => ? [V4u: $i] :
% 1.17/1.34 ( ( mem @ V4u @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V2y ) @ V4u ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) @ V3z ) @ V4u ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ECR__def,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2ECR @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2EWCR__def,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2EWCR @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27a )
% 1.17/1.34 => ! [V3z: $i] :
% 1.17/1.34 ( ( mem @ V3z @ A_27a )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V3z ) ) )
% 1.17/1.34 => ? [V4u: $i] :
% 1.17/1.34 ( ( mem @ V4u @ A_27a )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2y ) @ V4u ) )
% 1.17/1.34 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3z ) @ V4u ) ) ) ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2ESN__def,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2ESN @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(ax_thm_2Erelation_2Enf__def,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.34 => ! [V1x: $i] :
% 1.17/1.34 ( ( mem @ V1x @ A_27a )
% 1.17/1.34 => ( ( p @ ( ap @ ( ap @ ( c_2Erelation_2Enf @ A_27a @ A_27b ) @ V0R ) @ V1x ) )
% 1.17/1.34 <=> ! [V2y: $i] :
% 1.17/1.34 ( ( mem @ V2y @ A_27b )
% 1.17/1.34 => ~ ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ercdiamond__diamond,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ercdiamond @ A_27a ) @ V0R ) )
% 1.17/1.34 <=> ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ediamond__RC__diamond,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ ( ap @ ( c_2Erelation_2ERC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Ediamond__TC__diamond,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2Eestablish__CR,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2Ercdiamond @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2ECR @ A_27a ) @ V0R ) ) )
% 1.17/1.34 & ( ( p @ ( ap @ ( c_2Erelation_2Ediamond @ A_27a ) @ V0R ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2ECR @ A_27a ) @ V0R ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(conj_thm_2Erelation_2ENewmans__lemma,axiom,
% 1.17/1.34 ! [A_27a: del,V0R: $i] :
% 1.17/1.34 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.34 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWCR @ A_27a ) @ V0R ) )
% 1.17/1.34 & ( p @ ( ap @ ( c_2Erelation_2ESN @ A_27a ) @ V0R ) ) )
% 1.17/1.34 => ( p @ ( ap @ ( c_2Erelation_2ECR @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 %------------------------------------------------------------------------------
% 1.17/1.34 %------------------------------------------------------------------------------
% 1.17/1.34 thf(tp_ty_2Eoption_2Eoption,type,
% 1.17/1.34 ty_2Eoption_2Eoption: del > del ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EIS__NONE,type,
% 1.17/1.34 c_2Eoption_2EIS__NONE: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EIS__NONE,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EIS__SOME,type,
% 1.17/1.34 c_2Eoption_2EIS__SOME: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EIS__SOME,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2ENONE,type,
% 1.17/1.34 c_2Eoption_2ENONE: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2ENONE,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2ENONE @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__ALL,type,
% 1.17/1.34 c_2Eoption_2EOPTION__ALL: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__ALL,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__APPLY,type,
% 1.17/1.34 c_2Eoption_2EOPTION__APPLY: del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__APPLY,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__APPLY @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( arr @ A_27b @ A_27a ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__BIND,type,
% 1.17/1.34 c_2Eoption_2EOPTION__BIND: del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__BIND,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__CHOICE,type,
% 1.17/1.34 c_2Eoption_2EOPTION__CHOICE: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__CHOICE,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__CHOICE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(stp_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,type,
% 1.17/1.34 tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone: $tType ).
% 1.17/1.34
% 1.17/1.34 thf(stp_inj_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,type,
% 1.17/1.34 inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone: tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone > $i ).
% 1.17/1.34
% 1.17/1.34 thf(stp_surj_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,type,
% 1.17/1.34 surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone: $i > tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone ).
% 1.17/1.34
% 1.17/1.34 thf(stp_inj_surj_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,axiom,
% 1.17/1.34 ! [X: tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone] :
% 1.17/1.34 ( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ X ) )
% 1.17/1.34 = X ) ).
% 1.17/1.34
% 1.17/1.34 thf(stp_inj_mem_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,axiom,
% 1.17/1.34 ! [X: tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ X ) @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(stp_iso_mem_c_ty_2Eoption_2Eoption_ty_2Eone_2Eone,axiom,
% 1.17/1.34 ! [X: $i] :
% 1.17/1.34 ( ( mem @ X @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) )
% 1.17/1.34 => ( X
% 1.17/1.34 = ( inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ X ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__GUARD,type,
% 1.17/1.34 c_2Eoption_2EOPTION__GUARD: $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__GUARD,axiom,
% 1.17/1.34 mem @ c_2Eoption_2EOPTION__GUARD @ ( arr @ bool @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__IGNORE__BIND,type,
% 1.17/1.34 c_2Eoption_2EOPTION__IGNORE__BIND: del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__IGNORE__BIND,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__JOIN,type,
% 1.17/1.34 c_2Eoption_2EOPTION__JOIN: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__JOIN,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__MAP,type,
% 1.17/1.34 c_2Eoption_2EOPTION__MAP: del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__MAP,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__MAP2,type,
% 1.17/1.34 c_2Eoption_2EOPTION__MAP2: del > del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__MAP2,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27c ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTION__MCOMP,type,
% 1.17/1.34 c_2Eoption_2EOPTION__MCOMP: del > del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTION__MCOMP,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Eoption_2EOPTION__MCOMP @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( arr @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2EOPTREL,type,
% 1.17/1.34 c_2Eoption_2EOPTREL: del > del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2EOPTREL,axiom,
% 1.17/1.34 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2ESOME,type,
% 1.17/1.34 c_2Eoption_2ESOME: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2ESOME,axiom,
% 1.17/1.34 ! [A_27a: del] : ( mem @ ( c_2Eoption_2ESOME @ A_27a ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
% 1.17/1.34
% 1.17/1.34 thf(tp_c_2Eoption_2ETHE,type,
% 1.17/1.34 c_2Eoption_2ETHE: del > $i ).
% 1.17/1.34
% 1.17/1.34 thf(mem_c_2Eoption_2ETHE,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eoption_2ETHE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27a ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eoption_2Eoption__ABS,type,
% 1.17/1.35 c_2Eoption_2Eoption__ABS: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eoption_2Eoption__ABS,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eoption_2Eoption__CASE,type,
% 1.17/1.35 c_2Eoption_2Eoption__CASE: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eoption_2Eoption__CASE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27b ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eoption_2Eoption__REP,type,
% 1.17/1.35 c_2Eoption_2Eoption__REP: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eoption_2Eoption__REP,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eoption_2Eoption__REP @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eoption_2Esome,type,
% 1.17/1.35 c_2Eoption_2Esome: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eoption_2Esome,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eoption_2Esome @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2Eoption__TY__DEF,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ? [V0rep: $i] :
% 1.17/1.35 ( ( mem @ V0rep @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) ) )
% 1.17/1.35 & ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 @ ( lam @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone )
% 1.17/1.35 @ ^ [V1x: $i] : c_2Ebool_2ET ) )
% 1.17/1.35 @ V0rep ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2Eoption__REP__ABS__DEF,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ! [V0a: $i] :
% 1.17/1.35 ( ( mem @ V0a @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( ap @ ( c_2Eoption_2Eoption__REP @ A_27a ) @ V0a ) )
% 1.17/1.35 = V0a ) )
% 1.17/1.35 & ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone ) )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( lam @ ( ty_2Esum_2Esum @ A_27a @ ty_2Eone_2Eone )
% 1.17/1.35 @ ^ [V2x: $i] : c_2Ebool_2ET )
% 1.17/1.35 @ V1r ) )
% 1.17/1.35 <=> ( ( ap @ ( c_2Eoption_2Eoption__REP @ A_27a ) @ ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ V1r ) )
% 1.17/1.35 = V1r ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2ESOME__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ ty_2Eone_2Eone ) @ V0x ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2ENONE__DEF,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ( c_2Eoption_2ENONE @ A_27a )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2Eoption__ABS @ A_27a ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ ty_2Eone_2Eone ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__Axiom,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0e: $i] :
% 1.17/1.35 ( ( mem @ V0e @ A_27b )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ? [V2fn: $i] :
% 1.17/1.35 ( ( mem @ V2fn @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27b ) )
% 1.17/1.35 & ( ( ap @ V2fn @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = V0e )
% 1.17/1.35 & ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( ap @ V2fn @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) )
% 1.17/1.35 = ( ap @ V1f @ V3x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__induction,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 & ! [V1a: $i] :
% 1.17/1.35 ( ( mem @ V1a @ A_27a )
% 1.17/1.35 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1a ) ) ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__nchotomy,axiom,
% 1.17/1.35 ! [A_27a: del,V0opt: $i] :
% 1.17/1.35 ( ( mem @ V0opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( V0opt
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 | ? [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 & ( V0opt
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2Eoption__case__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] :
% 1.17/1.35 ( ! [V0v: $i] :
% 1.17/1.35 ( ( mem @ V0v @ A_27b )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V0v ) @ V1f )
% 1.17/1.35 = V0v ) ) )
% 1.17/1.35 & ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ! [V3v: $i] :
% 1.17/1.35 ( ( mem @ V3v @ A_27b )
% 1.17/1.35 => ! [V4f: $i] :
% 1.17/1.35 ( ( mem @ V4f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) @ V3v ) @ V4f )
% 1.17/1.35 = ( ap @ V4f @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EFORALL__OPTION,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
% 1.17/1.35 => ( ! [V1opt: $i] :
% 1.17/1.35 ( ( mem @ V1opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( p @ ( ap @ V0P @ V1opt ) ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 & ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EEXISTS__OPTION,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
% 1.17/1.35 => ( ? [V1opt: $i] :
% 1.17/1.35 ( ( mem @ V1opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 & ( p @ ( ap @ V0P @ V1opt ) ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 | ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2ESOME__11,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1y ) )
% 1.17/1.35 <=> ( V0x = V1y ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2ENOT__NONE__SOME,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ( ( c_2Eoption_2ENONE @ A_27a )
% 1.17/1.35 != ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2ENOT__SOME__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
% 1.17/1.35 != ( c_2Eoption_2ENONE @ A_27a ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__MAP__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] :
% 1.17/1.35 ( ! [V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ ( ap @ V0f @ V1x ) ) ) ) )
% 1.17/1.35 & ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V2f ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EIS__SOME__DEF,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ! [V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) )
% 1.17/1.35 <=> $true ) )
% 1.17/1.35 & ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 <=> $false ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EIS__NONE__DEF,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ! [V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) )
% 1.17/1.35 <=> $false ) )
% 1.17/1.35 & ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 <=> $true ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2ETHE__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) )
% 1.17/1.35 = V0x ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27c ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1x ) @ V2y )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27c ) @ V2y ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ ( ap @ ( c_2Eoption_2ETHE @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27c ) @ V2y ) ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__JOIN__DEF,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ! [V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0x ) )
% 1.17/1.35 = V0x ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP2__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27b )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27c )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) )
% 1.17/1.35 & ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EIS__SOME__EXISTS,axiom,
% 1.17/1.35 ! [A_27a: del,V0opt: $i] :
% 1.17/1.35 ( ( mem @ V0opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V0opt ) )
% 1.17/1.35 <=> ? [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 & ( V0opt
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EIS__NONE__EQ__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V0x ) )
% 1.17/1.35 <=> ( V0x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2ENOT__IS__SOME__EQ__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V0x ) )
% 1.17/1.35 <=> ( V0x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__case__ID,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0x ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 1.17/1.35 = V0x ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__case__SOME__ID,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0x ) @ V0x ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 1.17/1.35 = V0x ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__CLAUSES,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0e: $i] :
% 1.17/1.35 ( ( mem @ V0e @ A_27b )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V2e: $i] :
% 1.17/1.35 ( ( mem @ V2e @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ! [V4y: $i] :
% 1.17/1.35 ( ( mem @ V4y @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4y ) )
% 1.17/1.35 <=> ( V3x = V4y ) ) ) )
% 1.17/1.35 & ! [V5x: $i] :
% 1.17/1.35 ( ( mem @ V5x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5x ) )
% 1.17/1.35 = V5x ) )
% 1.17/1.35 & ! [V6x: $i] :
% 1.17/1.35 ( ( mem @ V6x @ A_27a )
% 1.17/1.35 => ( ( c_2Eoption_2ENONE @ A_27a )
% 1.17/1.35 != ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) ) )
% 1.17/1.35 & ! [V7x: $i] :
% 1.17/1.35 ( ( mem @ V7x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V7x )
% 1.17/1.35 != ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 & ! [V8x: $i] :
% 1.17/1.35 ( ( mem @ V8x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V8x ) ) )
% 1.17/1.35 <=> $true ) )
% 1.17/1.35 & ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 <=> $false )
% 1.17/1.35 & ! [V9x: $i] :
% 1.17/1.35 ( ( mem @ V9x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V9x ) )
% 1.17/1.35 <=> ( V9x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) )
% 1.17/1.35 & ! [V10x: $i] :
% 1.17/1.35 ( ( mem @ V10x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V10x ) )
% 1.17/1.35 <=> ( V10x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) )
% 1.17/1.35 & ! [V11x: $i] :
% 1.17/1.35 ( ( mem @ V11x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V11x ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V11x ) )
% 1.17/1.35 = V11x ) ) )
% 1.17/1.35 & ! [V12x: $i] :
% 1.17/1.35 ( ( mem @ V12x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V12x ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 1.17/1.35 = V12x ) )
% 1.17/1.35 & ! [V13x: $i] :
% 1.17/1.35 ( ( mem @ V13x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V13x ) @ V13x ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 1.17/1.35 = V13x ) )
% 1.17/1.35 & ! [V14x: $i] :
% 1.17/1.35 ( ( mem @ V14x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V14x ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V14x ) @ V0e ) @ V1f )
% 1.17/1.35 = V0e ) ) )
% 1.17/1.35 & ! [V15x: $i] :
% 1.17/1.35 ( ( mem @ V15x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V15x ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V15x ) @ V0e ) @ V1f )
% 1.17/1.35 = ( ap @ V1f @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V15x ) ) ) ) )
% 1.17/1.35 & ! [V16x: $i] :
% 1.17/1.35 ( ( mem @ V16x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V16x ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V16x ) @ V2e ) @ ( c_2Eoption_2ESOME @ A_27a ) )
% 1.17/1.35 = V16x ) ) )
% 1.17/1.35 & ! [V17v: $i] :
% 1.17/1.35 ( ( mem @ V17v @ A_27b )
% 1.17/1.35 => ! [V18f: $i] :
% 1.17/1.35 ( ( mem @ V18f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V17v ) @ V18f )
% 1.17/1.35 = V17v ) ) )
% 1.17/1.35 & ! [V19x: $i] :
% 1.17/1.35 ( ( mem @ V19x @ A_27a )
% 1.17/1.35 => ! [V20v: $i] :
% 1.17/1.35 ( ( mem @ V20v @ A_27b )
% 1.17/1.35 => ! [V21f: $i] :
% 1.17/1.35 ( ( mem @ V21f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V19x ) ) @ V20v ) @ V21f )
% 1.17/1.35 = ( ap @ V21f @ V19x ) ) ) ) )
% 1.17/1.35 & ! [V22f: $i] :
% 1.17/1.35 ( ( mem @ V22f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V23x: $i] :
% 1.17/1.35 ( ( mem @ V23x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V22f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V23x ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ ( ap @ V22f @ V23x ) ) ) ) )
% 1.17/1.35 & ! [V24f: $i] :
% 1.17/1.35 ( ( mem @ V24f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V24f ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) )
% 1.17/1.35 & ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ! [V25x: $i] :
% 1.17/1.35 ( ( mem @ V25x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V25x ) )
% 1.17/1.35 = V25x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__case__compute,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1e: $i] :
% 1.17/1.35 ( ( mem @ V1e @ A_27b )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V0x ) @ V1e ) @ V2f )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V0x ) ) @ ( ap @ V2f @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V0x ) ) ) @ V1e ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EIF__EQUALS__OPTION,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ bool )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27a )
% 1.17/1.35 => ( ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 <=> ~ ( p @ V0P ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 <=> ( p @ V0P ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) )
% 1.17/1.35 <=> ( ( p @ V0P )
% 1.17/1.35 & ( V1x = V2y ) ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) )
% 1.17/1.35 <=> ( ~ ( p @ V0P )
% 1.17/1.35 & ( V1x = V2y ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EIF__NONE__EQUALS__OPTION,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ bool )
% 1.17/1.35 => ! [V1X: $i] :
% 1.17/1.35 ( ( mem @ V1X @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ V1X ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 <=> ( ( p @ V0P )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V1X ) ) ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V1X )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V1X ) )
% 1.17/1.35 => ( p @ V0P ) ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ V1X ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) )
% 1.17/1.35 <=> ( ( p @ V0P )
% 1.17/1.35 & ( V1X
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0P ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V1X )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) )
% 1.17/1.35 <=> ( ~ ( p @ V0P )
% 1.17/1.35 & ( V1X
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP__EQ__SOME,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V0f ) @ V1x )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V2y ) )
% 1.17/1.35 <=> ? [V3z: $i] :
% 1.17/1.35 ( ( mem @ V3z @ A_27a )
% 1.17/1.35 & ( V1x
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3z ) )
% 1.17/1.35 & ( V2y
% 1.17/1.35 = ( ap @ V0f @ V3z ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V0f ) @ V1x )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) )
% 1.17/1.35 <=> ( V1x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a ) @ V0f ) @ V1x )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 <=> ( V1x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) )
% 1.17/1.35 & ( ( ( c_2Eoption_2ENONE @ A_27a )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a ) @ V0f ) @ V1x ) )
% 1.17/1.35 <=> ( V1x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP__COMPOSE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27c @ A_27b ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27c @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27c ) @ V1g ) @ V2x ) )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1g ) ) @ V2x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP__CONG,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0opt1: $i] :
% 1.17/1.35 ( ( mem @ V0opt1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1opt2: $i] :
% 1.17/1.35 ( ( mem @ V1opt2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2f1: $i] :
% 1.17/1.35 ( ( mem @ V2f1 @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V3f2: $i] :
% 1.17/1.35 ( ( mem @ V3f2 @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ( V0opt1 = V1opt2 )
% 1.17/1.35 & ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 => ( ( V1opt2
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4x ) )
% 1.17/1.35 => ( ( ap @ V2f1 @ V4x )
% 1.17/1.35 = ( ap @ V3f2 @ V4x ) ) ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V2f1 ) @ V0opt1 )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V3f2 ) @ V1opt2 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EIS__SOME__MAP,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V0f ) @ V1x ) ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__JOIN__EQ__SOME,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ V0x )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1y ) )
% 1.17/1.35 <=> ( V0x
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1y ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP2__SOME,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1o1: $i] :
% 1.17/1.35 ( ( mem @ V1o1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2o2: $i] :
% 1.17/1.35 ( ( mem @ V2o2 @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ! [V3v: $i] :
% 1.17/1.35 ( ( mem @ V3v @ A_27c )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27c @ A_27a @ A_27b ) @ V0f ) @ V1o1 ) @ V2o2 )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V3v ) )
% 1.17/1.35 <=> ? [V4x1: $i] :
% 1.17/1.35 ( ( mem @ V4x1 @ A_27a )
% 1.17/1.35 & ? [V5x2: $i] :
% 1.17/1.35 ( ( mem @ V5x2 @ A_27b )
% 1.17/1.35 & ( V1o1
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4x1 ) )
% 1.17/1.35 & ( V2o2
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V5x2 ) )
% 1.17/1.35 & ( V3v
% 1.17/1.35 = ( ap @ ( ap @ V0f @ V4x1 ) @ V5x2 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP2__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1o1: $i] :
% 1.17/1.35 ( ( mem @ V1o1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2o2: $i] :
% 1.17/1.35 ( ( mem @ V2o2 @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27c @ A_27a @ A_27b ) @ V0f ) @ V1o1 ) @ V2o2 )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27c ) )
% 1.17/1.35 <=> ( ( V1o1
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 | ( V2o2
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP2__cong,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0x1: $i] :
% 1.17/1.35 ( ( mem @ V0x1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1x2: $i] :
% 1.17/1.35 ( ( mem @ V1x2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2y1: $i] :
% 1.17/1.35 ( ( mem @ V2y1 @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ! [V3y2: $i] :
% 1.17/1.35 ( ( mem @ V3y2 @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ! [V4f1: $i] :
% 1.17/1.35 ( ( mem @ V4f1 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V5f2: $i] :
% 1.17/1.35 ( ( mem @ V5f2 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ( ( ( V0x1 = V1x2 )
% 1.17/1.35 & ( V2y1 = V3y2 )
% 1.17/1.35 & ! [V6x: $i] :
% 1.17/1.35 ( ( mem @ V6x @ A_27a )
% 1.17/1.35 => ! [V7y: $i] :
% 1.17/1.35 ( ( mem @ V7y @ A_27b )
% 1.17/1.35 => ( ( ( V1x2
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) )
% 1.17/1.35 & ( V3y2
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V7y ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ V4f1 @ V6x ) @ V7y )
% 1.17/1.35 = ( ap @ ( ap @ V5f2 @ V6x ) @ V7y ) ) ) ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27c @ A_27a @ A_27b ) @ V4f1 ) @ V0x1 ) @ V2y1 )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27c @ A_27a @ A_27b ) @ V5f2 ) @ V1x2 ) @ V3y2 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MAP__CASE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V0f ) @ V1x )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ V1x ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) @ A_27b ) @ ( c_2Eoption_2ESOME @ A_27b ) ) @ V0f ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__BIND__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] :
% 1.17/1.35 ( ! [V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ V0f )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 & ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27b )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ V2f )
% 1.17/1.35 = ( ap @ V2f @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__BIND__cong,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0o1: $i] :
% 1.17/1.35 ( ( mem @ V0o1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1o2: $i] :
% 1.17/1.35 ( ( mem @ V1o2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2f1: $i] :
% 1.17/1.35 ( ( mem @ V2f1 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ! [V3f2: $i] :
% 1.17/1.35 ( ( mem @ V3f2 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ( ( ( V0o1 = V1o2 )
% 1.17/1.35 & ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 => ( ( V1o2
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4x ) )
% 1.17/1.35 => ( ( ap @ V2f1 @ V4x )
% 1.17/1.35 = ( ap @ V3f2 @ V4x ) ) ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27b @ A_27a ) @ V0o1 ) @ V2f1 )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27b @ A_27a ) @ V1o2 ) @ V3f2 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 => ( ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27b @ A_27a ) @ V0p ) @ V1f )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) )
% 1.17/1.35 <=> ( ( V0p
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 | ? [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 & ( V0p
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) )
% 1.17/1.35 & ( ( ap @ V1f @ V3x )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) ) ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27b @ A_27a ) @ V0p ) @ V1f )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V2y ) )
% 1.17/1.35 <=> ? [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 & ( V0p
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4x ) )
% 1.17/1.35 & ( ( ap @ V1f @ V4x )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V2y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EIS__SOME__BIND,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27b @ A_27a ) @ V0x ) @ V1g ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V0x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__IGNORE__BIND__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0m1: $i] :
% 1.17/1.35 ( ( mem @ V0m1 @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ! [V1m2: $i] :
% 1.17/1.35 ( ( mem @ V1m2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27a @ A_27b ) @ V0m1 ) @ V1m2 )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27b ) @ V0m1 ) @ ( ap @ ( c_2Ecombin_2EK @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27b ) @ V1m2 ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__IGNORE__BIND__thm,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0m: $i] :
% 1.17/1.35 ( ( mem @ V0m @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1v: $i] :
% 1.17/1.35 ( ( mem @ V1v @ A_27c )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ V0m )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27a @ A_27c ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V1v ) ) @ V0m )
% 1.17/1.35 = V0m ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0m1: $i] :
% 1.17/1.35 ( ( mem @ V0m1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1m2: $i] :
% 1.17/1.35 ( ( mem @ V1m2 @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 => ( ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27b @ A_27a ) @ V0m1 ) @ V1m2 )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) )
% 1.17/1.35 <=> ( ( V0m1
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 | ( V1m2
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) ) )
% 1.17/1.35 & ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__IGNORE__BIND @ A_27b @ A_27a ) @ V0m1 ) @ V1m2 )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V2y ) )
% 1.17/1.35 <=> ? [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 & ( V0m1
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) )
% 1.17/1.35 & ( V1m2
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V2y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__GUARD__def,axiom,
% 1.17/1.35 ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ c_2Eoption_2EOPTION__GUARD @ c_2Ebool_2ET ) )
% 1.17/1.35 = ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Eone_2Eone ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) )
% 1.17/1.35 & ( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ c_2Eoption_2EOPTION__GUARD @ c_2Ebool_2EF ) )
% 1.17/1.35 = ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( c_2Eoption_2ENONE @ ty_2Eone_2Eone ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__GUARD__COND,axiom,
% 1.17/1.35 ! [V0b: $i] :
% 1.17/1.35 ( ( mem @ V0b @ bool )
% 1.17/1.35 => ( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ c_2Eoption_2EOPTION__GUARD @ V0b ) )
% 1.17/1.35 = ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Eone_2Eone ) ) @ V0b ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Eone_2Eone ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Eone_2Eone ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__GUARD__EQ__THM,axiom,
% 1.17/1.35 ! [V0b: $i] :
% 1.17/1.35 ( ( mem @ V0b @ bool )
% 1.17/1.35 => ( ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ c_2Eoption_2EOPTION__GUARD @ V0b ) )
% 1.17/1.35 = ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Eone_2Eone ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) )
% 1.17/1.35 <=> ( p @ V0b ) )
% 1.17/1.35 & ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( ap @ c_2Eoption_2EOPTION__GUARD @ V0b ) )
% 1.17/1.35 = ( surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone @ ( c_2Eoption_2ENONE @ ty_2Eone_2Eone ) ) )
% 1.17/1.35 <=> ~ ( p @ V0b ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__CHOICE__def,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ! [V0m2: $i] :
% 1.17/1.35 ( ( mem @ V0m2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__CHOICE @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V0m2 )
% 1.17/1.35 = V0m2 ) )
% 1.17/1.35 & ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2m2: $i] :
% 1.17/1.35 ( ( mem @ V2m2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__CHOICE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ V2m2 )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__CHOICE__EQ__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,V0m1: $i] :
% 1.17/1.35 ( ( mem @ V0m1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1m2: $i] :
% 1.17/1.35 ( ( mem @ V1m2 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__CHOICE @ A_27a ) @ V0m1 ) @ V1m2 )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 <=> ( ( V0m1
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ( V1m2
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__CHOICE__NONE,axiom,
% 1.17/1.35 ! [A_27a: del,V0m1: $i] :
% 1.17/1.35 ( ( mem @ V0m1 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__CHOICE @ A_27a ) @ V0m1 ) @ ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 = V0m1 ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__MCOMP__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0g: $i] :
% 1.17/1.35 ( ( mem @ V0g @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ! [V2m: $i] :
% 1.17/1.35 ( ( mem @ V2m @ A_27c )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27a @ A_27b @ A_27c ) @ V0g ) @ V1f ) @ V2m )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27b ) @ ( ap @ V1f @ V2m ) ) @ V0g ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MCOMP__ASSOC,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27d @ ( ty_2Eoption_2Eoption @ A_27c ) ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27d ) ) )
% 1.17/1.35 => ! [V2h: $i] :
% 1.17/1.35 ( ( mem @ V2h @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27c @ A_27d @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27d @ A_27b @ A_27a ) @ V1g ) @ V2h ) )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27c @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27c @ A_27d @ A_27b ) @ V0f ) @ V1g ) ) @ V2h ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__MCOMP__ID,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0g: $i] :
% 1.17/1.35 ( ( mem @ V0g @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ A_27d ) ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27d @ A_27c @ A_27c ) @ V0g ) @ ( c_2Eoption_2ESOME @ A_27c ) )
% 1.17/1.35 = V0g )
% 1.17/1.35 & ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MCOMP @ A_27b @ A_27b @ A_27a ) @ ( c_2Eoption_2ESOME @ A_27b ) ) @ V1f )
% 1.17/1.35 = V1f ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__APPLY__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] :
% 1.17/1.35 ( ! [V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ ( arr @ A_27b @ A_27a ) ) ) @ V0x )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 & ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ ( arr @ A_27b @ A_27a ) ) @ V1f ) ) @ V2x )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a ) @ V1f ) @ V2x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__APPLY__MAP2,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ ( arr @ A_27b @ A_27c ) ) @ V0f ) @ V1x ) ) @ V2y )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27c @ A_27a @ A_27b ) @ V0f ) @ V1x ) @ V2y ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2ESOME__SOME__APPLY,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27b )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ ( arr @ A_27b @ A_27a ) ) @ V0f ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ V0f @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2ESOME__APPLY__PERMUTE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( ty_2Eoption_2Eoption @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) )
% 1.17/1.35 = ( ap
% 1.17/1.35 @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27b @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 @ ( ap @ ( c_2Eoption_2ESOME @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27b ) )
% 1.17/1.35 @ ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.35 @ ^ [V2f: $i] : ( ap @ V2f @ V1x ) ) ) )
% 1.17/1.35 @ V0f ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__APPLY__o,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( ty_2Eoption_2Eoption @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( ty_2Eoption_2Eoption @ ( arr @ A_27a @ A_27b ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27c @ A_27a ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ ( arr @ A_27a @ A_27c ) @ ( arr @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) ) @ ( arr @ A_27b @ A_27c ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( arr @ ( arr @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) ) ) ) @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) ) ) @ V0f ) ) @ V1g ) ) @ V2x )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27c @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__APPLY @ A_27b @ A_27a ) @ V1g ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTREL__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.35 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.35 <=> ( ( ( V1x
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ( V2y
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27b ) ) )
% 1.17/1.35 | ? [V3x0: $i] :
% 1.17/1.35 ( ( mem @ V3x0 @ A_27a )
% 1.17/1.35 & ? [V4y0: $i] :
% 1.17/1.35 ( ( mem @ V4y0 @ A_27b )
% 1.17/1.35 & ( V1x
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x0 ) )
% 1.17/1.35 & ( V2y
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V4y0 ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V0R @ V3x0 ) @ V4y0 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTREL__MONO,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V1Q: $i] :
% 1.17/1.35 ( ( mem @ V1Q @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ ( ty_2Eoption_2Eoption @ A_27b ) )
% 1.17/1.35 => ( ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 => ! [V5y: $i] :
% 1.17/1.35 ( ( mem @ V5y @ A_27b )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ V0P @ V4x ) @ V5y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1Q @ V4x ) @ V5y ) ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ V0P ) @ V2x ) @ V3y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ V1Q ) @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTREL__refl,axiom,
% 1.17/1.35 ! [A_27a: del,V0R: $i] :
% 1.17/1.35 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V1x ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ V2x ) @ V2x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2Esome__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eoption_2Esome @ A_27a ) @ V0P )
% 1.17/1.35 = ( ap
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V1x: $i] : ( ap @ V0P @ V1x ) ) ) )
% 1.17/1.35 @ ( ap @ ( c_2Eoption_2ESOME @ A_27a )
% 1.17/1.35 @ ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2x: $i] : ( ap @ V0P @ V2x ) ) ) ) )
% 1.17/1.35 @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Esome__intro,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1Q: $i] :
% 1.17/1.35 ( ( mem @ V1Q @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
% 1.17/1.35 => ( ( ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0P @ V2x ) )
% 1.17/1.35 => ( p @ ( ap @ V1Q @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) )
% 1.17/1.35 & ( ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ~ ( p @ ( ap @ V0P @ V3x ) ) )
% 1.17/1.35 => ( p @ ( ap @ V1Q @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) )
% 1.17/1.35 => ( p @ ( ap @ V1Q @ ( ap @ ( c_2Eoption_2Esome @ A_27a ) @ V0P ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Esome__elim,axiom,
% 1.17/1.35 ! [A_27a: del,V0Q: $i] :
% 1.17/1.35 ( ( mem @ V0Q @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
% 1.17/1.35 => ! [V1P: $i] :
% 1.17/1.35 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( p @ ( ap @ V0Q @ ( ap @ ( c_2Eoption_2Esome @ A_27a ) @ V1P ) ) )
% 1.17/1.35 => ( ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ V1P @ V2x ) )
% 1.17/1.35 & ( p @ ( ap @ V0Q @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) )
% 1.17/1.35 | ( ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ~ ( p @ ( ap @ V1P @ V3x ) ) )
% 1.17/1.35 & ( p @ ( ap @ V0Q @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Esome__F,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ( ap @ ( c_2Eoption_2Esome @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V0x: $i] : c_2Ebool_2EF ) )
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Esome__EQ,axiom,
% 1.17/1.35 ! [A_27a: del,V0y: $i] :
% 1.17/1.35 ( ( mem @ V0y @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( c_2Eoption_2Esome @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V0y ) ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0y ) )
% 1.17/1.35 & ( ( ap @ ( c_2Eoption_2Esome @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0y ) @ V2x ) ) )
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0y ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__case__cong,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0v_27: $i] :
% 1.17/1.35 ( ( mem @ V0v_27 @ A_27b )
% 1.17/1.35 => ! [V1f_27: $i] :
% 1.17/1.35 ( ( mem @ V1f_27 @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V2M: $i] :
% 1.17/1.35 ( ( mem @ V2M @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V3M_27: $i] :
% 1.17/1.35 ( ( mem @ V3M_27 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V4v: $i] :
% 1.17/1.35 ( ( mem @ V4v @ A_27b )
% 1.17/1.35 => ! [V5f: $i] :
% 1.17/1.35 ( ( mem @ V5f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ( V2M = V3M_27 )
% 1.17/1.35 & ( ( V3M_27
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 => ( V4v = V0v_27 ) )
% 1.17/1.35 & ! [V6x: $i] :
% 1.17/1.35 ( ( mem @ V6x @ A_27a )
% 1.17/1.35 => ( ( V3M_27
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) )
% 1.17/1.35 => ( ( ap @ V5f @ V6x )
% 1.17/1.35 = ( ap @ V1f_27 @ V6x ) ) ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V2M ) @ V4v ) @ V5f )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V3M_27 ) @ V0v_27 ) @ V1f_27 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eoption_2EOPTION__ALL__def,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ! [V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ V0P ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.35 <=> $true ) )
% 1.17/1.35 & ! [V1P: $i] :
% 1.17/1.35 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ V1P ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) )
% 1.17/1.35 <=> ( p @ ( ap @ V1P @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__ALL__MONO,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1P_27: $i] :
% 1.17/1.35 ( ( mem @ V1P_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V2opt: $i] :
% 1.17/1.35 ( ( mem @ V2opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0P @ V3x ) )
% 1.17/1.35 => ( p @ ( ap @ V1P_27 @ V3x ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ V0P ) @ V2opt ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ V1P_27 ) @ V2opt ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2EOPTION__ALL__CONG,axiom,
% 1.17/1.35 ! [A_27a: del,V0opt: $i] :
% 1.17/1.35 ( ( mem @ V0opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1opt_27: $i] :
% 1.17/1.35 ( ( mem @ V1opt_27 @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V2P: $i] :
% 1.17/1.35 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V3P_27: $i] :
% 1.17/1.35 ( ( mem @ V3P_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( ( V0opt = V1opt_27 )
% 1.17/1.35 & ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 => ( ( V1opt_27
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4x ) )
% 1.17/1.35 => ( ( p @ ( ap @ V2P @ V4x ) )
% 1.17/1.35 <=> ( p @ ( ap @ V3P_27 @ V4x ) ) ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ V2P ) @ V0opt ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__ALL @ A_27a ) @ V3P_27 ) @ V1opt_27 ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__case__eq,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0opt: $i] :
% 1.17/1.35 ( ( mem @ V0opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ! [V1nc: $i] :
% 1.17/1.35 ( ( mem @ V1nc @ A_27b )
% 1.17/1.35 => ! [V2sc: $i] :
% 1.17/1.35 ( ( mem @ V2sc @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V3v: $i] :
% 1.17/1.35 ( ( mem @ V3v @ A_27b )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V0opt ) @ V1nc ) @ V2sc )
% 1.17/1.35 = V3v )
% 1.17/1.35 <=> ( ( ( V0opt
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.35 & ( V1nc = V3v ) )
% 1.17/1.35 | ? [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 & ( V0opt
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4x ) )
% 1.17/1.35 & ( ( ap @ V2sc @ V4x )
% 1.17/1.35 = V3v ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__Induct,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
% 1.17/1.35 => ( ( ! [V1a: $i] :
% 1.17/1.35 ( ( mem @ V1a @ A_27a )
% 1.17/1.35 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1a ) ) ) )
% 1.17/1.35 & ( p @ ( ap @ V0P @ ( c_2Eoption_2ENONE @ A_27a ) ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Eoption__CASES,axiom,
% 1.17/1.35 ! [A_27a: del,V0opt: $i] :
% 1.17/1.35 ( ( mem @ V0opt @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.35 => ( ? [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 & ( V0opt
% 1.17/1.35 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) )
% 1.17/1.35 | ( V0opt
% 1.17/1.35 = ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eoption_2Edatatype__option,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0option: $i] :
% 1.17/1.35 ( ( mem @ V0option @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ A_27b ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ A_27b ) @ ( ap @ ( ap @ V0option @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ESOME @ A_27a ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 %------------------------------------------------------------------------------
% 1.17/1.35 %------------------------------------------------------------------------------
% 1.17/1.35 thf(tp_ty_2Epair_2Eprod,type,
% 1.17/1.35 ty_2Epair_2Eprod: del > del > del ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2E_23_23,type,
% 1.17/1.35 c_2Epair_2E_23_23: del > del > del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2E_23_23,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] : ( mem @ ( c_2Epair_2E_23_23 @ A_27a @ A_27b @ A_27c @ A_27d ) @ ( arr @ ( arr @ A_27a @ A_27c ) @ ( arr @ ( arr @ A_27b @ A_27d ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27c @ A_27d ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2E_2C,type,
% 1.17/1.35 c_2Epair_2E_2C: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2E_2C,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2EABS__prod,type,
% 1.17/1.35 c_2Epair_2EABS__prod: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2EABS__prod,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2EABS__prod @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2ECURRY,type,
% 1.17/1.35 c_2Epair_2ECURRY: del > del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2ECURRY,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2EFST,type,
% 1.17/1.35 c_2Epair_2EFST: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2EFST,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2ELEX,type,
% 1.17/1.35 c_2Epair_2ELEX: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2ELEX,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2EPROD__ALL,type,
% 1.17/1.35 c_2Epair_2EPROD__ALL: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2EPROD__ALL,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2EREP__prod,type,
% 1.17/1.35 c_2Epair_2EREP__prod: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2EREP__prod,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2EREP__prod @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2ERPROD,type,
% 1.17/1.35 c_2Epair_2ERPROD: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2ERPROD,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2ERPROD @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2ESND,type,
% 1.17/1.35 c_2Epair_2ESND: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2ESND,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2ESWAP,type,
% 1.17/1.35 c_2Epair_2ESWAP: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2ESWAP,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epair_2ESWAP @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2EUNCURRY,type,
% 1.17/1.35 c_2Epair_2EUNCURRY: del > del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2EUNCURRY,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Epair_2Epair__CASE,type,
% 1.17/1.35 c_2Epair_2Epair__CASE: del > del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Epair_2Epair__CASE,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) @ A_27a ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2Eprod__TY__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] :
% 1.17/1.35 ? [V0rep: $i] :
% 1.17/1.35 ( ( mem @ V0rep @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) )
% 1.17/1.35 & ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 @ ( lam @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 @ ^ [V1p: $i] :
% 1.17/1.35 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2x: $i] :
% 1.17/1.35 ( ap @ ( c_2Ebool_2E_3F @ A_27b )
% 1.17/1.35 @ ( lam @ A_27b
% 1.17/1.35 @ ^ [V3y: $i] :
% 1.17/1.35 ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ V1p )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V4a: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V5b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4a ) @ V2x ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V5b ) @ V3y ) ) ) ) ) ) ) ) ) ) )
% 1.17/1.35 @ V0rep ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2EABS__REP__prod,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] :
% 1.17/1.35 ( ! [V0a: $i] :
% 1.17/1.35 ( ( mem @ V0a @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2EABS__prod @ A_27a @ A_27b ) @ ( ap @ ( c_2Epair_2EREP__prod @ A_27a @ A_27b ) @ V0a ) )
% 1.17/1.35 = V0a ) )
% 1.17/1.35 & ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( lam @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 @ ^ [V2p: $i] :
% 1.17/1.35 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3x: $i] :
% 1.17/1.35 ( ap @ ( c_2Ebool_2E_3F @ A_27b )
% 1.17/1.35 @ ( lam @ A_27b
% 1.17/1.35 @ ^ [V4y: $i] :
% 1.17/1.35 ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) @ V2p )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V5a: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V6b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V5a ) @ V3x ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V6b ) @ V4y ) ) ) ) ) ) ) ) ) )
% 1.17/1.35 @ V1r ) )
% 1.17/1.35 <=> ( ( ap @ ( c_2Epair_2EREP__prod @ A_27a @ A_27b ) @ ( ap @ ( c_2Epair_2EABS__prod @ A_27a @ A_27b ) @ V1r ) )
% 1.17/1.35 = V1r ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2ECOMMA__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27b )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EABS__prod @ A_27a @ A_27b )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2a: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V3b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2a ) @ V0x ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V3b ) @ V1y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPAIR__EQ,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27b )
% 1.17/1.35 => ! [V2a: $i] :
% 1.17/1.35 ( ( mem @ V2a @ A_27a )
% 1.17/1.35 => ! [V3b: $i] :
% 1.17/1.35 ( ( mem @ V3b @ A_27b )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2a ) @ V3b ) )
% 1.17/1.35 <=> ( ( V0x = V2a )
% 1.17/1.35 & ( V1y = V3b ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ECLOSED__PAIR__EQ,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27b )
% 1.17/1.35 => ! [V2a: $i] :
% 1.17/1.35 ( ( mem @ V2a @ A_27a )
% 1.17/1.35 => ! [V3b: $i] :
% 1.17/1.35 ( ( mem @ V3b @ A_27b )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2a ) @ V3b ) )
% 1.17/1.35 <=> ( ( V0x = V2a )
% 1.17/1.35 & ( V1y = V3b ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EABS__PAIR__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ? [V1q: $i] :
% 1.17/1.35 ( ( mem @ V1q @ A_27a )
% 1.17/1.35 & ? [V2r: $i] :
% 1.17/1.35 ( ( mem @ V2r @ A_27b )
% 1.17/1.35 & ( V0x
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1q ) @ V2r ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__CASES,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ? [V1q: $i] :
% 1.17/1.35 ( ( mem @ V1q @ A_27a )
% 1.17/1.35 & ? [V2r: $i] :
% 1.17/1.35 ( ( mem @ V2r @ A_27b )
% 1.17/1.35 & ( V0x
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1q ) @ V2r ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2EPAIR,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V0x ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V0x ) )
% 1.17/1.35 = V0x ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EFST,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27b )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y ) )
% 1.17/1.35 = V0x ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ESND,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27b )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y ) )
% 1.17/1.35 = V1y ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPAIR__FST__SND__EQ,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1q: $i] :
% 1.17/1.35 ( ( mem @ V1q @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( V0p = V1q )
% 1.17/1.35 <=> ( ( ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V0p )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1q ) )
% 1.17/1.35 & ( ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V0p )
% 1.17/1.35 = ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1q ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2ESWAP__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0a: $i] :
% 1.17/1.35 ( ( mem @ V0a @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2ESWAP @ A_27a @ A_27b ) @ V0a )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ ( ap @ ( c_2Epair_2ESND @ A_27b @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Epair_2EFST @ A_27b @ A_27a ) @ V0a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2ECURRY__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1x ) @ V2y )
% 1.17/1.35 = ( ap @ V0f @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2EUNCURRY,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1v: $i] :
% 1.17/1.35 ( ( mem @ V1v @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1v )
% 1.17/1.35 = ( ap @ ( ap @ V0f @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1v ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1v ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EUNCURRY__VAR,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1v: $i] :
% 1.17/1.35 ( ( mem @ V1v @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1v )
% 1.17/1.35 = ( ap @ ( ap @ V0f @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1v ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1v ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EELIM__UNCURRY,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f )
% 1.17/1.35 = ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
% 1.17/1.35 @ ^ [V1x: $i] : ( ap @ ( ap @ V0f @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EUNCURRY__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) )
% 1.17/1.35 = ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ECURRY__UNCURRY__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f ) )
% 1.17/1.35 = V0f ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EUNCURRY__CURRY__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c ) @ V0f ) )
% 1.17/1.35 = V0f ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ECURRY__ONE__ONE__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
% 1.17/1.35 => ( ( ( ap @ ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c ) @ V0f )
% 1.17/1.35 = ( ap @ ( c_2Epair_2ECURRY @ A_27a @ A_27b @ A_27c ) @ V1g ) )
% 1.17/1.35 <=> ( V0f = V1g ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EUNCURRY__ONE__ONE__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ( ( ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V1g ) )
% 1.17/1.35 <=> ( V0f = V1g ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__Axiom,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ? [V1fn: $i] :
% 1.17/1.35 ( ( mem @ V1fn @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
% 1.17/1.35 & ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27b )
% 1.17/1.35 => ( ( ap @ V1fn @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V3y ) )
% 1.17/1.35 = ( ap @ ( ap @ V0f @ V2x ) @ V3y ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EUNCURRY__CONG,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f_27: $i] :
% 1.17/1.35 ( ( mem @ V0f_27 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ! [V2M_27: $i] :
% 1.17/1.35 ( ( mem @ V2M_27 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V3M: $i] :
% 1.17/1.35 ( ( mem @ V3M @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ( V3M = V2M_27 )
% 1.17/1.35 & ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 => ! [V5y: $i] :
% 1.17/1.35 ( ( mem @ V5y @ A_27b )
% 1.17/1.35 => ( ( V2M_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V4x ) @ V5y ) )
% 1.17/1.35 => ( ( ap @ ( ap @ V1f @ V4x ) @ V5y )
% 1.17/1.35 = ( ap @ ( ap @ V0f_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V1f ) @ V3M )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ V0f_27 ) @ V2M_27 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ELAMBDA__PROD,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) )
% 1.17/1.35 => ( ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
% 1.17/1.35 @ ^ [V1p: $i] : ( ap @ V0P @ V1p ) )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2p1: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V3p2: $i] : ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2p1 ) @ V3p2 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EEXISTS__PROD,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.35 => ( ? [V1p: $i] :
% 1.17/1.35 ( ( mem @ V1p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 & ( p @ ( ap @ V0P @ V1p ) ) )
% 1.17/1.35 <=> ? [V2p__1: $i] :
% 1.17/1.35 ( ( mem @ V2p__1 @ A_27a )
% 1.17/1.35 & ? [V3p__2: $i] :
% 1.17/1.35 ( ( mem @ V3p__2 @ A_27b )
% 1.17/1.35 & ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2p__1 ) @ V3p__2 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EFORALL__PROD,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.35 => ( ! [V1p: $i] :
% 1.17/1.35 ( ( mem @ V1p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( p @ ( ap @ V0P @ V1p ) ) )
% 1.17/1.35 <=> ! [V2p__1: $i] :
% 1.17/1.35 ( ( mem @ V2p__1 @ A_27a )
% 1.17/1.35 => ! [V3p__2: $i] :
% 1.17/1.35 ( ( mem @ V3p__2 @ A_27b )
% 1.17/1.35 => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2p__1 ) @ V3p__2 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__induction,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.35 => ( ! [V1p__1: $i] :
% 1.17/1.35 ( ( mem @ V1p__1 @ A_27a )
% 1.17/1.35 => ! [V2p__2: $i] :
% 1.17/1.35 ( ( mem @ V2p__2 @ A_27b )
% 1.17/1.35 => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1p__1 ) @ V2p__2 ) ) ) ) )
% 1.17/1.35 => ! [V3p: $i] :
% 1.17/1.35 ( ( mem @ V3p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( p @ ( ap @ V0P @ V3p ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2EPROD__ALL__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1Q: $i] :
% 1.17/1.35 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V2p: $i] :
% 1.17/1.35 ( ( mem @ V2p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ V0P ) @ V1Q ) @ V2p ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0P @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V2p ) ) )
% 1.17/1.35 & ( p @ ( ap @ V1Q @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V2p ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPROD__ALL__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1Q: $i] :
% 1.17/1.35 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27b )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ V0P ) @ V1Q ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V3y ) ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0P @ V2x ) )
% 1.17/1.35 & ( p @ ( ap @ V1Q @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPROD__ALL__MONO,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1P_27: $i] :
% 1.17/1.35 ( ( mem @ V1P_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V2Q: $i] :
% 1.17/1.35 ( ( mem @ V2Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V3Q_27: $i] :
% 1.17/1.35 ( ( mem @ V3Q_27 @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V4p: $i] :
% 1.17/1.35 ( ( mem @ V4p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ! [V5x: $i] :
% 1.17/1.35 ( ( mem @ V5x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0P @ V5x ) )
% 1.17/1.35 => ( p @ ( ap @ V1P_27 @ V5x ) ) ) )
% 1.17/1.35 & ! [V6y: $i] :
% 1.17/1.35 ( ( mem @ V6y @ A_27b )
% 1.17/1.35 => ( ( p @ ( ap @ V2Q @ V6y ) )
% 1.17/1.35 => ( p @ ( ap @ V3Q_27 @ V6y ) ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ V0P ) @ V2Q ) @ V4p ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ V1P_27 ) @ V3Q_27 ) @ V4p ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPROD__ALL__CONG,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1p_27: $i] :
% 1.17/1.35 ( ( mem @ V1p_27 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V2P: $i] :
% 1.17/1.35 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V3P_27: $i] :
% 1.17/1.35 ( ( mem @ V3P_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V4Q: $i] :
% 1.17/1.35 ( ( mem @ V4Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V5Q_27: $i] :
% 1.17/1.35 ( ( mem @ V5Q_27 @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ( ( ( V0p = V1p_27 )
% 1.17/1.35 & ! [V6x: $i] :
% 1.17/1.35 ( ( mem @ V6x @ A_27a )
% 1.17/1.35 => ! [V7y: $i] :
% 1.17/1.35 ( ( mem @ V7y @ A_27b )
% 1.17/1.35 => ( ( V1p_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V6x ) @ V7y ) )
% 1.17/1.35 => ( ( p @ ( ap @ V2P @ V6x ) )
% 1.17/1.35 <=> ( p @ ( ap @ V3P_27 @ V6x ) ) ) ) ) )
% 1.17/1.35 & ! [V8x: $i] :
% 1.17/1.35 ( ( mem @ V8x @ A_27a )
% 1.17/1.35 => ! [V9y: $i] :
% 1.17/1.35 ( ( mem @ V9y @ A_27b )
% 1.17/1.35 => ( ( V1p_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V8x ) @ V9y ) )
% 1.17/1.35 => ( ( p @ ( ap @ V4Q @ V9y ) )
% 1.17/1.35 <=> ( p @ ( ap @ V5Q_27 @ V9y ) ) ) ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ V2P ) @ V4Q ) @ V0p ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2EPROD__ALL @ A_27a @ A_27b ) @ V3P_27 ) @ V5Q_27 ) @ V1p_27 ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EELIM__PEXISTS,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ? [V1p: $i] :
% 1.17/1.35 ( ( mem @ V1p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V0P @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1p ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1p ) ) ) )
% 1.17/1.35 <=> ? [V2p1: $i] :
% 1.17/1.35 ( ( mem @ V2p1 @ A_27a )
% 1.17/1.35 & ? [V3p2: $i] :
% 1.17/1.35 ( ( mem @ V3p2 @ A_27b )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V0P @ V2p1 ) @ V3p2 ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EELIM__PFORALL,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ! [V1p: $i] :
% 1.17/1.35 ( ( mem @ V1p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V0P @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1p ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1p ) ) ) )
% 1.17/1.35 <=> ! [V2p1: $i] :
% 1.17/1.35 ( ( mem @ V2p1 @ A_27a )
% 1.17/1.35 => ! [V3p2: $i] :
% 1.17/1.35 ( ( mem @ V3p2 @ A_27b )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V0P @ V2p1 ) @ V3p2 ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPFORALL__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) )
% 1.17/1.35 <=> ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3x: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V4y: $i] : ( ap @ ( ap @ V0P @ V3x ) @ V4y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPEXISTS__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ? [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 & ? [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) )
% 1.17/1.35 <=> ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3x: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V4y: $i] : ( ap @ ( ap @ V0P @ V3x ) @ V4y ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EELIM__PEXISTS__EVAL,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V1x: $i] : ( ap @ V0P @ V1x ) ) ) ) )
% 1.17/1.35 <=> ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Ebool_2E_3F @ A_27b ) @ ( ap @ V0P @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EELIM__PFORALL__EVAL,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V1x: $i] : ( ap @ V0P @ V1x ) ) ) ) )
% 1.17/1.35 <=> ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Ebool_2E_21 @ A_27b ) @ ( ap @ V0P @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2EPAIR__MAP,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27b @ A_27d ) )
% 1.17/1.35 => ! [V2p: $i] :
% 1.17/1.35 ( ( mem @ V2p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Epair_2E_23_23 @ A_27a @ A_27b @ A_27c @ A_27d ) @ V0f ) @ V1g ) @ V2p )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27c @ A_27d ) @ ( ap @ V0f @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V2p ) ) ) @ ( ap @ V1g @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V2p ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPAIR__MAP__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27c @ A_27d ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27c )
% 1.17/1.35 => ( ( ap @ ( ap @ ( ap @ ( c_2Epair_2E_23_23 @ A_27a @ A_27c @ A_27b @ A_27d ) @ V0f ) @ V1g ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27c ) @ V2x ) @ V3y ) )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27d ) @ ( ap @ V0f @ V2x ) ) @ ( ap @ V1g @ V3y ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EFST__PAIR__MAP,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.35 => ! [V2g: $i] :
% 1.17/1.35 ( ( mem @ V2g @ ( arr @ A_27b @ A_27d ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2EFST @ A_27c @ A_27d ) @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2E_23_23 @ A_27a @ A_27b @ A_27c @ A_27d ) @ V1f ) @ V2g ) @ V0p ) )
% 1.17/1.35 = ( ap @ V1f @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V0p ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ESND__PAIR__MAP,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.35 => ! [V2g: $i] :
% 1.17/1.35 ( ( mem @ V2g @ ( arr @ A_27b @ A_27d ) )
% 1.17/1.35 => ( ( ap @ ( c_2Epair_2ESND @ A_27c @ A_27d ) @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2E_23_23 @ A_27a @ A_27b @ A_27c @ A_27d ) @ V1f ) @ V2g ) @ V0p ) )
% 1.17/1.35 = ( ap @ V2g @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V0p ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ELET2__RAND,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27c @ A_27d ) )
% 1.17/1.35 => ! [V1M: $i] :
% 1.17/1.35 ( ( mem @ V1M @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V2N: $i] :
% 1.17/1.35 ( ( mem @ V2N @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
% 1.17/1.35 => ( ( ap @ V0P
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3x: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V4y: $i] : ( ap @ ( ap @ V2N @ V3x ) @ V4y ) ) ) ) )
% 1.17/1.35 @ V1M ) )
% 1.17/1.35 = ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27d )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27d )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V5x: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V6y: $i] : ( ap @ V0P @ ( ap @ ( ap @ V2N @ V5x ) @ V6y ) ) ) ) ) )
% 1.17/1.35 @ V1M ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ELET2__RATOR,axiom,
% 1.17/1.35 ! [A_27a1: del,A_27a2: del,A_27b: del,A_27c: del,V0M: $i] :
% 1.17/1.35 ( ( mem @ V0M @ ( ty_2Epair_2Eprod @ A_27a1 @ A_27a2 ) )
% 1.17/1.35 => ! [V1N: $i] :
% 1.17/1.35 ( ( mem @ V1N @ ( arr @ A_27a1 @ ( arr @ A_27a2 @ ( arr @ A_27b @ A_27c ) ) ) )
% 1.17/1.35 => ! [V2b: $i] :
% 1.17/1.35 ( ( mem @ V2b @ A_27b )
% 1.17/1.35 => ( ( ap
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ A_27a1 @ A_27a2 ) @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a1 @ A_27a2 @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.35 @ ( lam @ A_27a1
% 1.17/1.35 @ ^ [V3x: $i] :
% 1.17/1.35 ( lam @ A_27a2
% 1.17/1.35 @ ^ [V4y: $i] : ( ap @ ( ap @ V1N @ V3x ) @ V4y ) ) ) ) )
% 1.17/1.35 @ V0M )
% 1.17/1.35 @ V2b )
% 1.17/1.35 = ( ap
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ A_27a1 @ A_27a2 ) @ A_27c )
% 1.17/1.35 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a1 @ A_27a2 @ A_27c )
% 1.17/1.35 @ ( lam @ A_27a1
% 1.17/1.35 @ ^ [V5x: $i] :
% 1.17/1.35 ( lam @ A_27a2
% 1.17/1.35 @ ^ [V6y: $i] : ( ap @ ( ap @ ( ap @ V1N @ V5x ) @ V6y ) @ V2b ) ) ) ) )
% 1.17/1.35 @ V0M ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Eo__UNCURRY__R,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27d @ A_27c ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27b @ A_27d ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c @ A_27d ) @ V0f ) @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27d ) @ V1g ) )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( arr @ A_27b @ A_27c ) @ ( arr @ A_27b @ A_27d ) ) @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ A_27c @ A_27d ) @ V0f ) ) @ V1g ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EC__UNCURRY__L,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ ( arr @ A_27d @ A_27c ) ) ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27d )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Ecombin_2EC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27d @ A_27c ) @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( arr @ A_27d @ A_27c ) ) @ V0f ) ) @ V1x )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ A_27a @ A_27d @ ( arr @ A_27b @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( arr @ A_27d @ ( arr @ A_27b @ A_27c ) ) @ ( arr @ A_27b @ ( arr @ A_27d @ A_27c ) ) ) @ ( c_2Ecombin_2EC @ A_27b @ A_27d @ A_27c ) ) @ V0f ) ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ES__UNCURRY__R,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( arr @ A_27d @ A_27c ) ) )
% 1.17/1.35 => ! [V1g: $i] :
% 1.17/1.35 ( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27b @ A_27d ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Ecombin_2ES @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27d @ A_27c ) @ V0f ) @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27d ) @ V1g ) )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2ES @ A_27a @ ( arr @ A_27b @ A_27d ) @ ( arr @ A_27b @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( arr @ ( arr @ A_27b @ A_27d ) @ ( arr @ A_27b @ A_27c ) ) @ ( arr @ A_27b @ ( arr @ A_27d @ A_27c ) ) ) @ ( c_2Ecombin_2ES @ A_27b @ A_27d @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ( arr @ A_27b @ ( arr @ A_27d @ A_27c ) ) @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ ( arr @ A_27d @ A_27c ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0f ) ) @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) ) ) ) @ V1g ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EFORALL__UNCURRY,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool ) @ V0f ) ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( c_2Ebool_2E_21 @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ ( arr @ A_27b @ bool ) ) @ ( c_2Ebool_2E_21 @ A_27b ) ) @ V0f ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EPAIR__FUN__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ bool ) )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) )
% 1.17/1.35 @ ( lam @ ( arr @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) )
% 1.17/1.35 @ ^ [V1f: $i] : ( ap @ V0P @ V1f ) ) ) )
% 1.17/1.35 <=> ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F_21 @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) ) )
% 1.17/1.35 @ ( lam @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.35 @ ^ [V2p: $i] :
% 1.17/1.35 ( ap @ V0P
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Epair_2EFST @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) ) @ V2p ) @ V3a ) ) @ ( ap @ ( ap @ ( c_2Epair_2ESND @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) ) @ V2p ) @ V3a ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2Epair__CASE__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1f )
% 1.17/1.35 = ( ap @ ( ap @ V1f @ ( ap @ ( c_2Epair_2EFST @ A_27b @ A_27c ) @ V0p ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27b @ A_27c ) @ V0p ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__case__thm,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27b )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27c )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27c ) @ V0x ) @ V1y ) ) @ V2f )
% 1.17/1.35 = ( ap @ ( ap @ V2f @ V0x ) @ V1y ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__case__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27b )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27c )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27c ) @ V0x ) @ V1y ) ) @ V2f )
% 1.17/1.35 = ( ap @ ( ap @ V2f @ V0x ) @ V1y ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__case__cong,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0f_27: $i] :
% 1.17/1.35 ( ( mem @ V0f_27 @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ! [V1M: $i] :
% 1.17/1.35 ( ( mem @ V1M @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) )
% 1.17/1.35 => ! [V2M_27: $i] :
% 1.17/1.35 ( ( mem @ V2M_27 @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) )
% 1.17/1.35 => ! [V3f: $i] :
% 1.17/1.35 ( ( mem @ V3f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ( ( ( V1M = V2M_27 )
% 1.17/1.35 & ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27b )
% 1.17/1.35 => ! [V5y: $i] :
% 1.17/1.35 ( ( mem @ V5y @ A_27c )
% 1.17/1.35 => ( ( V2M_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27c ) @ V4x ) @ V5y ) )
% 1.17/1.35 => ( ( ap @ ( ap @ V3f @ V4x ) @ V5y )
% 1.17/1.35 = ( ap @ ( ap @ V0f_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ V1M ) @ V3f )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ V2M_27 ) @ V0f_27 ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Epair__case__eq,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
% 1.17/1.35 => ! [V2v: $i] :
% 1.17/1.35 ( ( mem @ V2v @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ A_27a @ A_27b @ A_27c ) @ V0p ) @ V1f )
% 1.17/1.35 = V2v )
% 1.17/1.35 <=> ? [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27b )
% 1.17/1.35 & ? [V4y: $i] :
% 1.17/1.35 ( ( mem @ V4y @ A_27c )
% 1.17/1.35 & ( V0p
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27c ) @ V3x ) @ V4y ) )
% 1.17/1.35 & ( ( ap @ ( ap @ V1f @ V3x ) @ V4y )
% 1.17/1.35 = V2v ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Edatatype__pair,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,A_27c: del,V0pair: $i] :
% 1.17/1.35 ( ( mem @ V0pair @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ A_27c ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ A_27c ) @ ( ap @ V0pair @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2ELEX__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2s: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V3t: $i] :
% 1.17/1.35 ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V4u: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V5v: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ V0R1 @ V2s ) @ V4u ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2s ) @ V4u ) ) @ ( ap @ ( ap @ V1R2 @ V3t ) @ V5v ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ELEX__DEF__THM,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V2a: $i] :
% 1.17/1.35 ( ( mem @ V2a @ A_27a )
% 1.17/1.35 => ! [V3b: $i] :
% 1.17/1.35 ( ( mem @ V3b @ A_27b )
% 1.17/1.35 => ! [V4c: $i] :
% 1.17/1.35 ( ( mem @ V4c @ A_27a )
% 1.17/1.35 => ! [V5d: $i] :
% 1.17/1.35 ( ( mem @ V5d @ A_27b )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2a ) @ V3b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V4c ) @ V5d ) ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ ( ap @ V0R1 @ V2a ) @ V4c ) )
% 1.17/1.35 | ( ( V2a = V4c )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1R2 @ V3b ) @ V5d ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ELEX__MONO,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2R3: $i] :
% 1.17/1.35 ( ( mem @ V2R3 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V3R4: $i] :
% 1.17/1.35 ( ( mem @ V3R4 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V5y: $i] :
% 1.17/1.35 ( ( mem @ V5y @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ! [V6x: $i] :
% 1.17/1.35 ( ( mem @ V6x @ A_27a )
% 1.17/1.35 => ! [V7y: $i] :
% 1.17/1.35 ( ( mem @ V7y @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ V0R1 @ V6x ) @ V7y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1R2 @ V6x ) @ V7y ) ) ) ) )
% 1.17/1.35 & ! [V8x: $i] :
% 1.17/1.35 ( ( mem @ V8x @ A_27b )
% 1.17/1.35 => ! [V9y: $i] :
% 1.17/1.35 ( ( mem @ V9y @ A_27b )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ V2R3 @ V8x ) @ V9y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V3R4 @ V8x ) @ V9y ) ) ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V2R3 ) @ V4x ) @ V5y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V1R2 ) @ V3R4 ) @ V4x ) @ V5y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EWF__LEX,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.35 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1Q: $i] :
% 1.17/1.35 ( ( mem @ V1Q @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27b ) @ V1Q ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Erelation_2EWF @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R ) @ V1Q ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Epair_2ERPROD__DEF,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Epair_2ERPROD @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 )
% 1.17/1.35 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V2s: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V3t: $i] :
% 1.17/1.35 ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V4u: $i] :
% 1.17/1.35 ( lam @ A_27b
% 1.17/1.35 @ ^ [V5v: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ V0R1 @ V2s ) @ V4u ) ) @ ( ap @ ( ap @ V1R2 @ V3t ) @ V5v ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EWF__RPROD,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.35 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1Q: $i] :
% 1.17/1.35 ( ( mem @ V1Q @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27b ) @ V1Q ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Erelation_2EWF @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2ERPROD @ A_27a @ A_27b ) @ V0R ) @ V1Q ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Etotal__LEX,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Erelation_2Etotal @ A_27a ) @ V0R1 ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Erelation_2Etotal @ A_27b ) @ V1R2 ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Erelation_2Etotal @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Etransitive__LEX,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R1 ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27b ) @ V1R2 ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Ereflexive__LEX,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27a ) @ V0R1 ) )
% 1.17/1.35 | ( p @ ( ap @ ( c_2Erelation_2Ereflexive @ A_27b ) @ V1R2 ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2Esymmetric__LEX,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27a ) @ V0R1 ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ A_27b ) @ V1R2 ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Erelation_2Esymmetric @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ELEX__CONG,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0R1: $i] :
% 1.17/1.35 ( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V1R2: $i] :
% 1.17/1.35 ( ( mem @ V1R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V2v1: $i] :
% 1.17/1.35 ( ( mem @ V2v1 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V3v2: $i] :
% 1.17/1.35 ( ( mem @ V3v2 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V4R1_27: $i] :
% 1.17/1.35 ( ( mem @ V4R1_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V5R2_27: $i] :
% 1.17/1.35 ( ( mem @ V5R2_27 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ! [V6v1_27: $i] :
% 1.17/1.35 ( ( mem @ V6v1_27 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V7v2_27: $i] :
% 1.17/1.35 ( ( mem @ V7v2_27 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( ( V2v1 = V6v1_27 )
% 1.17/1.35 & ( V3v2 = V7v2_27 )
% 1.17/1.35 & ! [V8a: $i] :
% 1.17/1.35 ( ( mem @ V8a @ A_27a )
% 1.17/1.35 => ! [V9b: $i] :
% 1.17/1.35 ( ( mem @ V9b @ A_27b )
% 1.17/1.35 => ! [V10c: $i] :
% 1.17/1.35 ( ( mem @ V10c @ A_27a )
% 1.17/1.35 => ! [V11d: $i] :
% 1.17/1.35 ( ( mem @ V11d @ A_27b )
% 1.17/1.35 => ( ( ( V6v1_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V8a ) @ V9b ) )
% 1.17/1.35 & ( V7v2_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V10c ) @ V11d ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ V0R1 @ V8a ) @ V10c ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ V4R1_27 @ V8a ) @ V10c ) ) ) ) ) ) ) )
% 1.17/1.35 & ! [V12a: $i] :
% 1.17/1.35 ( ( mem @ V12a @ A_27a )
% 1.17/1.35 => ! [V13b: $i] :
% 1.17/1.35 ( ( mem @ V13b @ A_27b )
% 1.17/1.35 => ! [V14c: $i] :
% 1.17/1.35 ( ( mem @ V14c @ A_27a )
% 1.17/1.35 => ! [V15d: $i] :
% 1.17/1.35 ( ( mem @ V15d @ A_27b )
% 1.17/1.35 => ( ( ( V6v1_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V12a ) @ V13b ) )
% 1.17/1.35 & ( V7v2_27
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V14c ) @ V15d ) )
% 1.17/1.35 & ( V12a = V14c ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ V1R2 @ V13b ) @ V15d ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ V5R2_27 @ V13b ) @ V15d ) ) ) ) ) ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V0R1 ) @ V1R2 ) @ V2v1 ) @ V3v2 ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Epair_2ELEX @ A_27a @ A_27b ) @ V4R1_27 ) @ V5R2_27 ) @ V6v1_27 ) @ V7v2_27 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2EFST__EQ__EQUIV,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V0p )
% 1.17/1.35 = V1x )
% 1.17/1.35 <=> ? [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27b )
% 1.17/1.35 & ( V0p
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Epair_2ESND__EQ__EQUIV,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) )
% 1.17/1.35 => ! [V1y: $i] :
% 1.17/1.35 ( ( mem @ V1y @ A_27a )
% 1.17/1.35 => ( ( ( ap @ ( c_2Epair_2ESND @ A_27b @ A_27a ) @ V0p )
% 1.17/1.35 = V1y )
% 1.17/1.35 <=> ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27b )
% 1.17/1.35 & ( V0p
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27a ) @ V2x ) @ V1y ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 %------------------------------------------------------------------------------
% 1.17/1.35 %------------------------------------------------------------------------------
% 1.17/1.35 thf(tp_c_2Eprim__rec_2E_3C,type,
% 1.17/1.35 c_2Eprim__rec_2E_3C: $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2E_3C,axiom,
% 1.17/1.35 mem @ c_2Eprim__rec_2E_3C @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2EPRE,type,
% 1.17/1.35 c_2Eprim__rec_2EPRE: $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2EPRE,axiom,
% 1.17/1.35 mem @ c_2Eprim__rec_2EPRE @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.35
% 1.17/1.35 thf(stp_fo_c_2Eprim__rec_2EPRE,type,
% 1.17/1.35 fo__c_2Eprim__rec_2EPRE: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.35
% 1.17/1.35 thf(stp_eq_fo_c_2Eprim__rec_2EPRE,axiom,
% 1.17/1.35 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eprim__rec_2EPRE @ X0 ) )
% 1.17/1.35 = ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2EPRIM__REC,type,
% 1.17/1.35 c_2Eprim__rec_2EPRIM__REC: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2EPRIM__REC,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eprim__rec_2EPRIM__REC @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2EPRIM__REC__FUN,type,
% 1.17/1.35 c_2Eprim__rec_2EPRIM__REC__FUN: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2EPRIM__REC__FUN,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eprim__rec_2EPRIM__REC__FUN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2ESIMP__REC,type,
% 1.17/1.35 c_2Eprim__rec_2ESIMP__REC: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2ESIMP__REC,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eprim__rec_2ESIMP__REC @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2ESIMP__REC__REL,type,
% 1.17/1.35 c_2Eprim__rec_2ESIMP__REC__REL: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2ESIMP__REC__REL,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2Emeasure,type,
% 1.17/1.35 c_2Eprim__rec_2Emeasure: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2Emeasure,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eprim__rec_2Emeasure @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eprim__rec_2Ewellfounded,type,
% 1.17/1.35 c_2Eprim__rec_2Ewellfounded: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eprim__rec_2Ewellfounded,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eprim__rec_2Ewellfounded @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2ELESS__DEF,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.35 <=> ? [V2P: $i] :
% 1.17/1.35 ( ( mem @ V2P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.35 & ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ V2P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.35 => ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.35 & ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.35 & ~ ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EINV__SUC__EQ,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.35 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 <=> ( V0m = V1n ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2EPRE__DEF,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.35 = ( surj__ty_2Enum_2Enum
% 1.17/1.35 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.35 @ ( ap @ ( c_2Emin_2E_40 @ ty_2Enum_2Enum )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V1n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ V1n ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EPRE,axiom,
% 1.17/1.35 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.35 = fo__c_2Enum_2E0 )
% 1.17/1.35 & ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.35 = V0m ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__REFL,axiom,
% 1.17/1.35 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ESUC__LESS,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ENOT__LESS__0,axiom,
% 1.17/1.35 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__0,axiom,
% 1.17/1.35 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__0__0,axiom,
% 1.17/1.35 p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__MONO,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__MONO__REV,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__MONO__EQ,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ETC__IM__RTC__SUC,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Erelation_2ETC @ ty_2Enum_2Enum )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V2x: $i] :
% 1.17/1.35 ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V3y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3y ) @ ( ap @ c_2Enum_2ESUC @ V2x ) ) ) ) )
% 1.17/1.35 @ ( inj__ty_2Enum_2Enum @ V0m ) )
% 1.17/1.35 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 <=> ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Erelation_2ERTC @ ty_2Enum_2Enum )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V4x: $i] :
% 1.17/1.35 ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V5y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V5y ) @ ( ap @ c_2Enum_2ESUC @ V4x ) ) ) ) )
% 1.17/1.35 @ ( inj__ty_2Enum_2Enum @ V0m ) )
% 1.17/1.35 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ERTC__IM__TC,axiom,
% 1.17/1.35 ! [A_27a: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ! [V1m: $i] :
% 1.17/1.35 ( ( mem @ V1m @ A_27a )
% 1.17/1.35 => ! [V2n: $i] :
% 1.17/1.35 ( ( mem @ V2n @ A_27a )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Erelation_2ERTC @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3x: $i] :
% 1.17/1.35 ( lam @ A_27a
% 1.17/1.35 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4y ) @ ( ap @ V0f @ V3x ) ) ) ) )
% 1.17/1.35 @ ( ap @ V0f @ V1m ) )
% 1.17/1.35 @ V2n ) )
% 1.17/1.35 <=> ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( c_2Erelation_2ETC @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V5x: $i] :
% 1.17/1.35 ( lam @ A_27a
% 1.17/1.35 @ ^ [V6y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V6y ) @ ( ap @ V0f @ V5x ) ) ) ) )
% 1.17/1.35 @ V1m )
% 1.17/1.35 @ V2n ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__ALT,axiom,
% 1.17/1.35 ( c_2Eprim__rec_2E_3C
% 1.17/1.35 = ( ap @ ( c_2Erelation_2ETC @ ty_2Enum_2Enum )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V0x: $i] :
% 1.17/1.35 ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V1y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V1y ) @ ( ap @ c_2Enum_2ESUC @ V0x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__SUC__REFL,axiom,
% 1.17/1.35 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__SUC,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__LEMMA1,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 => ( ( V0m = V1n )
% 1.17/1.35 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__LEMMA2,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ( V0m = V1n )
% 1.17/1.35 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__THM,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 <=> ( ( V0m = V1n )
% 1.17/1.35 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__SUC__IMP,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.35 => ( ( V0m != V1n )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EEQ__LESS,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.35 = V1n )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ESUC__ID,axiom,
% 1.17/1.35 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.35 != V0n ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ENOT__LESS__EQ,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( V0m = V1n )
% 1.17/1.35 => ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__NOT__EQ,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.35 => ( V0m != V1n ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2ESIMP__REC__REL,axiom,
% 1.17/1.35 ! [A_27a: del,V0fun: $i] :
% 1.17/1.35 ( ( mem @ V0fun @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ V0fun ) @ V1x ) @ V2f ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.35 <=> ( ( ( ap @ V0fun @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.35 = V1x )
% 1.17/1.35 & ! [V4m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.35 => ( ( ap @ V0fun @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4m ) ) )
% 1.17/1.35 = ( ap @ V2f @ ( ap @ V0fun @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ESIMP__REC__EXISTS,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ? [V3fun: $i] :
% 1.17/1.35 ( ( mem @ V3fun @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ V3fun ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ! [V2g1: $i] :
% 1.17/1.35 ( ( mem @ V2g1 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 => ! [V3g2: $i] :
% 1.17/1.35 ( ( mem @ V3g2 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 => ! [V4m1: tp__ty_2Enum_2Enum,V5m2: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ V2g1 ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V4m1 ) ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ V3g2 ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V5m2 ) ) ) )
% 1.17/1.35 => ! [V6n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6n ) ) @ ( inj__ty_2Enum_2Enum @ V4m1 ) ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6n ) ) @ ( inj__ty_2Enum_2Enum @ V5m2 ) ) ) )
% 1.17/1.35 => ( ( ap @ V2g1 @ ( inj__ty_2Enum_2Enum @ V6n ) )
% 1.17/1.35 = ( ap @ V3g2 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V3y: $i] :
% 1.17/1.35 ( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 @ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27a )
% 1.17/1.35 @ ^ [V4g: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ V4g ) @ V0x ) @ V1f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3y ) @ ( ap @ V4g @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2ESIMP__REC,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f_27: $i] :
% 1.17/1.35 ( ( mem @ V1f_27 @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ? [V3g: $i] :
% 1.17/1.35 ( ( mem @ V3g @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC__REL @ A_27a ) @ V3g ) @ V0x ) @ V1f_27 ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.35 & ( ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC @ A_27a ) @ V0x ) @ V1f_27 ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
% 1.17/1.35 = ( ap @ V3g @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ELESS__SUC__SUC,axiom,
% 1.17/1.35 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2ESIMP__REC__THM,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.35 = V0x )
% 1.17/1.35 & ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC @ A_27a ) @ V0x ) @ V1f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
% 1.17/1.35 = ( ap @ V1f @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2EPRIM__REC__FUN,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC__FUN @ A_27a ) @ V0x ) @ V1f )
% 1.17/1.35 = ( ap
% 1.17/1.35 @ ( ap @ ( c_2Eprim__rec_2ESIMP__REC @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V2n: $i] : V0x ) )
% 1.17/1.35 @ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27a )
% 1.17/1.35 @ ^ [V3fun: $i] :
% 1.17/1.35 ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V4n: $i] : ( ap @ ( ap @ V1f @ ( ap @ V3fun @ ( ap @ c_2Eprim__rec_2EPRE @ V4n ) ) ) @ V4n ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EPRIM__REC__EQN,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) )
% 1.17/1.35 => ( ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC__FUN @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
% 1.17/1.35 = V0x )
% 1.17/1.35 & ! [V3m: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC__FUN @ A_27a ) @ V0x ) @ V1f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) )
% 1.17/1.35 = ( ap @ ( ap @ V1f @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC__FUN @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2EPRIM__REC,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) )
% 1.17/1.35 => ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2m ) )
% 1.17/1.35 = ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC__FUN @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EPRIM__REC__THM,axiom,
% 1.17/1.35 ! [A_27a: del,V0x: $i] :
% 1.17/1.35 ( ( mem @ V0x @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) )
% 1.17/1.35 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.35 = V0x )
% 1.17/1.35 & ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC @ A_27a ) @ V0x ) @ V1f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
% 1.17/1.35 = ( ap @ ( ap @ V1f @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2EPRIM__REC @ A_27a ) @ V0x ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EDC,axiom,
% 1.17/1.35 ! [A_27a: del,V0P: $i] :
% 1.17/1.35 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1R: $i] :
% 1.17/1.35 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2a: $i] :
% 1.17/1.35 ( ( mem @ V2a @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0P @ V2a ) )
% 1.17/1.35 & ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0P @ V3x ) )
% 1.17/1.35 => ? [V4y: $i] :
% 1.17/1.35 ( ( mem @ V4y @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ V0P @ V4y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1R @ V3x ) @ V4y ) ) ) ) ) )
% 1.17/1.35 => ? [V5f: $i] :
% 1.17/1.35 ( ( mem @ V5f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 & ( ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.35 = V2a )
% 1.17/1.35 & ! [V6n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( p @ ( ap @ V0P @ ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1R @ ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ V5f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2Enum__Axiom__old,axiom,
% 1.17/1.35 ! [A_27a: del,V0e: $i] :
% 1.17/1.35 ( ( mem @ V0e @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) )
% 1.17/1.35 => ( p
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 @ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27a )
% 1.17/1.35 @ ^ [V2fn1: $i] :
% 1.17/1.35 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V2fn1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0e ) )
% 1.17/1.35 @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V3n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V2fn1 @ ( ap @ c_2Enum_2ESUC @ V3n ) ) ) @ ( ap @ ( ap @ V1f @ ( ap @ V2fn1 @ V3n ) ) @ V3n ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2Enum__Axiom,axiom,
% 1.17/1.35 ! [A_27a: del,V0e: $i] :
% 1.17/1.35 ( ( mem @ V0e @ A_27a )
% 1.17/1.35 => ! [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) )
% 1.17/1.35 => ? [V2fn: $i] :
% 1.17/1.35 ( ( mem @ V2fn @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 & ( ( ap @ V2fn @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.35 = V0e )
% 1.17/1.35 & ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.35 ( ( ap @ V2fn @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.35 = ( ap @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ V2fn @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2Ewellfounded__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0R: $i] :
% 1.17/1.35 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eprim__rec_2Ewellfounded @ A_27a ) @ V0R ) )
% 1.17/1.35 <=> ~ ? [V1f: $i] :
% 1.17/1.35 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.35 & ! [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EWF__IFF__WELLFOUNDED,axiom,
% 1.17/1.35 ! [A_27a: del,V0R: $i] :
% 1.17/1.35 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V0R ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( c_2Eprim__rec_2Ewellfounded @ A_27a ) @ V0R ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EWF__PRED,axiom,
% 1.17/1.35 ( p
% 1.17/1.35 @ ( ap @ ( c_2Erelation_2EWF @ ty_2Enum_2Enum )
% 1.17/1.35 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V0x: $i] :
% 1.17/1.35 ( lam @ ty_2Enum_2Enum
% 1.17/1.35 @ ^ [V1y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V1y ) @ ( ap @ c_2Enum_2ESUC @ V0x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EWF__LESS,axiom,
% 1.17/1.35 p @ ( ap @ ( c_2Erelation_2EWF @ ty_2Enum_2Enum ) @ c_2Eprim__rec_2E_3C ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eprim__rec_2Emeasure__def,axiom,
% 1.17/1.35 ! [A_27a: del] :
% 1.17/1.35 ( ( c_2Eprim__rec_2Emeasure @ A_27a )
% 1.17/1.35 = ( ap @ ( c_2Erelation_2Einv__image @ A_27a @ ty_2Enum_2Enum ) @ c_2Eprim__rec_2E_3C ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2EWF__measure,axiom,
% 1.17/1.35 ! [A_27a: del,V0m: $i] :
% 1.17/1.35 ( ( mem @ V0m @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( c_2Eprim__rec_2Emeasure @ A_27a ) @ V0m ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eprim__rec_2Emeasure__thm,axiom,
% 1.17/1.35 ! [A_27a: del,V0f: $i] :
% 1.17/1.35 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.35 => ! [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 => ! [V2y: $i] :
% 1.17/1.35 ( ( mem @ V2y @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eprim__rec_2Emeasure @ A_27a ) @ V0f ) @ V1x ) @ V2y ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ V1x ) ) @ ( ap @ V0f @ V2y ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 %------------------------------------------------------------------------------
% 1.17/1.35 %------------------------------------------------------------------------------
% 1.17/1.35 thf(tp_c_2Eposet_2Ebottom,type,
% 1.17/1.35 c_2Eposet_2Ebottom: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Ebottom,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Ebottom @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Ecarrier,type,
% 1.17/1.35 c_2Eposet_2Ecarrier: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Ecarrier,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Ecarrier @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Echain,type,
% 1.17/1.35 c_2Eposet_2Echain: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Echain,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Echain @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Ecomplete,type,
% 1.17/1.35 c_2Eposet_2Ecomplete: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Ecomplete,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Ecomplete @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ bool ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Econtinuous,type,
% 1.17/1.35 c_2Eposet_2Econtinuous: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Econtinuous,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Econtinuous @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Edown__continuous,type,
% 1.17/1.35 c_2Eposet_2Edown__continuous: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Edown__continuous,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Edown__continuous @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Efunction,type,
% 1.17/1.35 c_2Eposet_2Efunction: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Efunction,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eposet_2Efunction @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Egfp,type,
% 1.17/1.35 c_2Eposet_2Egfp: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Egfp,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Egfp @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Eglb,type,
% 1.17/1.35 c_2Eposet_2Eglb: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Eglb,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Eglb @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Elfp,type,
% 1.17/1.35 c_2Eposet_2Elfp: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Elfp,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Elfp @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Elub,type,
% 1.17/1.35 c_2Eposet_2Elub: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Elub,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Elub @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Emonotonic,type,
% 1.17/1.35 c_2Eposet_2Emonotonic: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Emonotonic,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Emonotonic @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Epointwise__lift,type,
% 1.17/1.35 c_2Eposet_2Epointwise__lift: del > del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Epointwise__lift,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eposet_2Epointwise__lift @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27b @ bool ) @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Eposet,type,
% 1.17/1.35 c_2Eposet_2Eposet: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Eposet,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Eposet @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ bool ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Erelation,type,
% 1.17/1.35 c_2Eposet_2Erelation: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Erelation,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Erelation @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Etop,type,
% 1.17/1.35 c_2Eposet_2Etop: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Etop,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Etop @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(tp_c_2Eposet_2Eup__continuous,type,
% 1.17/1.35 c_2Eposet_2Eup__continuous: del > $i ).
% 1.17/1.35
% 1.17/1.35 thf(mem_c_2Eposet_2Eup__continuous,axiom,
% 1.17/1.35 ! [A_27a: del] : ( mem @ ( c_2Eposet_2Eup__continuous @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Efunction__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0a: $i] :
% 1.17/1.35 ( ( mem @ V0a @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1b: $i] :
% 1.17/1.35 ( ( mem @ V1b @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Efunction @ A_27a @ A_27b ) @ V0a ) @ V1b ) @ V2f ) )
% 1.17/1.35 <=> ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0a @ V3x ) )
% 1.17/1.35 => ( p @ ( ap @ V1b @ ( ap @ V2f @ V3x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Eposet__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) )
% 1.17/1.35 <=> ( ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V2x ) ) )
% 1.17/1.35 & ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V3x ) @ V3x ) ) ) )
% 1.17/1.35 & ! [V4x: $i] :
% 1.17/1.35 ( ( mem @ V4x @ A_27a )
% 1.17/1.35 => ! [V5y: $i] :
% 1.17/1.35 ( ( mem @ V5y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V4x ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V5y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V4x ) @ V5y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V5y ) @ V4x ) ) )
% 1.17/1.35 => ( V4x = V5y ) ) ) )
% 1.17/1.35 & ! [V6x: $i] :
% 1.17/1.35 ( ( mem @ V6x @ A_27a )
% 1.17/1.35 => ! [V7y: $i] :
% 1.17/1.35 ( ( mem @ V7y @ A_27a )
% 1.17/1.35 => ! [V8z: $i] :
% 1.17/1.35 ( ( mem @ V8z @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V6x ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V7y ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V8z ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V6x ) @ V7y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V7y ) @ V8z ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V6x ) @ V8z ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Ecarrier__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) )
% 1.17/1.35 = V0s ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Erelation__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ( ap @ ( c_2Eposet_2Erelation @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) )
% 1.17/1.35 = V1r ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Etop__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Etop @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2x ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0s @ V2x ) )
% 1.17/1.35 & ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0s @ V3y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V3y ) @ V2x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Ebottom__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Ebottom @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2x ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0s @ V2x ) )
% 1.17/1.35 & ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ V0s @ V3y ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V2x ) @ V3y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Echain__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2c: $i] :
% 1.17/1.35 ( ( mem @ V2c @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Echain @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2c ) )
% 1.17/1.35 <=> ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ! [V4y: $i] :
% 1.17/1.35 ( ( mem @ V4y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V4y ) )
% 1.17/1.35 & ( p @ ( ap @ V2c @ V3x ) )
% 1.17/1.35 & ( p @ ( ap @ V2c @ V4y ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ V1r @ V3x ) @ V4y ) )
% 1.17/1.35 | ( p @ ( ap @ ( ap @ V1r @ V4y ) @ V3x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Elub__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2p: $i] :
% 1.17/1.35 ( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2p ) @ V3x ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.35 & ! [V4y: $i] :
% 1.17/1.35 ( ( mem @ V4y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V4y ) )
% 1.17/1.35 & ( p @ ( ap @ V2p @ V4y ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V4y ) @ V3x ) ) ) )
% 1.17/1.35 & ! [V5z: $i] :
% 1.17/1.35 ( ( mem @ V5z @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V5z ) )
% 1.17/1.35 & ! [V6y: $i] :
% 1.17/1.35 ( ( mem @ V6y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V6y ) )
% 1.17/1.35 & ( p @ ( ap @ V2p @ V6y ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V6y ) @ V5z ) ) ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V3x ) @ V5z ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Eglb__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2p: $i] :
% 1.17/1.35 ( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2p ) @ V3x ) )
% 1.17/1.35 <=> ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.35 & ! [V4y: $i] :
% 1.17/1.35 ( ( mem @ V4y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V4y ) )
% 1.17/1.35 & ( p @ ( ap @ V2p @ V4y ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V3x ) @ V4y ) ) ) )
% 1.17/1.35 & ! [V5z: $i] :
% 1.17/1.35 ( ( mem @ V5z @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V5z ) )
% 1.17/1.35 & ! [V6y: $i] :
% 1.17/1.35 ( ( mem @ V6y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ V0s @ V6y ) )
% 1.17/1.35 & ( p @ ( ap @ V2p @ V6y ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V5z ) @ V6y ) ) ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V5z ) @ V3x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Ecomplete__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.35 <=> ! [V1c: $i] :
% 1.17/1.35 ( ( mem @ V1c @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ V0p ) @ V1c ) @ V2x ) ) )
% 1.17/1.35 & ? [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ V0p ) @ V1c ) @ V3x ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Eposet__nonempty,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) )
% 1.17/1.35 => ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Eposet__refl,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V2x ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V2x ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Eposet__antisym,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V2x ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V3y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V2x ) @ V3y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V3y ) @ V2x ) ) )
% 1.17/1.35 => ( V2x = V3y ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Eposet__trans,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 => ! [V3y: $i] :
% 1.17/1.35 ( ( mem @ V3y @ A_27a )
% 1.17/1.35 => ! [V4z: $i] :
% 1.17/1.35 ( ( mem @ V4z @ A_27a )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V2x ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V3y ) )
% 1.17/1.35 & ( p @ ( ap @ V0s @ V4z ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V2x ) @ V3y ) )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ V1r @ V3y ) @ V4z ) ) )
% 1.17/1.35 => ( p @ ( ap @ ( ap @ V1r @ V2x ) @ V4z ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Elub__pred,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2p: $i] :
% 1.17/1.35 ( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0s @ V4j ) ) @ ( ap @ V2p @ V4j ) ) ) )
% 1.17/1.35 @ V3x ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2p ) @ V3x ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Eglb__pred,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2p: $i] :
% 1.17/1.35 ( ( mem @ V2p @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.35 => ( ( p
% 1.17/1.35 @ ( ap
% 1.17/1.35 @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V4j: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0s @ V4j ) ) @ ( ap @ V2p @ V4j ) ) ) )
% 1.17/1.35 @ V3x ) )
% 1.17/1.35 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2p ) @ V3x ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Ecomplete__up,axiom,
% 1.17/1.35 ! [A_27a: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.35 => ! [V1c: $i] :
% 1.17/1.35 ( ( mem @ V1c @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.35 => ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ V0p ) @ V1c ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Ecomplete__down,axiom,
% 1.17/1.35 ! [A_27a: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.35 => ! [V1c: $i] :
% 1.17/1.35 ( ( mem @ V1c @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.35 => ? [V2x: $i] :
% 1.17/1.35 ( ( mem @ V2x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ V0p ) @ V1c ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Ecomplete__top,axiom,
% 1.17/1.35 ! [A_27a: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) ) )
% 1.17/1.35 => ? [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( c_2Eposet_2Etop @ A_27a ) @ V0p ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Ecomplete__bottom,axiom,
% 1.17/1.35 ! [A_27a: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.35 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.35 & ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) ) )
% 1.17/1.35 => ? [V1x: $i] :
% 1.17/1.35 ( ( mem @ V1x @ A_27a )
% 1.17/1.35 & ( p @ ( ap @ ( ap @ ( c_2Eposet_2Ebottom @ A_27a ) @ V0p ) @ V1x ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Epointwise__lift__def,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0t: $i] :
% 1.17/1.35 ( ( mem @ V0t @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1s: $i] :
% 1.17/1.35 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ! [V2r: $i] :
% 1.17/1.35 ( ( mem @ V2r @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.35 => ( ( ap @ ( ap @ ( c_2Eposet_2Epointwise__lift @ A_27a @ A_27b ) @ V0t ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27b @ bool ) @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) ) @ V1s ) @ V2r ) )
% 1.17/1.35 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Eposet_2Efunction @ A_27a @ A_27b ) @ V0t ) @ V1s ) )
% 1.17/1.35 @ ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.35 @ ^ [V3f: $i] :
% 1.17/1.35 ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.35 @ ^ [V4g: $i] :
% 1.17/1.35 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 1.17/1.35 @ ( lam @ A_27a
% 1.17/1.35 @ ^ [V5x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0t @ V5x ) ) @ ( ap @ ( ap @ V2r @ ( ap @ V3f @ V5x ) ) @ ( ap @ V4g @ V5x ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(conj_thm_2Eposet_2Ecomplete__pointwise,axiom,
% 1.17/1.35 ! [A_27a: del,A_27b: del,V0p: $i] :
% 1.17/1.35 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.35 => ! [V1t: $i] :
% 1.17/1.35 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.35 => ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ ( arr @ A_27b @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Eposet_2Epointwise__lift @ A_27b @ A_27a ) @ V1t ) @ V0p ) ) ) ) ) ) ).
% 1.17/1.35
% 1.17/1.35 thf(ax_thm_2Eposet_2Emonotonic__def,axiom,
% 1.17/1.35 ! [A_27a: del,V0s: $i] :
% 1.17/1.35 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.35 => ! [V1r: $i] :
% 1.17/1.35 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.35 => ! [V2f: $i] :
% 1.17/1.35 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.35 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Emonotonic @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2f ) )
% 1.17/1.35 <=> ! [V3x: $i] :
% 1.17/1.35 ( ( mem @ V3x @ A_27a )
% 1.17/1.36 => ! [V4y: $i] :
% 1.17/1.36 ( ( mem @ V4y @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.36 & ( p @ ( ap @ V0s @ V4y ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ V1r @ V3x ) @ V4y ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ V1r @ ( ap @ V2f @ V3x ) ) @ ( ap @ V2f @ V4y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Eposet_2Eup__continuous__def,axiom,
% 1.17/1.36 ! [A_27a: del,V0s: $i] :
% 1.17/1.36 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.36 => ! [V1r: $i] :
% 1.17/1.36 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V2f: $i] :
% 1.17/1.36 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Eup__continuous @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2f ) )
% 1.17/1.36 <=> ! [V3c: $i] :
% 1.17/1.36 ( ( mem @ V3c @ ( arr @ A_27a @ bool ) )
% 1.17/1.36 => ! [V4x: $i] :
% 1.17/1.36 ( ( mem @ V4x @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Echain @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V3c ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V3c ) @ V4x ) ) )
% 1.17/1.36 => ( p
% 1.17/1.36 @ ( ap
% 1.17/1.36 @ ( ap @ ( ap @ ( c_2Eposet_2Elub @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) )
% 1.17/1.36 @ ( lam @ A_27a
% 1.17/1.36 @ ^ [V5y: $i] :
% 1.17/1.36 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.36 @ ( lam @ A_27a
% 1.17/1.36 @ ^ [V6z: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0s @ V6z ) ) @ ( ap @ V3c @ V6z ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V5y ) @ ( ap @ V2f @ V6z ) ) ) ) ) ) )
% 1.17/1.36 @ ( ap @ V2f @ V4x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Eposet_2Edown__continuous__def,axiom,
% 1.17/1.36 ! [A_27a: del,V0s: $i] :
% 1.17/1.36 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.36 => ! [V1r: $i] :
% 1.17/1.36 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V2f: $i] :
% 1.17/1.36 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Edown__continuous @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2f ) )
% 1.17/1.36 <=> ! [V3c: $i] :
% 1.17/1.36 ( ( mem @ V3c @ ( arr @ A_27a @ bool ) )
% 1.17/1.36 => ! [V4x: $i] :
% 1.17/1.36 ( ( mem @ V4x @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Echain @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V3c ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V3c ) @ V4x ) ) )
% 1.17/1.36 => ( p
% 1.17/1.36 @ ( ap
% 1.17/1.36 @ ( ap @ ( ap @ ( c_2Eposet_2Eglb @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) )
% 1.17/1.36 @ ( lam @ A_27a
% 1.17/1.36 @ ^ [V5y: $i] :
% 1.17/1.36 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.36 @ ( lam @ A_27a
% 1.17/1.36 @ ^ [V6z: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0s @ V6z ) ) @ ( ap @ V3c @ V6z ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V5y ) @ ( ap @ V2f @ V6z ) ) ) ) ) ) )
% 1.17/1.36 @ ( ap @ V2f @ V4x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Eposet_2Econtinuous__def,axiom,
% 1.17/1.36 ! [A_27a: del,V0p: $i] :
% 1.17/1.36 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Econtinuous @ A_27a ) @ V0p ) @ V1f ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ ( c_2Eposet_2Eup__continuous @ A_27a ) @ V0p ) @ V1f ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( c_2Eposet_2Edown__continuous @ A_27a ) @ V0p ) @ V1f ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Eposet_2Elfp__def,axiom,
% 1.17/1.36 ! [A_27a: del,V0s: $i] :
% 1.17/1.36 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.36 => ! [V1r: $i] :
% 1.17/1.36 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V2f: $i] :
% 1.17/1.36 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ! [V3x: $i] :
% 1.17/1.36 ( ( mem @ V3x @ A_27a )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elfp @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2f ) @ V3x ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.36 & ( ( ap @ V2f @ V3x )
% 1.17/1.36 = V3x )
% 1.17/1.36 & ! [V4y: $i] :
% 1.17/1.36 ( ( mem @ V4y @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ V0s @ V4y ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ V1r @ ( ap @ V2f @ V4y ) ) @ V4y ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ V1r @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Eposet_2Egfp__def,axiom,
% 1.17/1.36 ! [A_27a: del,V0s: $i] :
% 1.17/1.36 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.36 => ! [V1r: $i] :
% 1.17/1.36 ( ( mem @ V1r @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V2f: $i] :
% 1.17/1.36 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ! [V3x: $i] :
% 1.17/1.36 ( ( mem @ V3x @ A_27a )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Egfp @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) @ V0s ) @ V1r ) ) @ V2f ) @ V3x ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0s @ V3x ) )
% 1.17/1.36 & ( ( ap @ V2f @ V3x )
% 1.17/1.36 = V3x )
% 1.17/1.36 & ! [V4y: $i] :
% 1.17/1.36 ( ( mem @ V4y @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ V0s @ V4y ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ V1r @ V4y ) @ ( ap @ V2f @ V4y ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ V1r @ V4y ) @ V3x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Eposet_2Elfp__unique,axiom,
% 1.17/1.36 ! [A_27a: del,V0p: $i] :
% 1.17/1.36 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ! [V2x: $i] :
% 1.17/1.36 ( ( mem @ V2x @ A_27a )
% 1.17/1.36 => ! [V3x_27: $i] :
% 1.17/1.36 ( ( mem @ V3x_27 @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elfp @ A_27a ) @ V0p ) @ V1f ) @ V2x ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elfp @ A_27a ) @ V0p ) @ V1f ) @ V3x_27 ) ) )
% 1.17/1.36 => ( V2x = V3x_27 ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Eposet_2Egfp__unique,axiom,
% 1.17/1.36 ! [A_27a: del,V0p: $i] :
% 1.17/1.36 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ! [V2x: $i] :
% 1.17/1.36 ( ( mem @ V2x @ A_27a )
% 1.17/1.36 => ! [V3x_27: $i] :
% 1.17/1.36 ( ( mem @ V3x_27 @ A_27a )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Egfp @ A_27a ) @ V0p ) @ V1f ) @ V2x ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Egfp @ A_27a ) @ V0p ) @ V1f ) @ V3x_27 ) ) )
% 1.17/1.36 => ( V2x = V3x_27 ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Eposet_2Eknaster__tarski__lfp,axiom,
% 1.17/1.36 ! [A_27a: del,V0p: $i] :
% 1.17/1.36 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Efunction @ A_27a @ A_27a ) @ ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ V0p ) ) @ ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ V0p ) ) @ V1f ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( c_2Eposet_2Emonotonic @ A_27a ) @ V0p ) @ V1f ) ) )
% 1.17/1.36 => ? [V2x: $i] :
% 1.17/1.36 ( ( mem @ V2x @ A_27a )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elfp @ A_27a ) @ V0p ) @ V1f ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Eposet_2Eknaster__tarski__gfp,axiom,
% 1.17/1.36 ! [A_27a: del,V0p: $i] :
% 1.17/1.36 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Efunction @ A_27a @ A_27a ) @ ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ V0p ) ) @ ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ V0p ) ) @ V1f ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( c_2Eposet_2Emonotonic @ A_27a ) @ V0p ) @ V1f ) ) )
% 1.17/1.36 => ? [V2x: $i] :
% 1.17/1.36 ( ( mem @ V2x @ A_27a )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Egfp @ A_27a ) @ V0p ) @ V1f ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Eposet_2Eknaster__tarski,axiom,
% 1.17/1.36 ! [A_27a: del,V0p: $i] :
% 1.17/1.36 ( ( mem @ V0p @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( c_2Eposet_2Eposet @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( c_2Eposet_2Ecomplete @ A_27a ) @ V0p ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Efunction @ A_27a @ A_27a ) @ ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ V0p ) ) @ ( ap @ ( c_2Eposet_2Ecarrier @ A_27a ) @ V0p ) ) @ V1f ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( c_2Eposet_2Emonotonic @ A_27a ) @ V0p ) @ V1f ) ) )
% 1.17/1.36 => ( ? [V2x: $i] :
% 1.17/1.36 ( ( mem @ V2x @ A_27a )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Elfp @ A_27a ) @ V0p ) @ V1f ) @ V2x ) ) )
% 1.17/1.36 & ? [V3x: $i] :
% 1.17/1.36 ( ( mem @ V3x @ A_27a )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eposet_2Egfp @ A_27a ) @ V0p ) @ V1f ) @ V3x ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 %------------------------------------------------------------------------------
% 1.17/1.36 %------------------------------------------------------------------------------
% 1.17/1.36 thf(tp_c_2Earithmetic_2E_2A,type,
% 1.17/1.36 c_2Earithmetic_2E_2A: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2E_2A,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2E_2A @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2E_2A,type,
% 1.17/1.36 fo__c_2Earithmetic_2E_2A: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2E_2A,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2E_2A @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2E_2B,type,
% 1.17/1.36 c_2Earithmetic_2E_2B: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2E_2B,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2E_2B @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2E_2B,type,
% 1.17/1.36 fo__c_2Earithmetic_2E_2B: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2E_2B @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2E_2D,type,
% 1.17/1.36 c_2Earithmetic_2E_2D: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2E_2D,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2E_2D @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2E_2D,type,
% 1.17/1.36 fo__c_2Earithmetic_2E_2D: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2E_2D @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2E_3C_3D,type,
% 1.17/1.36 c_2Earithmetic_2E_3C_3D: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2E_3C_3D,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2E_3C_3D @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2E_3E,type,
% 1.17/1.36 c_2Earithmetic_2E_3E: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2E_3E,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2E_3E @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2E_3E_3D,type,
% 1.17/1.36 c_2Earithmetic_2E_3E_3D: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2E_3E_3D,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2E_3E_3D @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EABS__DIFF,type,
% 1.17/1.36 c_2Earithmetic_2EABS__DIFF: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EABS__DIFF,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EABS__DIFF @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EABS__DIFF,type,
% 1.17/1.36 fo__c_2Earithmetic_2EABS__DIFF: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EABS__DIFF,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EABS__DIFF @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EBIT1,type,
% 1.17/1.36 c_2Earithmetic_2EBIT1: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EBIT1,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EBIT1 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EBIT1,type,
% 1.17/1.36 fo__c_2Earithmetic_2EBIT1: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EBIT1,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EBIT1 @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EBIT2,type,
% 1.17/1.36 c_2Earithmetic_2EBIT2: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EBIT2,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EBIT2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EBIT2,type,
% 1.17/1.36 fo__c_2Earithmetic_2EBIT2: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EBIT2,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EBIT2 @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EDIV,type,
% 1.17/1.36 c_2Earithmetic_2EDIV: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EDIV,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EDIV @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EDIV,type,
% 1.17/1.36 fo__c_2Earithmetic_2EDIV: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EDIV,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EDIV @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EDIV2,type,
% 1.17/1.36 c_2Earithmetic_2EDIV2: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EDIV2,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EDIV2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EDIV2,type,
% 1.17/1.36 fo__c_2Earithmetic_2EDIV2: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EDIV2,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EDIV2 @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
% 1.17/1.36 tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $tType ).
% 1.17/1.36
% 1.17/1.36 thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
% 1.17/1.36 inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > $i ).
% 1.17/1.36
% 1.17/1.36 thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
% 1.17/1.36 surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
% 1.17/1.36 ! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) )
% 1.17/1.36 = X ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
% 1.17/1.36 ! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
% 1.17/1.36 ! [X: $i] :
% 1.17/1.36 ( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
% 1.17/1.36 => ( X
% 1.17/1.36 = ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
% 1.17/1.36 tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $tType ).
% 1.17/1.36
% 1.17/1.36 thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
% 1.17/1.36 inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > $i ).
% 1.17/1.36
% 1.17/1.36 thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
% 1.17/1.36 surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
% 1.17/1.36 ! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) )
% 1.17/1.36 = X ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
% 1.17/1.36 ! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
% 1.17/1.36 ! [X: $i] :
% 1.17/1.36 ( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( X
% 1.17/1.36 = ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EDIVMOD,type,
% 1.17/1.36 c_2Earithmetic_2EDIVMOD: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EDIVMOD,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EDIVMOD @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EEVEN,type,
% 1.17/1.36 c_2Earithmetic_2EEVEN: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EEVEN,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EEVEN @ ( arr @ ty_2Enum_2Enum @ bool ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EEXP,type,
% 1.17/1.36 c_2Earithmetic_2EEXP: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EEXP,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EEXP @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EEXP,type,
% 1.17/1.36 fo__c_2Earithmetic_2EEXP: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EEXP,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EEXP @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EFACT,type,
% 1.17/1.36 c_2Earithmetic_2EFACT: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EFACT,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EFACT @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EFACT,type,
% 1.17/1.36 fo__c_2Earithmetic_2EFACT: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EFACT,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EFACT @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EFUNPOW,type,
% 1.17/1.36 c_2Earithmetic_2EFUNPOW: del > $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EFUNPOW,axiom,
% 1.17/1.36 ! [A_27a: del] : ( mem @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EMAX,type,
% 1.17/1.36 c_2Earithmetic_2EMAX: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EMAX,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EMAX @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EMAX,type,
% 1.17/1.36 fo__c_2Earithmetic_2EMAX: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EMAX,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMAX @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EMIN,type,
% 1.17/1.36 c_2Earithmetic_2EMIN: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EMIN,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EMIN @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EMIN,type,
% 1.17/1.36 fo__c_2Earithmetic_2EMIN: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EMIN,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMIN @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EMOD,type,
% 1.17/1.36 c_2Earithmetic_2EMOD: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EMOD,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EMOD @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EMOD,type,
% 1.17/1.36 fo__c_2Earithmetic_2EMOD: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EMOD,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2EMOD @ X0 @ X1 ) )
% 1.17/1.36 = ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EMODEQ,type,
% 1.17/1.36 c_2Earithmetic_2EMODEQ: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EMODEQ,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EMODEQ @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2ENRC,type,
% 1.17/1.36 c_2Earithmetic_2ENRC: del > $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2ENRC,axiom,
% 1.17/1.36 ! [A_27a: del] : ( mem @ ( c_2Earithmetic_2ENRC @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2ENUMERAL,type,
% 1.17/1.36 c_2Earithmetic_2ENUMERAL: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2ENUMERAL,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2ENUMERAL @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2ENUMERAL,type,
% 1.17/1.36 fo__c_2Earithmetic_2ENUMERAL: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2ENUMERAL,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2ENUMERAL @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EODD,type,
% 1.17/1.36 c_2Earithmetic_2EODD: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EODD,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EODD @ ( arr @ ty_2Enum_2Enum @ bool ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2EZERO,type,
% 1.17/1.36 c_2Earithmetic_2EZERO: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2EZERO,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2EZERO @ ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2EZERO,type,
% 1.17/1.36 fo__c_2Earithmetic_2EZERO: tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2EZERO,axiom,
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO )
% 1.17/1.36 = c_2Earithmetic_2EZERO ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2Efindq,type,
% 1.17/1.36 c_2Earithmetic_2Efindq: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2Efindq,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2Efindq @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2Efindq,type,
% 1.17/1.36 fo__c_2Earithmetic_2Efindq: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2Efindq,axiom,
% 1.17/1.36 ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2Efindq @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2Efindq @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2Enat__elim____magic,type,
% 1.17/1.36 c_2Earithmetic_2Enat__elim____magic: $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2Enat__elim____magic,axiom,
% 1.17/1.36 mem @ c_2Earithmetic_2Enat__elim____magic @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.36
% 1.17/1.36 thf(stp_fo_c_2Earithmetic_2Enat__elim____magic,type,
% 1.17/1.36 fo__c_2Earithmetic_2Enat__elim____magic: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.36
% 1.17/1.36 thf(stp_eq_fo_c_2Earithmetic_2Enat__elim____magic,axiom,
% 1.17/1.36 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2Enat__elim____magic @ X0 ) )
% 1.17/1.36 = ( ap @ c_2Earithmetic_2Enat__elim____magic @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(tp_c_2Earithmetic_2Enum__CASE,type,
% 1.17/1.36 c_2Earithmetic_2Enum__CASE: del > $i ).
% 1.17/1.36
% 1.17/1.36 thf(mem_c_2Earithmetic_2Enum__CASE,axiom,
% 1.17/1.36 ! [A_27a: del] : ( mem @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ A_27a ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EADD,axiom,
% 1.17/1.36 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V0n )
% 1.17/1.36 & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2ENUMERAL__DEF,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 = V0x ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EALT__ZERO,axiom,
% 1.17/1.36 fo__c_2Earithmetic_2EZERO = fo__c_2Enum_2E0 ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EBIT1,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EBIT2,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2Enat__elim____magic,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2Enat__elim____magic @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V0n ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2ESUB,axiom,
% 1.17/1.36 ( ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EMULT,axiom,
% 1.17/1.36 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EEXP,axiom,
% 1.17/1.36 ( ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EGREATER__DEF,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2ELESS__OR__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( V0m = V1n ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EGREATER__OR__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( V0m = V1n ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EEVEN,axiom,
% 1.17/1.36 ( ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 <=> $true )
% 1.17/1.36 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ~ ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EODD,axiom,
% 1.17/1.36 ( ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 <=> $false )
% 1.17/1.36 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2Enum__case__def,axiom,
% 1.17/1.36 ! [A_27a: del] :
% 1.17/1.36 ( ! [V0v: $i] :
% 1.17/1.36 ( ( mem @ V0v @ A_27a )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0v ) @ V1f )
% 1.17/1.36 = V0v ) ) )
% 1.17/1.36 & ! [V2n: tp__ty_2Enum_2Enum,V3v: $i] :
% 1.17/1.36 ( ( mem @ V3v @ A_27a )
% 1.17/1.36 => ! [V4f: $i] :
% 1.17/1.36 ( ( mem @ V4f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3v ) @ V4f )
% 1.17/1.36 = ( ap @ V4f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EFUNPOW,axiom,
% 1.17/1.36 ! [A_27a: del] :
% 1.17/1.36 ( ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ! [V1x: $i] :
% 1.17/1.36 ( ( mem @ V1x @ A_27a )
% 1.17/1.36 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1x )
% 1.17/1.36 = V1x ) ) )
% 1.17/1.36 & ! [V2f: $i] :
% 1.17/1.36 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.36 => ! [V3n: tp__ty_2Enum_2Enum,V4x: $i] :
% 1.17/1.36 ( ( mem @ V4x @ A_27a )
% 1.17/1.36 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V2f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V4x )
% 1.17/1.36 = ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V2f ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ V2f @ V4x ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2ENRC,axiom,
% 1.17/1.36 ! [A_27a: del] :
% 1.17/1.36 ( ! [V0R: $i] :
% 1.17/1.36 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V1x: $i] :
% 1.17/1.36 ( ( mem @ V1x @ A_27a )
% 1.17/1.36 => ! [V2y: $i] :
% 1.17/1.36 ( ( mem @ V2y @ A_27a )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1x ) @ V2y ) )
% 1.17/1.36 <=> ( V1x = V2y ) ) ) ) )
% 1.17/1.36 & ! [V3R: $i] :
% 1.17/1.36 ( ( mem @ V3R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V4n: tp__ty_2Enum_2Enum,V5x: $i] :
% 1.17/1.36 ( ( mem @ V5x @ A_27a )
% 1.17/1.36 => ! [V6y: $i] :
% 1.17/1.36 ( ( mem @ V6y @ A_27a )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V3R ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ V5x ) @ V6y ) )
% 1.17/1.36 <=> ? [V7z: $i] :
% 1.17/1.36 ( ( mem @ V7z @ A_27a )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ V3R @ V5x ) @ V7z ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V3R ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ V7z ) @ V6y ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EONE,axiom,
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ETWO,axiom,
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENORM__0,axiom,
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2Enum__case__compute,axiom,
% 1.17/1.36 ! [A_27a: del,V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ A_27a )
% 1.17/1.36 => ! [V1g: $i] :
% 1.17/1.36 ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V0f ) @ V1g )
% 1.17/1.36 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0f ) @ ( ap @ V1g @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__NOT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( fo__c_2Enum_2E0
% 1.17/1.36 != ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = V0m ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__CLAUSES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__SYM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__COMM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__ASSOC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2Enum__CASES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ? [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__ZERO__LT__ZERO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0n != fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ( V0n = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__OR__EQ__ALT,axiom,
% 1.17/1.36 ( c_2Earithmetic_2E_3C_3D
% 1.17/1.36 = ( ap @ ( c_2Erelation_2ERTC @ ty_2Enum_2Enum )
% 1.17/1.36 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.36 @ ^ [V0x: $i] :
% 1.17/1.36 ( lam @ ty_2Enum_2Enum
% 1.17/1.36 @ ^ [V1y: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V1y ) @ ( ap @ c_2Enum_2ESUC @ V0x ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2Etransitive__LESS,axiom,
% 1.17/1.36 p @ ( ap @ ( c_2Erelation_2Etransitive @ ty_2Enum_2Enum ) @ c_2Eprim__rec_2E_3C ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__TRANS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__ANTISYM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__REV,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__MONO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__LESS__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2Etransitive__measure,axiom,
% 1.17/1.36 ! [A_27a: del,V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Eprim__rec_2Emeasure @ A_27a ) @ V0f ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__OR,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EOR__LESS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__LESS__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__SUC__EQ__COR,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 != V1n ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__NOT__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( V1n
% 1.17/1.36 != ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__0__CASES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( fo__c_2Enum_2E0 = V0m )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__CASES__IMP,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( V0m != V1n ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__CASES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__INV__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 => ( V1n = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__STRONG__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__SUC__REFL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__ADD__NONZERO,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V1n != fo__c_2Enum_2E0 )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__LESS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__LESS__EQUAL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__ANTISYM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 <=> ( V0n = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = V0m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__MONO__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__EQ__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__SUB1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 = V0m ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EPRE__SUB1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__LEFT__1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = V0m ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__RIGHT__1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 = V0m ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__CLAUSES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__SYM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__COMM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ERIGHT__ADD__DISTRIB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELEFT__ADD__DISTRIB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__ASSOC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EPRE__SUB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__EQ__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__EQ__1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 <=> ( ( ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 & ( V1n = fo__c_2Enum_2E0 ) )
% 1.17/1.36 | ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( V1n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__INV__0__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 <=> ( V1n = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EPRE__SUC__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = V1n ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EINV__PRE__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( V0m = V1n ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__SUC__NOT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__EQ__SUB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V2p )
% 1.17/1.36 <=> ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__ADD__INV,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__ADD__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__ADD__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__ADD__LCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( V0m = V1n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__MONO__ADD__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__LESS__TRANS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__LESS__EQ__TRANS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum,V3q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V3q ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V3q ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__REFL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__MULT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MONO__MULT2,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum,V3j: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ERIGHT__SUB__DISTRIB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELEFT__SUB__DISTRIB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__ADD__1,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__ADD,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__ODD__EQ__EVEN,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 != ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQUAL__ANTISYM,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 => ( V0n = V1m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__ADD__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__OR__EQ__ADD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 | ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EWOP,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ? [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 & ! [V3m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ECOMPLETE__INDUCTION,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 => ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EFORALL__NUM__THM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 & ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__SUB,axiom,
% 1.17/1.36 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__PLUS,axiom,
% 1.17/1.36 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EINV__PRE__LESS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EINV__PRE__LESS__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EPRE__LESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LESS__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__EQ__EQ__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V0m )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LESS__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LESS__OR,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__SUB__ADD__LESS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ETIMES2,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MULT__MONO,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__MONO__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) )
% 1.17/1.36 <=> ( V0m = V1i ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__SUC__EQ,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) )
% 1.17/1.36 <=> ( V2n = V1m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__EXP__MONO,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) )
% 1.17/1.36 <=> ( V2n = V3m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEQ__ADD__LCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( V1n = V2p ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEQ__ADD__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( V0m = V1n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEQ__MULT__LCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( V1n = V2p ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEQ__MULT__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( V1n = V2p ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__SUB,axiom,
% 1.17/1.36 ! [V0a: tp__ty_2Enum_2Enum,V1c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) )
% 1.17/1.36 = V0a ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__ADD__SUB,axiom,
% 1.17/1.36 ! [V0c: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.36 => ! [V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__EQUAL__0,axiom,
% 1.17/1.36 ! [V0c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__SUB__LESS,axiom,
% 1.17/1.36 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.36 => ! [V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__SUB,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum,V1c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 => ! [V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__IMP__LESS__ADD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 => ! [V2p: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LESS__EQ__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) )
% 1.17/1.36 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LESS__SUC,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__CANCEL,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.36 <=> ( V1n = V2m ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ECANCEL__SUB,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) )
% 1.17/1.36 <=> ( V1n = V2m ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__EXP__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 != fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__LESS__EXP,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__OR__EVEN,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ? [V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.36 | ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EXP__SUC__MONO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__LESS__CASES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0m = V1n )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EGREATER__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__CASES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQUAL__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V1n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__EQ__EXISTS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V1n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__EQ__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__EQ__1,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 <=> ( ( V0x
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 & ( V1y
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__EQ__ID,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V1n )
% 1.17/1.36 <=> ( ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 | ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MULT2,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__LESS__MULT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__LESS__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EFACT,axiom,
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EFACT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EFACT__LESS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__ODD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__EVEN,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ~ ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__OR__ODD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 | ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__AND__ODD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ~ ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__MULT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 | ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ~ ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__MULT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__DOUBLE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__DOUBLE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__ODD__EXISTS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ? [V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ? [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__EXISTS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ? [V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__EXISTS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ? [V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__EXP__IFF,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEVEN__EXP,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__EXP__IFF,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( V0n = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EODD__EXP,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEQ__LESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0m = V1n )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__ADD__LCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__ADD__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__LEQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__NUM__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0m != V1n )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__GREATER,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__GREATER__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__ONE__ADD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__ADD__SYM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__LESS__EQ__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__MULT__LCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__MULT__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( V1n = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__MULT__LCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__MULT__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( V1n = fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( V0m = fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( V1n = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__ADD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__SUB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__SUB,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__SUC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__LESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__LESS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__LEFT__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 <=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 = V1n )
% 1.17/1.36 | ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__RIGHT__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = V2p )
% 1.17/1.36 <=> ( ( V0m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 | ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE,axiom,
% 1.17/1.36 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 <=> ( V0n = fo__c_2Enum_2E0 ) )
% 1.17/1.36 & ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ( ( V1m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDA,axiom,
% 1.17/1.36 ! [V0k: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ? [V2r: tp__ty_2Enum_2Enum,V3q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V0k
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EDIVISION,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V1k
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EDIV2__def,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__ONE,axiom,
% 1.17/1.36 ! [V0k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0k ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__1,axiom,
% 1.17/1.36 ! [V0k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0k ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__LESS__EQ,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1k: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__UNIQUE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum,V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ? [V3r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V1k
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V3r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V2q ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__UNIQUE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ? [V3q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V1k
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V2r ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__MULT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1r ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V2q ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__MOD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V1k ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__EQ__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__MOD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__DIV,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__MULT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1r ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V1r ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__TIMES,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1q: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__TIMES__SUB,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__PLUS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1j: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__MOD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELESS__DIV__EQ__ZERO,axiom,
% 1.17/1.36 ! [V0r: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__DIV,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V1q ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__DIV__ADD__DIV,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1x: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2r ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__DIV__RWT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1m: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__MULT__MOD,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 => ! [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__ONE,axiom,
% 1.17/1.36 ! [V0q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0q ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.36 = V0q ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__1,axiom,
% 1.17/1.36 ! [V0q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0q ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 = V0q ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIVMOD__ID,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__DIV__DIV__MULT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 => ! [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__PRE,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 = V0m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__LESS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1d: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1d ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1d ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__LESS,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__MODULUS,axiom,
% 1.17/1.36 ( ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.36 & ! [V2n: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__MODULUS__LEFT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EADD__MODULUS__RIGHT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__P,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1p: tp__ty_2Enum_2Enum,V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) )
% 1.17/1.36 <=> ? [V3k: tp__ty_2Enum_2Enum,V4r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V1p
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3k ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) @ ( inj__ty_2Enum_2Enum @ V4r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4r ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) )
% 1.17/1.36 & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3k ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__P__UNIV,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ! [V3q: tp__ty_2Enum_2Enum,V4r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( V1m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V4r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4r ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3q ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__P,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1p: tp__ty_2Enum_2Enum,V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) )
% 1.17/1.36 <=> ? [V3k: tp__ty_2Enum_2Enum,V4r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V1p
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3k ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) @ ( inj__ty_2Enum_2Enum @ V4r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4r ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) )
% 1.17/1.36 & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4r ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__P__UNIV,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ! [V3q: tp__ty_2Enum_2Enum,V4r: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( V1m
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V4r ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4r ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4r ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__TIMES2,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ! [V1j: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__COMMON__FACTOR,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1p: tp__ty_2Enum_2Enum,V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2q ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EX__MOD__Y__EQ__X,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 = V0x )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__LE__MONOTONE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__LT1,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EX__LE__DIV,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EX__LT__DIV,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__LT__X,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__LE__X,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__EQ__X,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) )
% 1.17/1.36 = V0x )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EDIV__MOD__MOD__DIV,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__EQ__DIV,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 = V2z )
% 1.17/1.36 <=> ( ( V1y
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2z ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2z ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) )
% 1.17/1.36 <=> ( ( V1y
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) )
% 1.17/1.36 <=> ( ( V1y
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__EQ__0__DIVISOR,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ? [V2d: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( V1k
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2d ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__SUC,axiom,
% 1.17/1.36 ! [V0y: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.36 != ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__SUC__IFF,axiom,
% 1.17/1.36 ! [V0y: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) )
% 1.17/1.36 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.36 != ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EONE__MOD,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EONE__MOD__IFF,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__LESS__EQ,axiom,
% 1.17/1.36 ! [V0y: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2Enum__case__cong,axiom,
% 1.17/1.36 ! [A_27a: del,V0v_27: $i] :
% 1.17/1.36 ( ( mem @ V0v_27 @ A_27a )
% 1.17/1.36 => ! [V1f_27: $i] :
% 1.17/1.36 ( ( mem @ V1f_27 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ! [V2M: tp__ty_2Enum_2Enum,V3M_27: tp__ty_2Enum_2Enum,V4v: $i] :
% 1.17/1.36 ( ( mem @ V4v @ A_27a )
% 1.17/1.36 => ! [V5f: $i] :
% 1.17/1.36 ( ( mem @ V5f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ( ( ( V2M = V3M_27 )
% 1.17/1.36 & ( ( V3M_27 = fo__c_2Enum_2E0 )
% 1.17/1.36 => ( V4v = V0v_27 ) )
% 1.17/1.36 & ! [V6n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( V3M_27
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
% 1.17/1.36 => ( ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ V6n ) )
% 1.17/1.36 = ( ap @ V1f_27 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) )
% 1.17/1.36 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2M ) ) @ V4v ) @ V5f )
% 1.17/1.36 = ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3M_27 ) ) @ V0v_27 ) @ V1f_27 ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__ELIM__THM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS,axiom,
% 1.17/1.36 ! [A_27a: del,V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) )
% 1.17/1.36 => ! [V1g: $i] :
% 1.17/1.36 ( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ( ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ap @ V1g @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 = ( ap @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ( ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ap @ V1g @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.36 = ( ap @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
% 1.17/1.36 & ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ap @ V1g @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.36 = ( ap @ ( ap @ V0f @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESUB__ELIM__THM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.36 <=> ! [V3d: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( V2b
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.36 & ( ( V1a
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EPRE__ELIM__THM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ V0P @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( V1n = fo__c_2Enum_2E0 )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.36 & ( ( V1n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMULT__INCREASES,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 => ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ? [V2m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__EQ__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( ( V0n = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__LT__EXP,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 | ( V1y = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__1,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 = V0n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__EQ__1,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 <=> ( ( V0n
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 | ( V1m = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__LE__MONO,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 => ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__LT__MONO,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 => ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__INJECTIVE,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 => ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.36 <=> ( V1n = V2m ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__LE__IFF,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ( ( ( V0b = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( V2n = fo__c_2Enum_2E0 ) )
% 1.17/1.36 | ( ( V0b = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.36 | ( V0b
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.36 | ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EX__LE__X__EXP,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EX__LT__EXP__X,axiom,
% 1.17/1.36 ! [V0b: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EZERO__EXP,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EX__LT__EXP__X__IFF,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.36 | ( V0x = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__EXP__LT__MONO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__EXP__LE__MONO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.36 | ( V0n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__EXP__INJECTIVE,axiom,
% 1.17/1.36 ! [V0b1: tp__ty_2Enum_2Enum,V1b2: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b1 ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1b2 ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.36 <=> ( ( V2x = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( V0b1 = V1b2 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__SUB,axiom,
% 1.17/1.36 ! [V0p: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1q ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) )
% 1.17/1.36 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__SUB__NUMERAL,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__BASE__MULT,axiom,
% 1.17/1.36 ! [V0z: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXP__EXP__MULT,axiom,
% 1.17/1.36 ! [V0z: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EMAX__DEF,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EMIN__DEF,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__COMM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__COMM,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__ASSOC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__ASSOC,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__MAX__EQ,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( V0m = V1n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__MAX__LT,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.36 <=> ( V0m != V1n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__MAX__LE,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__MAX__PRED,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 => ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__LT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__LT,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__LE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__LE,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.36 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = V0n )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V0n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__EQ__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 & ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__EQ__0,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( ( V0m = fo__c_2Enum_2E0 )
% 1.17/1.36 | ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMIN__IDEM,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V0n ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EMAX__IDEM,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V0n ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXISTS__GREATEST,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ( ( ? [V1x: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.36 & ? [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ! [V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
% 1.17/1.36 => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) )
% 1.17/1.36 <=> ? [V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.36 & ! [V5y: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V5y ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.36 => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EEXISTS__NUM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 | ? [V2m: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EFORALL__NUM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 & ! [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EBOUNDED__FORALL__THM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) )
% 1.17/1.36 => ( ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.36 & ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EBOUNDED__EXISTS__THM,axiom,
% 1.17/1.36 ! [V0P: $i] :
% 1.17/1.36 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.36 => ! [V1c: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) )
% 1.17/1.36 => ( ? [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) )
% 1.17/1.36 & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.36 | ? [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.36 & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2Etransitive__monotone,axiom,
% 1.17/1.36 ! [A_27a: del,V0R: $i] :
% 1.17/1.36 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.36 => ! [V1f: $i] :
% 1.17/1.36 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.36 => ( ( ( p @ ( ap @ ( c_2Erelation_2Etransitive @ A_27a ) @ V0R ) )
% 1.17/1.36 & ! [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ V1f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) )
% 1.17/1.36 => ! [V3m: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ V0R @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__TC,axiom,
% 1.17/1.36 ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.36 => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE,axiom,
% 1.17/1.36 ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V0f ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED,axiom,
% 1.17/1.36 ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V0f ) )
% 1.17/1.36 => ! [V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ? [V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ! [V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.36 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EONE__ONE__UNBOUNDED,axiom,
% 1.17/1.36 ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V0f ) )
% 1.17/1.36 => ! [V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ? [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__UNBOUNDED,axiom,
% 1.17/1.36 ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.36 => ! [V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ? [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ENOT__STRICTLY__DECREASING,axiom,
% 1.17/1.36 ! [V0f: $i] :
% 1.17/1.36 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.36 => ~ ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(ax_thm_2Earithmetic_2EABS__DIFF__def,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__SYM,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__COMM,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__EQS,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__EQ__0,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.36 = fo__c_2Enum_2E0 )
% 1.17/1.36 <=> ( V0n = V1m ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__ZERO,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.36 = V0n )
% 1.17/1.36 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.36 = V0n ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__SUC,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__SUC__LE,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1z: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1z ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1z ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__PLUS__LE,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1z: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V1z ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1z ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__LE__SUM,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1z: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1z ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1z ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE,axiom,
% 1.17/1.36 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2z: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V2z ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__ADD__SAME,axiom,
% 1.17/1.36 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.36 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__SUB__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__SUB__RCANCEL,axiom,
% 1.17/1.36 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELE__SUB__LCANCEL,axiom,
% 1.17/1.36 ! [V0z: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0z ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 | ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2ELT__SUB__LCANCEL,axiom,
% 1.17/1.36 ! [V0z: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.36 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V0z ) ) ) )
% 1.17/1.36 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0z ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.36 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0z ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) ) ).
% 1.17/1.36
% 1.17/1.36 thf(conj_thm_2Earithmetic_2EABS__DIFF__SUMS,axiom,
% 1.17/1.36 ! [V0n1: tp__ty_2Enum_2Enum,V1n2: tp__ty_2Enum_2Enum,V2m1: tp__ty_2Enum_2Enum,V3m2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) @ ( inj__ty_2Enum_2Enum @ V1n2 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m1 ) ) @ ( inj__ty_2Enum_2Enum @ V3m2 ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) @ ( inj__ty_2Enum_2Enum @ V2m1 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( inj__ty_2Enum_2Enum @ V1n2 ) ) @ ( inj__ty_2Enum_2Enum @ V3m2 ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EFUNPOW__SUC,axiom,
% 1.17/1.37 ! [A_27a: del,V0f: $i] :
% 1.17/1.37 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
% 1.17/1.37 ( ( mem @ V2x @ A_27a )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2x )
% 1.17/1.37 = ( ap @ V0f @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EFUNPOW__0,axiom,
% 1.17/1.37 ! [A_27a: del,V0f: $i] :
% 1.17/1.37 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1x )
% 1.17/1.37 = V1x ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EFUNPOW__ADD,axiom,
% 1.17/1.37 ! [A_27a: del,V0f: $i] :
% 1.17/1.37 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1x )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1x ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EFUNPOW__1,axiom,
% 1.17/1.37 ! [A_27a: del,V0f: $i] :
% 1.17/1.37 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V1x )
% 1.17/1.37 = ( ap @ V0f @ V1x ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__0,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2y: $i] :
% 1.17/1.37 ( ( mem @ V2y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1x ) @ V2y ) )
% 1.17/1.37 <=> ( V1x = V2y ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__1,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2y: $i] :
% 1.17/1.37 ( ( mem @ V2y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V1x ) @ V2y ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__ADD__I,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3x: $i] :
% 1.17/1.37 ( ( mem @ V3x @ A_27a )
% 1.17/1.37 => ! [V4y: $i] :
% 1.17/1.37 ( ( mem @ V4y @ A_27a )
% 1.17/1.37 => ! [V5z: $i] :
% 1.17/1.37 ( ( mem @ V5z @ A_27a )
% 1.17/1.37 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V3x ) @ V4y ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V4y ) @ V5z ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3x ) @ V5z ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__ADD__E,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3x: $i] :
% 1.17/1.37 ( ( mem @ V3x @ A_27a )
% 1.17/1.37 => ! [V4z: $i] :
% 1.17/1.37 ( ( mem @ V4z @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3x ) @ V4z ) )
% 1.17/1.37 => ? [V5y: $i] :
% 1.17/1.37 ( ( mem @ V5y @ A_27a )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V3x ) @ V5y ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V5y ) @ V4z ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__ADD__EQN,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3x: $i] :
% 1.17/1.37 ( ( mem @ V3x @ A_27a )
% 1.17/1.37 => ! [V4z: $i] :
% 1.17/1.37 ( ( mem @ V4z @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3x ) @ V4z ) )
% 1.17/1.37 <=> ? [V5y: $i] :
% 1.17/1.37 ( ( mem @ V5y @ A_27a )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V3x ) @ V5y ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V5y ) @ V4z ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
% 1.17/1.37 ( ( mem @ V2x @ A_27a )
% 1.17/1.37 => ! [V3y: $i] :
% 1.17/1.37 ( ( mem @ V3y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2x ) @ V3y ) )
% 1.17/1.37 <=> ? [V4z: $i] :
% 1.17/1.37 ( ( mem @ V4z @ A_27a )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) @ V4z ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ V0R @ V4z ) @ V3y ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ENRC__RTC,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
% 1.17/1.37 ( ( mem @ V2x @ A_27a )
% 1.17/1.37 => ! [V3y: $i] :
% 1.17/1.37 ( ( mem @ V3y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) @ V3y ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V2x ) @ V3y ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ERTC__NRC,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2y: $i] :
% 1.17/1.37 ( ( mem @ V2y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.37 => ? [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ERTC__eq__NRC,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2y: $i] :
% 1.17/1.37 ( ( mem @ V2y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.37 <=> ? [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ETC__eq__NRC,axiom,
% 1.17/1.37 ! [A_27a: del,V0R: $i] :
% 1.17/1.37 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2y: $i] :
% 1.17/1.37 ( ( mem @ V2y @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ V0R ) @ V1x ) @ V2y ) )
% 1.17/1.37 <=> ? [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2ENRC @ A_27a ) @ V0R ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ELESS__EQUAL__DIFF,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ? [V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( V0m
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMOD__2,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EEVEN__MOD2,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ESUC__MOD,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EADD__MOD,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum,V3p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V3p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMOD__ELIM,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1x: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.37 & ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.37 & ! [V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EDOUBLE__LT,axiom,
% 1.17/1.37 ! [V0p: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EEXP2__LT,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ESUB__LESS,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2ESUB__MOD,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EONE__LT__MULT__IMP,axiom,
% 1.17/1.37 ! [V0p: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EONE__LT__MULT,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 <=> ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 | ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EONE__LT__EXP,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 <=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Earithmetic_2Efindq__def,axiom,
% 1.17/1.37 ( c_2Earithmetic_2Efindq
% 1.17/1.37 = ( ap
% 1.17/1.37 @ ( ap @ ( c_2Erelation_2EWFREC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( ap @ ( c_2Eprim__rec_2Emeasure @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
% 1.17/1.37 @ ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V0a: $i] :
% 1.17/1.37 ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1m: $i] :
% 1.17/1.37 ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2n: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V1m ) @ V2n ) ) ) ) ) ) ) )
% 1.17/1.37 @ ( lam @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum )
% 1.17/1.37 @ ^ [V3f: $i] :
% 1.17/1.37 ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V4a: $i] :
% 1.17/1.37 ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V5m: $i] :
% 1.17/1.37 ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V6n: $i] :
% 1.17/1.37 ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V6n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V4a )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V7d: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V5m ) @ V7d ) ) @ V4a ) @ ( ap @ V3f @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V4a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V5m ) @ V7d ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V6n ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2Efindq__thm,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3d: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V3d ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V3d ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2Efindq__eq__0,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 <=> ( V0a = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2Efindq__divisor,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Earithmetic_2EDIVMOD__DEF,axiom,
% 1.17/1.37 ( c_2Earithmetic_2EDIVMOD
% 1.17/1.37 = ( ap @ ( ap @ ( c_2Erelation_2EWFREC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( c_2Eprim__rec_2Emeasure @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) )
% 1.17/1.37 @ ( lam @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ^ [V0f: $i] :
% 1.17/1.37 ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1a: $i] :
% 1.17/1.37 ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2m: $i] :
% 1.17/1.37 ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3n: $i] :
% 1.17/1.37 ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2m ) @ V3n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1a ) @ V2m ) )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V4q: $i] : ( ap @ V0f @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V1a ) @ V4q ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2m ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ V3n ) @ V4q ) ) ) @ V3n ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V2m ) @ V3n ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EDIVMOD__THM,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
% 1.17/1.37 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3q: $i] : ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ V3q ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V3q ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMOD__SUB,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EDIV__SUB,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EDIVMOD__CORRECT,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.37 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EDIVMOD__CALC,axiom,
% 1.17/1.37 ( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) )
% 1.17/1.37 & ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Earithmetic_2EMODEQ__DEF,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m1: tp__ty_2Enum_2Enum,V2m2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ ( inj__ty_2Enum_2Enum @ V2m2 ) ) )
% 1.17/1.37 <=> ? [V3a: tp__ty_2Enum_2Enum,V4b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V4b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m2 ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__0__CONG,axiom,
% 1.17/1.37 ! [V0m1: tp__ty_2Enum_2Enum,V1m2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m1 ) ) @ ( inj__ty_2Enum_2Enum @ V1m2 ) ) )
% 1.17/1.37 <=> ( V0m1 = V1m2 ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m1: tp__ty_2Enum_2Enum,V2m2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ ( inj__ty_2Enum_2Enum @ V2m2 ) ) )
% 1.17/1.37 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2m2 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__THM,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m1: tp__ty_2Enum_2Enum,V2m2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ ( inj__ty_2Enum_2Enum @ V2m2 ) ) )
% 1.17/1.37 <=> ( ( ( V0n = fo__c_2Enum_2E0 )
% 1.17/1.37 & ( V1m1 = V2m2 ) )
% 1.17/1.37 | ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2m2 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__INTRO__CONG,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1e0: tp__ty_2Enum_2Enum,V2e1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1e0 ) ) @ ( inj__ty_2Enum_2Enum @ V2e1 ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1e0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2e1 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__PLUS__CONG,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x0: tp__ty_2Enum_2Enum,V2x1: tp__ty_2Enum_2Enum,V3y0: tp__ty_2Enum_2Enum,V4y1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x0 ) ) @ ( inj__ty_2Enum_2Enum @ V2x1 ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V3y0 ) ) @ ( inj__ty_2Enum_2Enum @ V4y1 ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x0 ) ) @ ( inj__ty_2Enum_2Enum @ V3y0 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2x1 ) ) @ ( inj__ty_2Enum_2Enum @ V4y1 ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__MULT__CONG,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x0: tp__ty_2Enum_2Enum,V2x1: tp__ty_2Enum_2Enum,V3y0: tp__ty_2Enum_2Enum,V4y1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x0 ) ) @ ( inj__ty_2Enum_2Enum @ V2x1 ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V3y0 ) ) @ ( inj__ty_2Enum_2Enum @ V4y1 ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1x0 ) ) @ ( inj__ty_2Enum_2Enum @ V3y0 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2x1 ) ) @ ( inj__ty_2Enum_2Enum @ V4y1 ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__REFL,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__SUC__CONG,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__EXP__CONG,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum,V3e: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V3e ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V3e ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EEXP__MOD,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2e: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__SYM,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__TRANS,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum,V3z: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V3z ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V3z ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__NUMERAL,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__MOD,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2EMODEQ__0,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ ( ap @ c_2Earithmetic_2EMODEQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2Enum__case__eq,axiom,
% 1.17/1.37 ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1zc: $i] :
% 1.17/1.37 ( ( mem @ V1zc @ A_27a )
% 1.17/1.37 => ! [V2sc: $i] :
% 1.17/1.37 ( ( mem @ V2sc @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ! [V3v: $i] :
% 1.17/1.37 ( ( mem @ V3v @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1zc ) @ V2sc )
% 1.17/1.37 = V3v )
% 1.17/1.37 <=> ( ( ( V0n = fo__c_2Enum_2E0 )
% 1.17/1.37 & ( V1zc = V3v ) )
% 1.17/1.37 | ? [V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( V0n
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) )
% 1.17/1.37 & ( ( ap @ V2sc @ ( inj__ty_2Enum_2Enum @ V4x ) )
% 1.17/1.37 = V3v ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Earithmetic_2Edatatype__num,axiom,
% 1.17/1.37 ! [A_27a: del,V0num: $i] :
% 1.17/1.37 ( ( mem @ V0num @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ A_27a ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ ( ap @ ( ap @ V0num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ c_2Enum_2ESUC ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 thf(tp_c_2Ewhile_2EHOARE__SPEC,type,
% 1.17/1.37 c_2Ewhile_2EHOARE__SPEC: del > del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Ewhile_2EHOARE__SPEC,axiom,
% 1.17/1.37 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewhile_2EHOARE__SPEC @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Ewhile_2ELEAST,type,
% 1.17/1.37 c_2Ewhile_2ELEAST: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Ewhile_2ELEAST,axiom,
% 1.17/1.37 mem @ c_2Ewhile_2ELEAST @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,type,
% 1.17/1.37 tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum: $tType ).
% 1.17/1.37
% 1.17/1.37 thf(stp_inj_c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,type,
% 1.17/1.37 inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum > $i ).
% 1.17/1.37
% 1.17/1.37 thf(stp_surj_c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,type,
% 1.17/1.37 surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum: $i > tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_inj_surj_c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,axiom,
% 1.17/1.37 ! [X: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ X ) )
% 1.17/1.37 = X ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_inj_mem_c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,axiom,
% 1.17/1.37 ! [X: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ X ) @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_iso_mem_c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,axiom,
% 1.17/1.37 ! [X: $i] :
% 1.17/1.37 ( ( mem @ X @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) )
% 1.17/1.37 => ( X
% 1.17/1.37 = ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ X ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Ewhile_2EOLEAST,type,
% 1.17/1.37 c_2Ewhile_2EOLEAST: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Ewhile_2EOLEAST,axiom,
% 1.17/1.37 mem @ c_2Ewhile_2EOLEAST @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Ewhile_2EOWHILE,type,
% 1.17/1.37 c_2Ewhile_2EOWHILE: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Ewhile_2EOWHILE,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Ewhile_2EWHILE,type,
% 1.17/1.37 c_2Ewhile_2EWHILE: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Ewhile_2EWHILE,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Ewhile_2EWHILE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EITERATION,axiom,
% 1.17/1.37 ! [A_27a: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1g: $i] :
% 1.17/1.37 ( ( mem @ V1g @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ? [V2f: $i] :
% 1.17/1.37 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 & ! [V3x: $i] :
% 1.17/1.37 ( ( mem @ V3x @ A_27a )
% 1.17/1.37 => ( ( ap @ V2f @ V3x )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ V0P @ V3x ) ) @ V3x ) @ ( ap @ V2f @ ( ap @ V1g @ V3x ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Ewhile_2EWHILE,axiom,
% 1.17/1.37 ! [A_27a: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1g: $i] :
% 1.17/1.37 ( ( mem @ V1g @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2x: $i] :
% 1.17/1.37 ( ( mem @ V2x @ A_27a )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EWHILE @ A_27a ) @ V0P ) @ V1g ) @ V2x )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ V0P @ V2x ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EWHILE @ A_27a ) @ V0P ) @ V1g ) @ ( ap @ V1g @ V2x ) ) ) @ V2x ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EWHILE__INDUCTION,axiom,
% 1.17/1.37 ! [A_27a: del,V0B: $i] :
% 1.17/1.37 ( ( mem @ V0B @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1C: $i] :
% 1.17/1.37 ( ( mem @ V1C @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2R: $i] :
% 1.17/1.37 ( ( mem @ V2R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V2R ) )
% 1.17/1.37 & ! [V3s: $i] :
% 1.17/1.37 ( ( mem @ V3s @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ V0B @ V3s ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ V2R @ ( ap @ V1C @ V3s ) ) @ V3s ) ) ) ) )
% 1.17/1.37 => ! [V4P: $i] :
% 1.17/1.37 ( ( mem @ V4P @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ( ! [V5s: $i] :
% 1.17/1.37 ( ( mem @ V5s @ A_27a )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0B @ V5s ) )
% 1.17/1.37 => ( p @ ( ap @ V4P @ ( ap @ V1C @ V5s ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V4P @ V5s ) ) ) )
% 1.17/1.37 => ! [V6v: $i] :
% 1.17/1.37 ( ( mem @ V6v @ A_27a )
% 1.17/1.37 => ( p @ ( ap @ V4P @ V6v ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Ewhile_2EHOARE__SPEC__DEF,axiom,
% 1.17/1.37 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1C: $i] :
% 1.17/1.37 ( ( mem @ V1C @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.37 => ! [V2Q: $i] :
% 1.17/1.37 ( ( mem @ V2Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EHOARE__SPEC @ A_27a @ A_27b ) @ V0P ) @ V1C ) @ V2Q ) )
% 1.17/1.37 <=> ! [V3s: $i] :
% 1.17/1.37 ( ( mem @ V3s @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ V0P @ V3s ) )
% 1.17/1.37 => ( p @ ( ap @ V2Q @ ( ap @ V1C @ V3s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EWHILE__RULE,axiom,
% 1.17/1.37 ! [A_27a: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1R: $i] :
% 1.17/1.37 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V2B: $i] :
% 1.17/1.37 ( ( mem @ V2B @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V3C: $i] :
% 1.17/1.37 ( ( mem @ V3C @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ V1R ) )
% 1.17/1.37 & ! [V4s: $i] :
% 1.17/1.37 ( ( mem @ V4s @ A_27a )
% 1.17/1.37 => ( ( p @ ( ap @ V2B @ V4s ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ V1R @ ( ap @ V3C @ V4s ) ) @ V4s ) ) ) ) )
% 1.17/1.37 => ( ( p
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ewhile_2EHOARE__SPEC @ A_27a @ A_27a )
% 1.17/1.37 @ ( lam @ A_27a
% 1.17/1.37 @ ^ [V5s: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V5s ) ) @ ( ap @ V2B @ V5s ) ) ) )
% 1.17/1.37 @ V3C )
% 1.17/1.37 @ V0P ) )
% 1.17/1.37 => ( p
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EHOARE__SPEC @ A_27a @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ewhile_2EWHILE @ A_27a ) @ V2B ) @ V3C ) )
% 1.17/1.37 @ ( lam @ A_27a
% 1.17/1.37 @ ^ [V6s: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V6s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V2B @ V6s ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Ewhile_2ELEAST__DEF,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ewhile_2ELEAST @ V0P ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EWHILE @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ c_2Enum_2ESUC ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELEAST__INTRO,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( ap @ c_2Ewhile_2ELEAST @ V0P ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELESS__LEAST,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Ewhile_2ELEAST @ V0P ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EFULL__LEAST__INTRO,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ V0P @ ( ap @ c_2Ewhile_2ELEAST @ V0P ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Ewhile_2ELEAST @ V0P ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELEAST__ELIM,axiom,
% 1.17/1.37 ! [V0Q: $i] :
% 1.17/1.37 ( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1P: $i] :
% 1.17/1.37 ( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ( ? [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1P @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.37 & ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ! [V4m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V1P @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) )
% 1.17/1.37 & ( p @ ( ap @ V1P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0Q @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0Q @ ( ap @ c_2Ewhile_2ELEAST @ V1P ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELEAST__EXISTS,axiom,
% 1.17/1.37 ! [V0p: $i] :
% 1.17/1.37 ( ( mem @ V0p @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0p @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 <=> ( ( p @ ( ap @ V0p @ ( ap @ c_2Ewhile_2ELEAST @ V0p ) ) )
% 1.17/1.37 & ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Ewhile_2ELEAST @ V0p ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V0p @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELEAST__EXISTS__IMP,axiom,
% 1.17/1.37 ! [V0p: $i] :
% 1.17/1.37 ( ( mem @ V0p @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0p @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ V0p @ ( ap @ c_2Ewhile_2ELEAST @ V0p ) ) )
% 1.17/1.37 & ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Ewhile_2ELEAST @ V0p ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V0p @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELEAST__EQ,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V1n ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) )
% 1.17/1.37 = V0x )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V2n ) ) ) )
% 1.17/1.37 = V0x ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2ELEAST__T,axiom,
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V0x: $i] : c_2Ebool_2ET ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Ewhile_2EOLEAST__def,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ c_2Ewhile_2EOLEAST @ V0P ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1n: $i] : ( ap @ V0P @ V1n ) ) ) )
% 1.17/1.37 @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2n: $i] : ( ap @ V0P @ V2n ) ) ) ) )
% 1.17/1.37 @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOLEAST__INTRO,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1Q: $i] :
% 1.17/1.37 ( ( mem @ V1Q @ ( arr @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) @ bool ) )
% 1.17/1.37 => ( ( ( ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.37 => ( p @ ( ap @ V1Q @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) )
% 1.17/1.37 & ! [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 & ! [V4m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V1Q @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V1Q @ ( ap @ c_2Ewhile_2EOLEAST @ V0P ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOLEAST__EQNS,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2EOLEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V1n ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.37 & ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2EOLEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2n: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V2n ) ) ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.37 & ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2EOLEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3n: $i] : c_2Ebool_2EF ) ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) )
% 1.17/1.37 & ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2EOLEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V4n: $i] : c_2Ebool_2ET ) ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOLEAST__EQ__NONE,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ c_2Ewhile_2EOLEAST @ V0P ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) )
% 1.17/1.37 <=> ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOLEAST__EQ__SOME,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ c_2Ewhile_2EOLEAST @ V0P ) )
% 1.17/1.37 = ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 <=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 & ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Ewhile_2EOWHILE__def,axiom,
% 1.17/1.37 ! [A_27a: del,V0G: $i] :
% 1.17/1.37 ( ( mem @ V0G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2s: $i] :
% 1.17/1.37 ( ( mem @ V2s @ A_27a )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V0G ) @ V1f ) @ V2s )
% 1.17/1.37 = ( ap
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) )
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3n: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0G @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V1f ) @ V3n ) @ V2s ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ ( c_2Eoption_2ESOME @ A_27a )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V1f )
% 1.17/1.37 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V4n: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0G @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V1f ) @ V4n ) @ V2s ) ) ) ) ) )
% 1.17/1.37 @ V2s ) ) )
% 1.17/1.37 @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOWHILE__THM,axiom,
% 1.17/1.37 ! [A_27a: del,V0G: $i] :
% 1.17/1.37 ( ( mem @ V0G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2s: $i] :
% 1.17/1.37 ( ( mem @ V2s @ A_27a )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V0G ) @ V1f ) @ V2s )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V0G @ V2s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V0G ) @ V1f ) @ ( ap @ V1f @ V2s ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOWHILE__EQ__NONE,axiom,
% 1.17/1.37 ! [A_27a: del,V0G: $i] :
% 1.17/1.37 ( ( mem @ V0G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2s: $i] :
% 1.17/1.37 ( ( mem @ V2s @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V0G ) @ V1f ) @ V2s )
% 1.17/1.37 = ( c_2Eoption_2ENONE @ A_27a ) )
% 1.17/1.37 <=> ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0G @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOWHILE__ENDCOND,axiom,
% 1.17/1.37 ! [A_27a: del,V0G: $i] :
% 1.17/1.37 ( ( mem @ V0G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2s: $i] :
% 1.17/1.37 ( ( mem @ V2s @ A_27a )
% 1.17/1.37 => ! [V3s_27: $i] :
% 1.17/1.37 ( ( mem @ V3s_27 @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V0G ) @ V1f ) @ V2s )
% 1.17/1.37 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3s_27 ) )
% 1.17/1.37 => ~ ( p @ ( ap @ V0G @ V3s_27 ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOWHILE__WHILE,axiom,
% 1.17/1.37 ! [A_27a: del,V0G: $i] :
% 1.17/1.37 ( ( mem @ V0G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V2s: $i] :
% 1.17/1.37 ( ( mem @ V2s @ A_27a )
% 1.17/1.37 => ! [V3s_27: $i] :
% 1.17/1.37 ( ( mem @ V3s_27 @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V0G ) @ V1f ) @ V2s )
% 1.17/1.37 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3s_27 ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EWHILE @ A_27a ) @ V0G ) @ V1f ) @ V2s )
% 1.17/1.37 = V3s_27 ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOWHILE__INV__IND,axiom,
% 1.17/1.37 ! [A_27a: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V1G: $i] :
% 1.17/1.37 ( ( mem @ V1G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V2f: $i] :
% 1.17/1.37 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V3s: $i] :
% 1.17/1.37 ( ( mem @ V3s @ A_27a )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0P @ V3s ) )
% 1.17/1.37 & ! [V4x: $i] :
% 1.17/1.37 ( ( mem @ V4x @ A_27a )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0P @ V4x ) )
% 1.17/1.37 & ( p @ ( ap @ V1G @ V4x ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( ap @ V2f @ V4x ) ) ) ) ) )
% 1.17/1.37 => ! [V5s_27: $i] :
% 1.17/1.37 ( ( mem @ V5s_27 @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V1G ) @ V2f ) @ V3s )
% 1.17/1.37 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5s_27 ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ V5s_27 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Ewhile_2EOWHILE__IND,axiom,
% 1.17/1.37 ! [A_27a: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1G: $i] :
% 1.17/1.37 ( ( mem @ V1G @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 => ! [V2f: $i] :
% 1.17/1.37 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ( ( ! [V3s: $i] :
% 1.17/1.37 ( ( mem @ V3s @ A_27a )
% 1.17/1.37 => ( ~ ( p @ ( ap @ V1G @ V3s ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ V0P @ V3s ) @ V3s ) ) ) )
% 1.17/1.37 & ! [V4s1: $i] :
% 1.17/1.37 ( ( mem @ V4s1 @ A_27a )
% 1.17/1.37 => ! [V5s2: $i] :
% 1.17/1.37 ( ( mem @ V5s2 @ A_27a )
% 1.17/1.37 => ( ( ( p @ ( ap @ V1G @ V4s1 ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ V0P @ ( ap @ V2f @ V4s1 ) ) @ V5s2 ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ V0P @ V4s1 ) @ V5s2 ) ) ) ) ) )
% 1.17/1.37 => ! [V6s1: $i] :
% 1.17/1.37 ( ( mem @ V6s1 @ A_27a )
% 1.17/1.37 => ! [V7s2: $i] :
% 1.17/1.37 ( ( mem @ V7s2 @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewhile_2EOWHILE @ A_27a ) @ V1G ) @ V2f ) @ V6s1 )
% 1.17/1.37 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V7s2 ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ V0P @ V6s1 ) @ V7s2 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 thf(tp_c_2Enumeral_2Eexactlog,type,
% 1.17/1.37 c_2Enumeral_2Eexactlog: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2Eexactlog,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2Eexactlog @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2Eexactlog,type,
% 1.17/1.37 fo__c_2Enumeral_2Eexactlog: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2Eexactlog,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2Eexactlog @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Enumeral_2Eexactlog @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2EiBIT__cases,type,
% 1.17/1.37 c_2Enumeral_2EiBIT__cases: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2EiBIT__cases,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Enumeral_2EiBIT__cases @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ A_27a ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2EiDUB,type,
% 1.17/1.37 c_2Enumeral_2EiDUB: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2EiDUB,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2EiDUB @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2EiDUB,type,
% 1.17/1.37 fo__c_2Enumeral_2EiDUB: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2EiDUB,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2EiDUB @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2EiSQR,type,
% 1.17/1.37 c_2Enumeral_2EiSQR: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2EiSQR,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2EiSQR @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2EiSQR,type,
% 1.17/1.37 fo__c_2Enumeral_2EiSQR: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2EiSQR,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2EiSQR @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Enumeral_2EiSQR @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2EiSUB,type,
% 1.17/1.37 c_2Enumeral_2EiSUB: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2EiSUB,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2EiSUB @ ( arr @ bool @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2EiZ,type,
% 1.17/1.37 c_2Enumeral_2EiZ: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2EiZ,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2EiZ @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2EiZ,type,
% 1.17/1.37 fo__c_2Enumeral_2EiZ: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2EiZ,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2EiZ @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Enumeral_2EiZ @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2EiiSUC,type,
% 1.17/1.37 c_2Enumeral_2EiiSUC: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2EiiSUC,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2EiiSUC @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2EiiSUC,type,
% 1.17/1.37 fo__c_2Enumeral_2EiiSUC: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2EiiSUC,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2EiiSUC @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2Einternal__mult,type,
% 1.17/1.37 c_2Enumeral_2Einternal__mult: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2Einternal__mult,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2Einternal__mult @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2Einternal__mult,type,
% 1.17/1.37 fo__c_2Enumeral_2Einternal__mult: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2Einternal__mult,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2Einternal__mult @ X0 @ X1 ) )
% 1.17/1.37 = ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2Eonecount,type,
% 1.17/1.37 c_2Enumeral_2Eonecount: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2Eonecount,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2Eonecount @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2Eonecount,type,
% 1.17/1.37 fo__c_2Enumeral_2Eonecount: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2Eonecount,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2Eonecount @ X0 @ X1 ) )
% 1.17/1.37 = ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Enumeral_2Etexp__help,type,
% 1.17/1.37 c_2Enumeral_2Etexp__help: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Enumeral_2Etexp__help,axiom,
% 1.17/1.37 mem @ c_2Enumeral_2Etexp__help @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Enumeral_2Etexp__help,type,
% 1.17/1.37 fo__c_2Enumeral_2Etexp__help: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Enumeral_2Etexp__help,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral_2Etexp__help @ X0 @ X1 ) )
% 1.17/1.37 = ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__suc,axiom,
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2EiZ,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = V0x ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2EiiSUC,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__distrib,axiom,
% 1.17/1.37 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = V0n )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = V1n )
% 1.17/1.37 & ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) ) )
% 1.17/1.37 & ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V5n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V5n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V6n: tp__ty_2Enum_2Enum,V7m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V7m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V6n ) ) @ ( inj__ty_2Enum_2Enum @ V7m ) ) ) ) )
% 1.17/1.37 & ! [V8n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V8n ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V9n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V9n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = V9n )
% 1.17/1.37 & ! [V10n: tp__ty_2Enum_2Enum,V11m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) ) )
% 1.17/1.37 & ! [V12n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V12n ) ) ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V13n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V13n ) ) ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V14n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V14n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ! [V15n: tp__ty_2Enum_2Enum,V16m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V16m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V15n ) ) @ ( inj__ty_2Enum_2Enum @ V16m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ! [V17n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V17n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V17n ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V18n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V18n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V18n ) ) ) ) )
% 1.17/1.37 & ! [V19n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V19n ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 <=> ( V19n = fo__c_2Earithmetic_2EZERO ) )
% 1.17/1.37 & ! [V20n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( fo__c_2Enum_2E0
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V20n ) ) ) )
% 1.17/1.37 <=> ( V20n = fo__c_2Earithmetic_2EZERO ) )
% 1.17/1.37 & ! [V21n: tp__ty_2Enum_2Enum,V22m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V21n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V22m ) ) ) )
% 1.17/1.37 <=> ( V21n = V22m ) )
% 1.17/1.37 & ! [V23n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V23n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ! [V24n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V24n ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V24n ) ) ) )
% 1.17/1.37 & ! [V25n: tp__ty_2Enum_2Enum,V26m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V25n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V26m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V25n ) ) @ ( inj__ty_2Enum_2Enum @ V26m ) ) ) )
% 1.17/1.37 & ! [V27n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V27n ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ! [V28n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V28n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V28n ) ) ) )
% 1.17/1.37 & ! [V29n: tp__ty_2Enum_2Enum,V30m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V29n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V30m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V30m ) ) @ ( inj__ty_2Enum_2Enum @ V29n ) ) ) )
% 1.17/1.37 & ! [V31n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V31n ) ) )
% 1.17/1.37 <=> $true )
% 1.17/1.37 & ! [V32n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V32n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V32n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 & ! [V33n: tp__ty_2Enum_2Enum,V34m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V33n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V34m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V33n ) ) @ ( inj__ty_2Enum_2Enum @ V34m ) ) ) )
% 1.17/1.37 & ! [V35n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ V35n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 <=> $true )
% 1.17/1.37 & ! [V36n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V36n ) ) )
% 1.17/1.37 <=> ( V36n = fo__c_2Enum_2E0 ) )
% 1.17/1.37 & ! [V37n: tp__ty_2Enum_2Enum,V38m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V37n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V38m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V38m ) ) @ ( inj__ty_2Enum_2Enum @ V37n ) ) ) )
% 1.17/1.37 & ! [V39n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V39n ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V39n ) ) ) )
% 1.17/1.37 & ! [V40n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V40n ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V40n ) ) ) )
% 1.17/1.37 & ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 & ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__iisuc,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__add,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = V0n )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 = V0n )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enumeral_2EiiSUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__eq,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( fo__c_2Earithmetic_2EZERO
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( fo__c_2Earithmetic_2EZERO
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( V0n = V1m ) )
% 1.17/1.37 & ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( V0n = V1m ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__lt,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 <=> $true )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 <=> $true )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__lte,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 <=> $true )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 <=> $false )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__pre,axiom,
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.37 & ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Ebit__initiality,axiom,
% 1.17/1.37 ! [A_27a: del,V0zf: $i] :
% 1.17/1.37 ( ( mem @ V0zf @ A_27a )
% 1.17/1.37 => ! [V1b1f: $i] :
% 1.17/1.37 ( ( mem @ V1b1f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) )
% 1.17/1.37 => ! [V2b2f: $i] :
% 1.17/1.37 ( ( mem @ V2b2f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) )
% 1.17/1.37 => ? [V3f: $i] :
% 1.17/1.37 ( ( mem @ V3f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 & ( ( ap @ V3f @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) )
% 1.17/1.37 = V0zf )
% 1.17/1.37 & ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ap @ V3f @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4n ) ) )
% 1.17/1.37 = ( ap @ ( ap @ V1b1f @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ ( ap @ V3f @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.37 & ! [V5n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ap @ V3f @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
% 1.17/1.37 = ( ap @ ( ap @ V2b2f @ ( inj__ty_2Enum_2Enum @ V5n ) ) @ ( ap @ V3f @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2EiBIT__cases,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ! [V0zf: $i] :
% 1.17/1.37 ( ( mem @ V0zf @ A_27a )
% 1.17/1.37 => ! [V1bf1: $i] :
% 1.17/1.37 ( ( mem @ V1bf1 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ! [V2bf2: $i] :
% 1.17/1.37 ( ( mem @ V2bf2 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ V0zf ) @ V1bf1 ) @ V2bf2 )
% 1.17/1.37 = V0zf ) ) ) )
% 1.17/1.37 & ! [V3n: tp__ty_2Enum_2Enum,V4zf: $i] :
% 1.17/1.37 ( ( mem @ V4zf @ A_27a )
% 1.17/1.37 => ! [V5bf1: $i] :
% 1.17/1.37 ( ( mem @ V5bf1 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ! [V6bf2: $i] :
% 1.17/1.37 ( ( mem @ V6bf2 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ A_27a ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V4zf ) @ V5bf1 ) @ V6bf2 )
% 1.17/1.37 = ( ap @ V5bf1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) )
% 1.17/1.37 & ! [V7n: tp__ty_2Enum_2Enum,V8zf: $i] :
% 1.17/1.37 ( ( mem @ V8zf @ A_27a )
% 1.17/1.37 => ! [V9bf1: $i] :
% 1.17/1.37 ( ( mem @ V9bf1 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ! [V10bf2: $i] :
% 1.17/1.37 ( ( mem @ V10bf2 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ A_27a ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) @ V8zf ) @ V9bf1 ) @ V10bf2 )
% 1.17/1.37 = ( ap @ V10bf2 @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2EiDUB,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2EiSUB__DEF,axiom,
% 1.17/1.37 ( ! [V0b: $i] :
% 1.17/1.37 ( ( mem @ V0b @ bool )
% 1.17/1.37 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ V0b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO ) )
% 1.17/1.37 & ! [V2b: $i] :
% 1.17/1.37 ( ( mem @ V2b @ bool )
% 1.17/1.37 => ! [V3n: tp__ty_2Enum_2Enum,V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ V2b ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V2b )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V5m: $i] : ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V5m ) ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V6m: $i] : ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V6m ) ) ) ) )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V7m: $i] : ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V7m ) ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V8m: $i] : ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V8m ) ) ) ) ) ) ) )
% 1.17/1.37 & ! [V9b: $i] :
% 1.17/1.37 ( ( mem @ V9b @ bool )
% 1.17/1.37 => ! [V10n: tp__ty_2Enum_2Enum,V11x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ V9b ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) @ ( inj__ty_2Enum_2Enum @ V11x ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V9b )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V11x ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V10n ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V12m: $i] : ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ V12m ) ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V13m: $i] : ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ V13m ) ) ) ) )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Enumeral_2EiBIT__cases @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V11x ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V10n ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V14m: $i] : ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ V14m ) ) ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V15m: $i] : ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ V15m ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Ebit__induction,axiom,
% 1.17/1.37 ! [V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.37 & ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) )
% 1.17/1.37 => ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2EiSUB__THM,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1b: $i] :
% 1.17/1.37 ( ( mem @ V1b @ bool )
% 1.17/1.37 => ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = V2n )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__sub,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ c_2Enumeral_2EiSUB @ c_2Ebool_2ET ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2EiDUB__removal,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__mult,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2EiSQR,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiSQR @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__exp,axiom,
% 1.17/1.37 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Enumeral_2EiSQR @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) )
% 1.17/1.37 & ! [V3n: tp__ty_2Enum_2Enum,V4m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Enumeral_2EiSQR @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ c_2Enumeral_2EiSQR @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V4m ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__evenodd,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 & ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ~ ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 & ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ( p @ ( ap @ c_2Earithmetic_2EODD @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__fact,axiom,
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EFACT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2EFACT @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EFACT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2EFACT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__funpow,axiom,
% 1.17/1.37 ! [A_27a: del,V0f: $i] :
% 1.17/1.37 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.37 => ! [V1x: $i] :
% 1.17/1.37 ( ( mem @ V1x @ A_27a )
% 1.17/1.37 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1x )
% 1.17/1.37 = V1x )
% 1.17/1.37 & ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ V1x )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) @ ( ap @ V0f @ V1x ) ) )
% 1.17/1.37 & ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ V1x )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ A_27a ) @ V0f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ V0f @ V1x ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__MIN,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__MAX,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = V0x )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = V0x )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Edivmod__POS,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.37 => ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
% 1.17/1.37 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3q: $i] : ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ V3q ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V3q ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Earithmetic_2Efindq @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC,axiom,
% 1.17/1.37 ( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) )
% 1.17/1.37 & ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) )
% 1.17/1.37 & ! [V4m: tp__ty_2Enum_2Enum,V5n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V4m ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4m ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) ) ) ) )
% 1.17/1.37 & ! [V6m: tp__ty_2Enum_2Enum,V7n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V6m ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EDIVMOD @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V6m ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__div2,axiom,
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = fo__c_2Enum_2E0 )
% 1.17/1.37 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2Etexp__help__def,axiom,
% 1.17/1.37 ( ! [V0acc: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0acc ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0acc ) ) ) )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum,V2acc: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2acc ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2acc ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Etexp__help__thm,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Etexp__help0,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Enumeral__texp__help,axiom,
% 1.17/1.37 ! [V0acc: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0acc ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0acc ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0acc ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0acc ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0acc ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0acc ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2ETWO__EXP__THM,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2Eonecount__def,axiom,
% 1.17/1.37 ( ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.37 = V0x )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) )
% 1.17/1.37 & ! [V3n: tp__ty_2Enum_2Enum,V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2Eexactlog__def,axiom,
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2Eexactlog @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2Eexactlog @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2Eexactlog @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2x ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ V2x ) ) ) )
% 1.17/1.37 @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Eonecount__characterisation,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 => ( V0n
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Enumeral_2Eonecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Eexactlog__characterisation,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2Eexactlog @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.37 => ( V0n
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Enumeral_2Einternal__mult__def,axiom,
% 1.17/1.37 c_2Enumeral_2Einternal__mult = c_2Earithmetic_2E_2A ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2EDIV2__BIT1,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.37 = V0x ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Eenumeral__mult,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ V3n ) ) @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EDIV2 @ V3n ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Enumeral_2Eexactlog @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V4m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ V4m ) ) @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EDIV2 @ V4m ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Enumeral_2Eexactlog @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V5m: $i] :
% 1.17/1.37 ( ap
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V6n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ V5m ) ) @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EDIV2 @ V5m ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ V6n ) ) @ ( ap @ ( ap @ c_2Enumeral_2Etexp__help @ ( ap @ c_2Earithmetic_2EDIV2 @ V6n ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Enumeral_2Eexactlog @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ c_2Enumeral_2Eexactlog @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Enumeral_2Einternal__mult__characterisation,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.37 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Enumeral_2EiZ @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Enumeral_2Einternal__mult @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 thf(tp_c_2Edivides_2EPRIMES,type,
% 1.17/1.37 c_2Edivides_2EPRIMES: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Edivides_2EPRIMES,axiom,
% 1.17/1.37 mem @ c_2Edivides_2EPRIMES @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Edivides_2EPRIMES,type,
% 1.17/1.37 fo__c_2Edivides_2EPRIMES: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Edivides_2EPRIMES,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Edivides_2EPRIMES @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Edivides_2Edivides,type,
% 1.17/1.37 c_2Edivides_2Edivides: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Edivides_2Edivides,axiom,
% 1.17/1.37 mem @ c_2Edivides_2Edivides @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Edivides_2Eprime,type,
% 1.17/1.37 c_2Edivides_2Eprime: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Edivides_2Eprime,axiom,
% 1.17/1.37 mem @ c_2Edivides_2Eprime @ ( arr @ ty_2Enum_2Enum @ bool ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Edivides_2Edivides__def,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 <=> ? [V2q: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( V1b
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2q ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EALL__DIVIDES__0,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EZERO__DIVIDES,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.37 <=> ( V0m = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__REFL,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__TRANS,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EONE__DIVIDES__ALL,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__ONE,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 <=> ( V0x
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__ADD__1,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__ADD__2,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__SUB,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__LE,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__LEQ__OR__ZERO,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 | ( V1n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2ENOT__LT__DIVIDES,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) )
% 1.17/1.37 => ~ ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__ANTISYM,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) )
% 1.17/1.37 => ( V0a = V1b ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__MULT,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__MULT__LEFT,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.37 <=> ( ( V1m = fo__c_2Enum_2E0 )
% 1.17/1.37 | ( V0n
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EDIVIDES__FACT,axiom,
% 1.17/1.37 ! [V0b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2ELEQ__DIVIDES__FACT,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2EFACT @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Edivides_2Eprime__def,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.37 <=> ( ( V0a
% 1.17/1.37 != ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ! [V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.37 => ( ( V1b = V0a )
% 1.17/1.37 | ( V1b
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2ENOT__PRIME__0,axiom,
% 1.17/1.37 ~ ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2ENOT__PRIME__1,axiom,
% 1.17/1.37 ~ ( p @ ( ap @ c_2Edivides_2Eprime @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIME__2,axiom,
% 1.17/1.37 p @ ( ap @ c_2Edivides_2Eprime @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIME__3,axiom,
% 1.17/1.37 p @ ( ap @ c_2Edivides_2Eprime @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIME__POS,axiom,
% 1.17/1.37 ! [V0p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EONE__LT__PRIME,axiom,
% 1.17/1.37 ! [V0p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2Eprime__divides__only__self,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.37 & ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 => ( V0m = V1n ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIME__FACTOR,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( V0n
% 1.17/1.37 != ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 => ? [V1p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V1p ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EEUCLID,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ? [V1p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) )
% 1.17/1.37 & ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Edivides_2EPRIMES__def,axiom,
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.37 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Edivides_2EPRIMES @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum
% 1.17/1.37 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1p: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Edivides_2Eprime @ V1p ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1p ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EprimePRIMES,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ c_2Edivides_2Eprime @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EINFINITE__PRIMES,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2ELT__PRIMES,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIMES__11,axiom,
% 1.17/1.37 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.37 => ( V0m = V1n ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EINDEX__LESS__PRIMES,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EEUCLID__PRIMES,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ? [V1i: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2ENEXT__LARGER__PRIME,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ? [V1i: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) )
% 1.17/1.37 & ! [V2j: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2j ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V2j ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIMES__NO__GAP,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum,V1p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.37 & ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) )
% 1.17/1.37 => $false ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIMES__ONTO,axiom,
% 1.17/1.37 ! [V0p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.37 => ? [V1i: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
% 1.17/1.37 = V0p ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EPRIME__INDEX,axiom,
% 1.17/1.37 ! [V0p: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.37 <=> ? [V1i: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( V0p
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EONE__LT__PRIMES,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2EZERO__LT__PRIMES,axiom,
% 1.17/1.37 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Edivides_2EPRIMES @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Edivides_2Ecompute__divides,axiom,
% 1.17/1.37 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.37 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 %------------------------------------------------------------------------------
% 1.17/1.37 thf(tp_ty_2Eind__type_2Erecspace,type,
% 1.17/1.37 ty_2Eind__type_2Erecspace: del > del ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EBOTTOM,type,
% 1.17/1.37 c_2Eind__type_2EBOTTOM: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EBOTTOM,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EBOTTOM @ A_27a ) @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ECONSTR,type,
% 1.17/1.37 c_2Eind__type_2ECONSTR: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ECONSTR,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EFCONS,type,
% 1.17/1.37 c_2Eind__type_2EFCONS: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EFCONS,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EFCONS @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EFNIL,type,
% 1.17/1.37 c_2Eind__type_2EFNIL: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EFNIL,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EFNIL @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EINJA,type,
% 1.17/1.37 c_2Eind__type_2EINJA: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EINJA,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EINJA @ A_27a ) @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EINJF,type,
% 1.17/1.37 c_2Eind__type_2EINJF: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EINJF,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EINJF @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EINJN,type,
% 1.17/1.37 c_2Eind__type_2EINJN: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EINJN,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EINJN @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EINJP,type,
% 1.17/1.37 c_2Eind__type_2EINJP: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EINJP,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EINJP @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EISO,type,
% 1.17/1.37 c_2Eind__type_2EISO: del > del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EISO,axiom,
% 1.17/1.37 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eind__type_2EISO @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ bool ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ENUMFST,type,
% 1.17/1.37 c_2Eind__type_2ENUMFST: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ENUMFST,axiom,
% 1.17/1.37 mem @ c_2Eind__type_2ENUMFST @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Eind__type_2ENUMFST,type,
% 1.17/1.37 fo__c_2Eind__type_2ENUMFST: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Eind__type_2ENUMFST,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eind__type_2ENUMFST @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Eind__type_2ENUMFST @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ENUMLEFT,type,
% 1.17/1.37 c_2Eind__type_2ENUMLEFT: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ENUMLEFT,axiom,
% 1.17/1.37 mem @ c_2Eind__type_2ENUMLEFT @ ( arr @ ty_2Enum_2Enum @ bool ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ENUMPAIR,type,
% 1.17/1.37 c_2Eind__type_2ENUMPAIR: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ENUMPAIR,axiom,
% 1.17/1.37 mem @ c_2Eind__type_2ENUMPAIR @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Eind__type_2ENUMPAIR,type,
% 1.17/1.37 fo__c_2Eind__type_2ENUMPAIR: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Eind__type_2ENUMPAIR,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eind__type_2ENUMPAIR @ X0 @ X1 ) )
% 1.17/1.37 = ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ENUMRIGHT,type,
% 1.17/1.37 c_2Eind__type_2ENUMRIGHT: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ENUMRIGHT,axiom,
% 1.17/1.37 mem @ c_2Eind__type_2ENUMRIGHT @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Eind__type_2ENUMRIGHT,type,
% 1.17/1.37 fo__c_2Eind__type_2ENUMRIGHT: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Eind__type_2ENUMRIGHT,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eind__type_2ENUMRIGHT @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Eind__type_2ENUMRIGHT @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ENUMSND,type,
% 1.17/1.37 c_2Eind__type_2ENUMSND: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ENUMSND,axiom,
% 1.17/1.37 mem @ c_2Eind__type_2ENUMSND @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.37
% 1.17/1.37 thf(stp_fo_c_2Eind__type_2ENUMSND,type,
% 1.17/1.37 fo__c_2Eind__type_2ENUMSND: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.37
% 1.17/1.37 thf(stp_eq_fo_c_2Eind__type_2ENUMSND,axiom,
% 1.17/1.37 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Eind__type_2ENUMSND @ X0 ) )
% 1.17/1.37 = ( ap @ c_2Eind__type_2ENUMSND @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2ENUMSUM,type,
% 1.17/1.37 c_2Eind__type_2ENUMSUM: $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2ENUMSUM,axiom,
% 1.17/1.37 mem @ c_2Eind__type_2ENUMSUM @ ( arr @ bool @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EZBOT,type,
% 1.17/1.37 c_2Eind__type_2EZBOT: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EZBOT,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EZBOT @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EZCONSTR,type,
% 1.17/1.37 c_2Eind__type_2EZCONSTR: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EZCONSTR,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2EZRECSPACE,type,
% 1.17/1.37 c_2Eind__type_2EZRECSPACE: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2EZRECSPACE,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ bool ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2Edest__rec,type,
% 1.17/1.37 c_2Eind__type_2Edest__rec: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2Edest__rec,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2Edest__rec @ A_27a ) @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(tp_c_2Eind__type_2Emk__rec,type,
% 1.17/1.37 c_2Eind__type_2Emk__rec: del > $i ).
% 1.17/1.37
% 1.17/1.37 thf(mem_c_2Eind__type_2Emk__rec,axiom,
% 1.17/1.37 ! [A_27a: del] : ( mem @ ( c_2Eind__type_2Emk__rec @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EINJ__INVERSE2,axiom,
% 1.17/1.37 ! [A_27A: del,A_27B: del,A_27C: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ A_27A @ ( arr @ A_27B @ A_27C ) ) )
% 1.17/1.37 => ( ! [V1x1: $i] :
% 1.17/1.37 ( ( mem @ V1x1 @ A_27A )
% 1.17/1.37 => ! [V2y1: $i] :
% 1.17/1.37 ( ( mem @ V2y1 @ A_27B )
% 1.17/1.37 => ! [V3x2: $i] :
% 1.17/1.37 ( ( mem @ V3x2 @ A_27A )
% 1.17/1.37 => ! [V4y2: $i] :
% 1.17/1.37 ( ( mem @ V4y2 @ A_27B )
% 1.17/1.37 => ( ( ( ap @ ( ap @ V0P @ V1x1 ) @ V2y1 )
% 1.17/1.37 = ( ap @ ( ap @ V0P @ V3x2 ) @ V4y2 ) )
% 1.17/1.37 <=> ( ( V1x1 = V3x2 )
% 1.17/1.37 & ( V2y1 = V4y2 ) ) ) ) ) ) )
% 1.17/1.37 => ? [V5X: $i] :
% 1.17/1.37 ( ( mem @ V5X @ ( arr @ A_27C @ A_27A ) )
% 1.17/1.37 & ? [V6Y: $i] :
% 1.17/1.37 ( ( mem @ V6Y @ ( arr @ A_27C @ A_27B ) )
% 1.17/1.37 & ! [V7x: $i] :
% 1.17/1.37 ( ( mem @ V7x @ A_27A )
% 1.17/1.37 => ! [V8y: $i] :
% 1.17/1.37 ( ( mem @ V8y @ A_27B )
% 1.17/1.37 => ( ( ( ap @ V5X @ ( ap @ ( ap @ V0P @ V7x ) @ V8y ) )
% 1.17/1.37 = V7x )
% 1.17/1.37 & ( ( ap @ V6Y @ ( ap @ ( ap @ V0P @ V7x ) @ V8y ) )
% 1.17/1.37 = V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2ENUMPAIR,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ENUMPAIR__INJ__LEMMA,axiom,
% 1.17/1.37 ! [V0x1: tp__ty_2Enum_2Enum,V1y1: tp__ty_2Enum_2Enum,V2x2: tp__ty_2Enum_2Enum,V3y2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V0x1 ) ) @ ( inj__ty_2Enum_2Enum @ V1y1 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V2x2 ) ) @ ( inj__ty_2Enum_2Enum @ V3y2 ) ) ) )
% 1.17/1.37 => ( V0x1 = V2x2 ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ENUMPAIR__INJ,axiom,
% 1.17/1.37 ! [V0x1: tp__ty_2Enum_2Enum,V1y1: tp__ty_2Enum_2Enum,V2x2: tp__ty_2Enum_2Enum,V3y2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V0x1 ) ) @ ( inj__ty_2Enum_2Enum @ V1y1 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V2x2 ) ) @ ( inj__ty_2Enum_2Enum @ V3y2 ) ) ) )
% 1.17/1.37 <=> ( ( V0x1 = V2x2 )
% 1.17/1.37 & ( V1y1 = V3y2 ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2ENUMPAIR__DEST,axiom,
% 1.17/1.37 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eind__type_2ENUMFST @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 = V0x )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eind__type_2ENUMSND @ ( ap @ ( ap @ c_2Eind__type_2ENUMPAIR @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 = V1y ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2ENUMSUM,axiom,
% 1.17/1.37 ! [V0b: $i] :
% 1.17/1.37 ( ( mem @ V0b @ bool )
% 1.17/1.37 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMSUM @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V0b ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ENUMSUM__INJ,axiom,
% 1.17/1.37 ! [V0b1: $i] :
% 1.17/1.37 ( ( mem @ V0b1 @ bool )
% 1.17/1.37 => ! [V1x1: tp__ty_2Enum_2Enum,V2b2: $i] :
% 1.17/1.37 ( ( mem @ V2b2 @ bool )
% 1.17/1.37 => ! [V3x2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMSUM @ V0b1 ) @ ( inj__ty_2Enum_2Enum @ V1x1 ) ) )
% 1.17/1.37 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Eind__type_2ENUMSUM @ V2b2 ) @ ( inj__ty_2Enum_2Enum @ V3x2 ) ) ) )
% 1.17/1.37 <=> ( ( ( p @ V0b1 )
% 1.17/1.37 <=> ( p @ V2b2 ) )
% 1.17/1.37 & ( V1x1 = V3x2 ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2ENUMSUM__DEST,axiom,
% 1.17/1.37 ! [V0x: $i] :
% 1.17/1.37 ( ( mem @ V0x @ bool )
% 1.17/1.37 => ! [V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( p @ ( ap @ c_2Eind__type_2ENUMLEFT @ ( ap @ ( ap @ c_2Eind__type_2ENUMSUM @ V0x ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 <=> ( p @ V0x ) )
% 1.17/1.37 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eind__type_2ENUMRIGHT @ ( ap @ ( ap @ c_2Eind__type_2ENUMSUM @ V0x ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.37 = V1y ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EINJN,axiom,
% 1.17/1.37 ! [A_27a: del,V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ap @ ( c_2Eind__type_2EINJN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
% 1.17/1.37 = ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1n: $i] :
% 1.17/1.37 ( lam @ A_27a
% 1.17/1.37 @ ^ [V2a: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V1n ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EINJN__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0n1: tp__ty_2Enum_2Enum,V1n2: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ( ap @ ( c_2Eind__type_2EINJN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n1 ) )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2EINJN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n2 ) ) )
% 1.17/1.37 <=> ( V0n1 = V1n2 ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EINJA,axiom,
% 1.17/1.37 ! [A_27a: del,V0a: $i] :
% 1.17/1.37 ( ( mem @ V0a @ A_27a )
% 1.17/1.37 => ( ( ap @ ( c_2Eind__type_2EINJA @ A_27a ) @ V0a )
% 1.17/1.37 = ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1n: $i] :
% 1.17/1.37 ( lam @ A_27a
% 1.17/1.37 @ ^ [V2b: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2b ) @ V0a ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EINJA__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0a1: $i] :
% 1.17/1.37 ( ( mem @ V0a1 @ A_27a )
% 1.17/1.37 => ! [V1a2: $i] :
% 1.17/1.37 ( ( mem @ V1a2 @ A_27a )
% 1.17/1.37 => ( ( ( ap @ ( c_2Eind__type_2EINJA @ A_27a ) @ V0a1 )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2EINJA @ A_27a ) @ V1a2 ) )
% 1.17/1.37 <=> ( V0a1 = V1a2 ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EINJF,axiom,
% 1.17/1.37 ! [A_27a: del,V0f: $i] :
% 1.17/1.37 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ( ap @ ( c_2Eind__type_2EINJF @ A_27a ) @ V0f )
% 1.17/1.37 = ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V1n: $i] : ( ap @ ( ap @ V0f @ ( ap @ c_2Eind__type_2ENUMFST @ V1n ) ) @ ( ap @ c_2Eind__type_2ENUMSND @ V1n ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EINJF__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0f1: $i] :
% 1.17/1.37 ( ( mem @ V0f1 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ! [V1f2: $i] :
% 1.17/1.37 ( ( mem @ V1f2 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ( ( ap @ ( c_2Eind__type_2EINJF @ A_27a ) @ V0f1 )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2EINJF @ A_27a ) @ V1f2 ) )
% 1.17/1.37 <=> ( V0f1 = V1f2 ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EINJP,axiom,
% 1.17/1.37 ! [A_27a: del,V0f1: $i] :
% 1.17/1.37 ( ( mem @ V0f1 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1f2: $i] :
% 1.17/1.37 ( ( mem @ V1f2 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( c_2Eind__type_2EINJP @ A_27a ) @ V0f1 ) @ V1f2 )
% 1.17/1.37 = ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V2n: $i] :
% 1.17/1.37 ( lam @ A_27a
% 1.17/1.37 @ ^ [V3a: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ c_2Eind__type_2ENUMLEFT @ V2n ) ) @ ( ap @ ( ap @ V0f1 @ ( ap @ c_2Eind__type_2ENUMRIGHT @ V2n ) ) @ V3a ) ) @ ( ap @ ( ap @ V1f2 @ ( ap @ c_2Eind__type_2ENUMRIGHT @ V2n ) ) @ V3a ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EINJP__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0f1: $i] :
% 1.17/1.37 ( ( mem @ V0f1 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1f1_27: $i] :
% 1.17/1.37 ( ( mem @ V1f1_27 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V2f2: $i] :
% 1.17/1.37 ( ( mem @ V2f2 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V3f2_27: $i] :
% 1.17/1.37 ( ( mem @ V3f2_27 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( c_2Eind__type_2EINJP @ A_27a ) @ V0f1 ) @ V2f2 )
% 1.17/1.37 = ( ap @ ( ap @ ( c_2Eind__type_2EINJP @ A_27a ) @ V1f1_27 ) @ V3f2_27 ) )
% 1.17/1.37 <=> ( ( V0f1 = V1f1_27 )
% 1.17/1.37 & ( V2f2 = V3f2_27 ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EZCONSTR,axiom,
% 1.17/1.37 ! [A_27a: del,V0c: tp__ty_2Enum_2Enum,V1i: $i] :
% 1.17/1.37 ( ( mem @ V1i @ A_27a )
% 1.17/1.37 => ! [V2r: $i] :
% 1.17/1.37 ( ( mem @ V2r @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ V1i ) @ V2r )
% 1.17/1.37 = ( ap @ ( ap @ ( c_2Eind__type_2EINJP @ A_27a ) @ ( ap @ ( c_2Eind__type_2EINJN @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0c ) ) ) ) @ ( ap @ ( ap @ ( c_2Eind__type_2EINJP @ A_27a ) @ ( ap @ ( c_2Eind__type_2EINJA @ A_27a ) @ V1i ) ) @ ( ap @ ( c_2Eind__type_2EINJF @ A_27a ) @ V2r ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EZBOT,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ( c_2Eind__type_2EZBOT @ A_27a )
% 1.17/1.37 = ( ap @ ( ap @ ( c_2Eind__type_2EINJP @ A_27a ) @ ( ap @ ( c_2Eind__type_2EINJN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.37 @ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 @ ( lam @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 @ ^ [V0z: $i] : c_2Ebool_2ET ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EZCONSTR__ZBOT,axiom,
% 1.17/1.37 ! [A_27a: del,V0c: tp__ty_2Enum_2Enum,V1i: $i] :
% 1.17/1.37 ( ( mem @ V1i @ A_27a )
% 1.17/1.37 => ! [V2r: $i] :
% 1.17/1.37 ( ( mem @ V2r @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ V1i ) @ V2r )
% 1.17/1.37 != ( c_2Eind__type_2EZBOT @ A_27a ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EZRECSPACE__def,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ( c_2Eind__type_2EZRECSPACE @ A_27a )
% 1.17/1.37 = ( lam @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 @ ^ [V0a0: $i] :
% 1.17/1.37 ( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ bool ) )
% 1.17/1.37 @ ( lam @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ bool )
% 1.17/1.37 @ ^ [V1ZRECSPACE_27: $i] :
% 1.17/1.37 ( ap
% 1.17/1.37 @ ( ap @ c_2Emin_2E_3D_3D_3E
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2E_21 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 @ ( lam @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) )
% 1.17/1.37 @ ^ [V2a0: $i] :
% 1.17/1.37 ( ap
% 1.17/1.37 @ ( ap @ c_2Emin_2E_3D_3D_3E
% 1.17/1.37 @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) @ V2a0 ) @ ( c_2Eind__type_2EZBOT @ A_27a ) ) )
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3c: $i] :
% 1.17/1.37 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.37 @ ( lam @ A_27a
% 1.17/1.37 @ ^ [V4i: $i] :
% 1.17/1.37 ( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 @ ( lam @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 @ ^ [V5r: $i] :
% 1.17/1.37 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) @ V2a0 ) @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ V3c ) @ V4i ) @ V5r ) ) )
% 1.17/1.37 @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V6n: $i] : ( ap @ V1ZRECSPACE_27 @ ( ap @ V5r @ V6n ) ) ) ) ) ) ) ) ) ) ) ) )
% 1.17/1.37 @ ( ap @ V1ZRECSPACE_27 @ V2a0 ) ) ) ) )
% 1.17/1.37 @ ( ap @ V1ZRECSPACE_27 @ V0a0 ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EZRECSPACE__rules,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ ( c_2Eind__type_2EZBOT @ A_27a ) ) )
% 1.17/1.37 & ! [V0c: tp__ty_2Enum_2Enum,V1i: $i] :
% 1.17/1.37 ( ( mem @ V1i @ A_27a )
% 1.17/1.37 => ! [V2r: $i] :
% 1.17/1.37 ( ( mem @ V2r @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ ( ap @ V2r @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ V1i ) @ V2r ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EZRECSPACE__ind,axiom,
% 1.17/1.37 ! [A_27a: del,V0ZRECSPACE_27: $i] :
% 1.17/1.37 ( ( mem @ V0ZRECSPACE_27 @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ bool ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0ZRECSPACE_27 @ ( c_2Eind__type_2EZBOT @ A_27a ) ) )
% 1.17/1.37 & ! [V1c: tp__ty_2Enum_2Enum,V2i: $i] :
% 1.17/1.37 ( ( mem @ V2i @ A_27a )
% 1.17/1.37 => ! [V3r: $i] :
% 1.17/1.37 ( ( mem @ V3r @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ! [V4n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0ZRECSPACE_27 @ ( ap @ V3r @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0ZRECSPACE_27 @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ V2i ) @ V3r ) ) ) ) ) ) )
% 1.17/1.37 => ! [V5a0: $i] :
% 1.17/1.37 ( ( mem @ V5a0 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ V5a0 ) )
% 1.17/1.37 => ( p @ ( ap @ V0ZRECSPACE_27 @ V5a0 ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EZRECSPACE__strongind,axiom,
% 1.17/1.37 ! [A_27a: del,V0ZRECSPACE_27: $i] :
% 1.17/1.37 ( ( mem @ V0ZRECSPACE_27 @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ bool ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0ZRECSPACE_27 @ ( c_2Eind__type_2EZBOT @ A_27a ) ) )
% 1.17/1.37 & ! [V1c: tp__ty_2Enum_2Enum,V2i: $i] :
% 1.17/1.37 ( ( mem @ V2i @ A_27a )
% 1.17/1.37 => ! [V3r: $i] :
% 1.17/1.37 ( ( mem @ V3r @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 => ( ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ ( ap @ V3r @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.37 & ( p @ ( ap @ V0ZRECSPACE_27 @ ( ap @ V3r @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0ZRECSPACE_27 @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ V2i ) @ V3r ) ) ) ) ) ) )
% 1.17/1.37 => ! [V5a0: $i] :
% 1.17/1.37 ( ( mem @ V5a0 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ V5a0 ) )
% 1.17/1.37 => ( p @ ( ap @ V0ZRECSPACE_27 @ V5a0 ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EZRECSPACE__cases,axiom,
% 1.17/1.37 ! [A_27a: del,V0a0: $i] :
% 1.17/1.37 ( ( mem @ V0a0 @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ V0a0 ) )
% 1.17/1.37 <=> ( ( V0a0
% 1.17/1.37 = ( c_2Eind__type_2EZBOT @ A_27a ) )
% 1.17/1.37 | ? [V1c: tp__ty_2Enum_2Enum,V2i: $i] :
% 1.17/1.37 ( ( mem @ V2i @ A_27a )
% 1.17/1.37 & ? [V3r: $i] :
% 1.17/1.37 ( ( mem @ V3r @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 & ( V0a0
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ V2i ) @ V3r ) )
% 1.17/1.37 & ! [V4n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ ( ap @ V3r @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2Erecspace__TY__DEF,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ? [V0rep: $i] :
% 1.17/1.37 ( ( mem @ V0rep @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.37 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) ) @ V0rep ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2Erecspace__repfns,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ! [V0a: $i] :
% 1.17/1.37 ( ( mem @ V0a @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
% 1.17/1.37 => ( ( ap @ ( c_2Eind__type_2Emk__rec @ A_27a ) @ ( ap @ ( c_2Eind__type_2Edest__rec @ A_27a ) @ V0a ) )
% 1.17/1.37 = V0a ) )
% 1.17/1.37 & ! [V1r: $i] :
% 1.17/1.37 ( ( mem @ V1r @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ V1r ) )
% 1.17/1.37 <=> ( ( ap @ ( c_2Eind__type_2Edest__rec @ A_27a ) @ ( ap @ ( c_2Eind__type_2Emk__rec @ A_27a ) @ V1r ) )
% 1.17/1.37 = V1r ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EBOTTOM,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ( c_2Eind__type_2EBOTTOM @ A_27a )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2Emk__rec @ A_27a ) @ ( c_2Eind__type_2EZBOT @ A_27a ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2ECONSTR,axiom,
% 1.17/1.37 ! [A_27a: del,V0c: tp__ty_2Enum_2Enum,V1i: $i] :
% 1.17/1.37 ( ( mem @ V1i @ A_27a )
% 1.17/1.37 => ! [V2r: $i] :
% 1.17/1.37 ( ( mem @ V2r @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ V1i ) @ V2r )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2Emk__rec @ A_27a )
% 1.17/1.37 @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EZCONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ V1i )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V3n: $i] : ( ap @ ( c_2Eind__type_2Edest__rec @ A_27a ) @ ( ap @ V2r @ V3n ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EMK__REC__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0x: $i] :
% 1.17/1.37 ( ( mem @ V0x @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ! [V1y: $i] :
% 1.17/1.37 ( ( mem @ V1y @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.37 => ( ( ( ap @ ( c_2Eind__type_2Emk__rec @ A_27a ) @ V0x )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2Emk__rec @ A_27a ) @ V1y ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ V0x ) )
% 1.17/1.37 & ( p @ ( ap @ ( c_2Eind__type_2EZRECSPACE @ A_27a ) @ V1y ) ) )
% 1.17/1.37 => ( V0x = V1y ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EDEST__REC__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0x: $i] :
% 1.17/1.37 ( ( mem @ V0x @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
% 1.17/1.37 => ! [V1y: $i] :
% 1.17/1.37 ( ( mem @ V1y @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
% 1.17/1.37 => ( ( ( ap @ ( c_2Eind__type_2Edest__rec @ A_27a ) @ V0x )
% 1.17/1.37 = ( ap @ ( c_2Eind__type_2Edest__rec @ A_27a ) @ V1y ) )
% 1.17/1.37 <=> ( V0x = V1y ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ECONSTR__BOT,axiom,
% 1.17/1.37 ! [A_27a: del,V0c: tp__ty_2Enum_2Enum,V1i: $i] :
% 1.17/1.37 ( ( mem @ V1i @ A_27a )
% 1.17/1.37 => ! [V2r: $i] :
% 1.17/1.37 ( ( mem @ V2r @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c ) ) @ V1i ) @ V2r )
% 1.17/1.37 != ( c_2Eind__type_2EBOTTOM @ A_27a ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ECONSTR__INJ,axiom,
% 1.17/1.37 ! [A_27a: del,V0c1: tp__ty_2Enum_2Enum,V1i1: $i] :
% 1.17/1.37 ( ( mem @ V1i1 @ A_27a )
% 1.17/1.37 => ! [V2r1: $i] :
% 1.17/1.37 ( ( mem @ V2r1 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
% 1.17/1.37 => ! [V3c2: tp__ty_2Enum_2Enum,V4i2: $i] :
% 1.17/1.37 ( ( mem @ V4i2 @ A_27a )
% 1.17/1.37 => ! [V5r2: $i] :
% 1.17/1.37 ( ( mem @ V5r2 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
% 1.17/1.37 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0c1 ) ) @ V1i1 ) @ V2r1 )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3c2 ) ) @ V4i2 ) @ V5r2 ) )
% 1.17/1.37 <=> ( ( V0c1 = V3c2 )
% 1.17/1.37 & ( V1i1 = V4i2 )
% 1.17/1.37 & ( V2r1 = V5r2 ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ECONSTR__IND,axiom,
% 1.17/1.37 ! [A_27a: del,V0P: $i] :
% 1.17/1.37 ( ( mem @ V0P @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ bool ) )
% 1.17/1.37 => ( ( ( p @ ( ap @ V0P @ ( c_2Eind__type_2EBOTTOM @ A_27a ) ) )
% 1.17/1.37 & ! [V1c: tp__ty_2Enum_2Enum,V2i: $i] :
% 1.17/1.37 ( ( mem @ V2i @ A_27a )
% 1.17/1.37 => ! [V3r: $i] :
% 1.17/1.37 ( ( mem @ V3r @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
% 1.17/1.37 => ( ! [V4n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ V3r @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1c ) ) @ V2i ) @ V3r ) ) ) ) ) ) )
% 1.17/1.37 => ! [V5x: $i] :
% 1.17/1.37 ( ( mem @ V5x @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
% 1.17/1.37 => ( p @ ( ap @ V0P @ V5x ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2ECONSTR__REC,axiom,
% 1.17/1.37 ! [A_27a: del,A_27b: del,V0Fn: $i] :
% 1.17/1.37 ( ( mem @ V0Fn @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27b ) @ A_27b ) ) ) ) )
% 1.17/1.37 => ? [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ A_27b ) )
% 1.17/1.37 & ! [V2c: tp__ty_2Enum_2Enum,V3i: $i] :
% 1.17/1.37 ( ( mem @ V3i @ A_27a )
% 1.17/1.37 => ! [V4r: $i] :
% 1.17/1.37 ( ( mem @ V4r @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
% 1.17/1.37 => ( ( ap @ V1f @ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ V3i ) @ V4r ) )
% 1.17/1.37 = ( ap @ ( ap @ ( ap @ ( ap @ V0Fn @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ V3i ) @ V4r )
% 1.17/1.37 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.37 @ ^ [V5n: $i] : ( ap @ V1f @ ( ap @ V4r @ V5n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EFCONS,axiom,
% 1.17/1.37 ! [A_27a: del] :
% 1.17/1.37 ( ! [V0a: $i] :
% 1.17/1.37 ( ( mem @ V0a @ A_27a )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.37 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ A_27a ) @ V0a ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.37 = V0a ) ) )
% 1.17/1.37 & ! [V2a: $i] :
% 1.17/1.37 ( ( mem @ V2a @ A_27a )
% 1.17/1.37 => ! [V3f: $i] :
% 1.17/1.37 ( ( mem @ V3f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.37 => ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ A_27a ) @ V2a ) @ V3f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) )
% 1.17/1.37 = ( ap @ V3f @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(ax_thm_2Eind__type_2EFNIL,axiom,
% 1.17/1.37 ! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.37 ( ( ap @ ( c_2Eind__type_2EFNIL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
% 1.17/1.37 = ( c_2Ebool_2EARB @ A_27a ) ) ).
% 1.17/1.37
% 1.17/1.37 thf(conj_thm_2Eind__type_2EFCONS__DEST,axiom,
% 1.17/1.37 ! [A_27a: del,V0a: $i] :
% 1.17/1.37 ( ( mem @ V0a @ A_27a )
% 1.17/1.37 => ! [V1f: $i] :
% 1.17/1.38 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.38 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ A_27a ) @ V0a ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0a ) @ ( ap @ V1f @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Eind__type_2EISO,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.38 => ! [V1g: $i] :
% 1.17/1.38 ( ( mem @ V1g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ ( c_2Eind__type_2EISO @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
% 1.17/1.38 <=> ( ! [V2x: $i] :
% 1.17/1.38 ( ( mem @ V2x @ A_27b )
% 1.17/1.38 => ( ( ap @ V0f @ ( ap @ V1g @ V2x ) )
% 1.17/1.38 = V2x ) )
% 1.17/1.38 & ! [V3y: $i] :
% 1.17/1.38 ( ( mem @ V3y @ A_27a )
% 1.17/1.38 => ( ( ap @ V1g @ ( ap @ V0f @ V3y ) )
% 1.17/1.38 = V3y ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Eind__type_2EISO__REFL,axiom,
% 1.17/1.38 ! [A_27a: del] :
% 1.17/1.38 ( p
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Eind__type_2EISO @ A_27a @ A_27a )
% 1.17/1.38 @ ( lam @ A_27a
% 1.17/1.38 @ ^ [V0x: $i] : V0x ) )
% 1.17/1.38 @ ( lam @ A_27a
% 1.17/1.38 @ ^ [V1x: $i] : V1x ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Eind__type_2EISO__FUN,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.38 => ! [V1f_27: $i] :
% 1.17/1.38 ( ( mem @ V1f_27 @ ( arr @ A_27c @ A_27a ) )
% 1.17/1.38 => ! [V2g: $i] :
% 1.17/1.38 ( ( mem @ V2g @ ( arr @ A_27b @ A_27d ) )
% 1.17/1.38 => ! [V3g_27: $i] :
% 1.17/1.38 ( ( mem @ V3g_27 @ ( arr @ A_27d @ A_27b ) )
% 1.17/1.38 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eind__type_2EISO @ A_27a @ A_27c ) @ V0f ) @ V1f_27 ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ ( c_2Eind__type_2EISO @ A_27b @ A_27d ) @ V2g ) @ V3g_27 ) ) )
% 1.17/1.38 => ( p
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Eind__type_2EISO @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27c @ A_27d ) )
% 1.17/1.38 @ ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.38 @ ^ [V4h: $i] :
% 1.17/1.38 ( lam @ A_27c
% 1.17/1.38 @ ^ [V5a_27: $i] : ( ap @ V2g @ ( ap @ V4h @ ( ap @ V1f_27 @ V5a_27 ) ) ) ) ) )
% 1.17/1.38 @ ( lam @ ( arr @ A_27c @ A_27d )
% 1.17/1.38 @ ^ [V6h: $i] :
% 1.17/1.38 ( lam @ A_27a
% 1.17/1.38 @ ^ [V7a: $i] : ( ap @ V3g_27 @ ( ap @ V6h @ ( ap @ V0f @ V7a ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Eind__type_2EISO__USAGE,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.38 => ! [V1g: $i] :
% 1.17/1.38 ( ( mem @ V1g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ ( c_2Eind__type_2EISO @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
% 1.17/1.38 => ( ! [V2P: $i] :
% 1.17/1.38 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.38 => ( ! [V3x: $i] :
% 1.17/1.38 ( ( mem @ V3x @ A_27a )
% 1.17/1.38 => ( p @ ( ap @ V2P @ V3x ) ) )
% 1.17/1.38 <=> ! [V4x: $i] :
% 1.17/1.38 ( ( mem @ V4x @ A_27b )
% 1.17/1.38 => ( p @ ( ap @ V2P @ ( ap @ V1g @ V4x ) ) ) ) ) )
% 1.17/1.38 & ! [V5P: $i] :
% 1.17/1.38 ( ( mem @ V5P @ ( arr @ A_27a @ bool ) )
% 1.17/1.38 => ( ? [V6x: $i] :
% 1.17/1.38 ( ( mem @ V6x @ A_27a )
% 1.17/1.38 & ( p @ ( ap @ V5P @ V6x ) ) )
% 1.17/1.38 <=> ? [V7x: $i] :
% 1.17/1.38 ( ( mem @ V7x @ A_27b )
% 1.17/1.38 & ( p @ ( ap @ V5P @ ( ap @ V1g @ V7x ) ) ) ) ) )
% 1.17/1.38 & ! [V8a: $i] :
% 1.17/1.38 ( ( mem @ V8a @ A_27a )
% 1.17/1.38 => ! [V9b: $i] :
% 1.17/1.38 ( ( mem @ V9b @ A_27b )
% 1.17/1.38 => ( ( V8a
% 1.17/1.38 = ( ap @ V1g @ V9b ) )
% 1.17/1.38 <=> ( ( ap @ V0f @ V8a )
% 1.17/1.38 = V9b ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 thf(tp_c_2EbasicSize_2Ebool__size,type,
% 1.17/1.38 c_2EbasicSize_2Ebool__size: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2EbasicSize_2Ebool__size,axiom,
% 1.17/1.38 mem @ c_2EbasicSize_2Ebool__size @ ( arr @ bool @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2EbasicSize_2Eone__size,type,
% 1.17/1.38 c_2EbasicSize_2Eone__size: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2EbasicSize_2Eone__size,axiom,
% 1.17/1.38 mem @ c_2EbasicSize_2Eone__size @ ( arr @ ty_2Eone_2Eone @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2EbasicSize_2Eone__size,type,
% 1.17/1.38 fo__c_2EbasicSize_2Eone__size: tp__ty_2Eone_2Eone > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2EbasicSize_2Eone__size,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Eone_2Eone] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2EbasicSize_2Eone__size @ X0 ) )
% 1.17/1.38 = ( ap @ c_2EbasicSize_2Eone__size @ ( inj__ty_2Eone_2Eone @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2EbasicSize_2Eoption__size,type,
% 1.17/1.38 c_2EbasicSize_2Eoption__size: del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2EbasicSize_2Eoption__size,axiom,
% 1.17/1.38 ! [A_27a: del] : ( mem @ ( c_2EbasicSize_2Eoption__size @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2EbasicSize_2Epair__size,type,
% 1.17/1.38 c_2EbasicSize_2Epair__size: del > del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2EbasicSize_2Epair__size,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EbasicSize_2Epair__size @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27b @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ty_2Enum_2Enum ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2EbasicSize_2Esum__size,type,
% 1.17/1.38 c_2EbasicSize_2Esum__size: del > del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2EbasicSize_2Esum__size,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EbasicSize_2Esum__size @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27b @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ty_2Enum_2Enum ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2EbasicSize_2Ebool__size__def,axiom,
% 1.17/1.38 ! [V0b: $i] :
% 1.17/1.38 ( ( mem @ V0b @ bool )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EbasicSize_2Ebool__size @ V0b ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2EbasicSize_2Epair__size__def,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V1g: $i] :
% 1.17/1.38 ( ( mem @ V1g @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ( ( ap @ ( ap @ ( c_2EbasicSize_2Epair__size @ A_27a @ A_27b ) @ V0f ) @ V1g )
% 1.17/1.38 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ty_2Enum_2Enum )
% 1.17/1.38 @ ( lam @ A_27a
% 1.17/1.38 @ ^ [V2x: $i] :
% 1.17/1.38 ( lam @ A_27b
% 1.17/1.38 @ ^ [V3y: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V2x ) ) @ ( ap @ V1g @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2EbasicSize_2Eone__size__def,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Eone_2Eone] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2EbasicSize_2Eone__size @ ( inj__ty_2Eone_2Eone @ V0x ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2EbasicSize_2Esum__size__def,axiom,
% 1.17/1.38 ! [A_27a: del,A_27b: del] :
% 1.17/1.38 ( ! [V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V1g: $i] :
% 1.17/1.38 ( ( mem @ V1g @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V2x: $i] :
% 1.17/1.38 ( ( mem @ V2x @ A_27a )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2EbasicSize_2Esum__size @ A_27a @ A_27b ) @ V0f ) @ V1g ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V2x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V2x ) ) ) ) ) )
% 1.17/1.38 & ! [V3f: $i] :
% 1.17/1.38 ( ( mem @ V3f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V4g: $i] :
% 1.17/1.38 ( ( mem @ V4g @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V5y: $i] :
% 1.17/1.38 ( ( mem @ V5y @ A_27b )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2EbasicSize_2Esum__size @ A_27a @ A_27b ) @ V3f ) @ V4g ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V5y ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ V4g @ V5y ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2EbasicSize_2Eoption__size__def,axiom,
% 1.17/1.38 ! [A_27a: del] :
% 1.17/1.38 ( ! [V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2EbasicSize_2Eoption__size @ A_27a ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) )
% 1.17/1.38 & ! [V1f: $i] :
% 1.17/1.38 ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V2x: $i] :
% 1.17/1.38 ( ( mem @ V2x @ A_27a )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2EbasicSize_2Eoption__size @ A_27a ) @ V1f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ V1f @ V2x ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 thf(tp_c_2Elogroot_2ELOG,type,
% 1.17/1.38 c_2Elogroot_2ELOG: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2ELOG,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2ELOG @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Elogroot_2ELOG,type,
% 1.17/1.38 fo__c_2Elogroot_2ELOG: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Elogroot_2ELOG,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Elogroot_2ELOG @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Elogroot_2EROOT,type,
% 1.17/1.38 c_2Elogroot_2EROOT: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2EROOT,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2EROOT @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Elogroot_2EROOT,type,
% 1.17/1.38 fo__c_2Elogroot_2EROOT: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Elogroot_2EROOT,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Elogroot_2EROOT @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Elogroot_2ESQRTd,type,
% 1.17/1.38 c_2Elogroot_2ESQRTd: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2ESQRTd,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2ESQRTd @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Elogroot_2EiSQRT0,type,
% 1.17/1.38 c_2Elogroot_2EiSQRT0: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2EiSQRT0,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2EiSQRT0 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Elogroot_2EiSQRT1,type,
% 1.17/1.38 c_2Elogroot_2EiSQRT1: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2EiSQRT1,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2EiSQRT1 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Elogroot_2EiSQRT2,type,
% 1.17/1.38 c_2Elogroot_2EiSQRT2: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2EiSQRT2,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2EiSQRT2 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Elogroot_2EiSQRT3,type,
% 1.17/1.38 c_2Elogroot_2EiSQRT3: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Elogroot_2EiSQRT3,axiom,
% 1.17/1.38 mem @ c_2Elogroot_2EiSQRT3 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELT__EXP__ISO,axiom,
% 1.17/1.38 ! [V0e: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0e ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELE__EXP__ISO,axiom,
% 1.17/1.38 ! [V0e: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0e ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EEXP__LT__ISO,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EEXP__LE__ISO,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EROOT__exists,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
% 1.17/1.38 => ? [V2rt: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2rt ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2rt ) ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2EROOT,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EROOT__UNIQUE,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = V2p ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__exists,axiom,
% 1.17/1.38 ? [V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
% 1.17/1.38 & ! [V1a: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2ELOG,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__UNIQUE,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = V2p ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__ADD1,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__BASE,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__EXP,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__1,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__DIV,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__ADD,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) )
% 1.17/1.38 = V2c ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__LE__MONO,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__RWT,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__EQ__0,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__MULT,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__add__digit,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EROOT__DIV,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EROOT__LE__MONO,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EEXP__MUL,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__ROOT,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2r: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V2r ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ V2r ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2ELOG__MOD,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ( V0n
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2EROOT__COMPUTE,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) )
% 1.17/1.38 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Enum_2ESUC @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) ) @ V2x ) @ ( ap @ c_2Enum_2ESUC @ V2x ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2ESQRTd__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2EiSQRT0__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.38 @ ^ [V1p: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2d: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2d ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V2d ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) )
% 1.17/1.38 @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2EiSQRT1__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.38 @ ^ [V1p: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2d: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2d ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2d ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) )
% 1.17/1.38 @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2EiSQRT2__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.38 @ ^ [V1p: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2d: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V3c: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V4e: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V4e ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V2d ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V3c ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ V2d ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V4e ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3c ) @ V2d ) ) ) )
% 1.17/1.38 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) )
% 1.17/1.38 @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Elogroot_2EiSQRT3__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT3 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.38 @ ^ [V1p: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2d: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V3c: $i] :
% 1.17/1.38 ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V4e: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V4e ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V2d ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V3c ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ V2d ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V4e ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ V3c ) ) @ V2d ) ) ) )
% 1.17/1.38 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ V1p ) ) ) ) )
% 1.17/1.38 @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2Enumeral__sqrt,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT3 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT0 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT2 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT0 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT1 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT2 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 & ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2ESQRTd @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Elogroot_2EiSQRT3 @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Elogroot_2Enumeral__root2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2EROOT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Elogroot_2ESQRTd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 thf(tp_c_2Egcd_2Egcd,type,
% 1.17/1.38 c_2Egcd_2Egcd: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Egcd_2Egcd,axiom,
% 1.17/1.38 mem @ c_2Egcd_2Egcd @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Egcd_2Egcd,type,
% 1.17/1.38 fo__c_2Egcd_2Egcd: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Egcd_2Egcd,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Egcd_2Egcd @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Egcd_2Eis__gcd,type,
% 1.17/1.38 c_2Egcd_2Eis__gcd: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Egcd_2Eis__gcd,axiom,
% 1.17/1.38 mem @ c_2Egcd_2Eis__gcd @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Egcd_2Elcm,type,
% 1.17/1.38 c_2Egcd_2Elcm: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Egcd_2Elcm,axiom,
% 1.17/1.38 mem @ c_2Egcd_2Elcm @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Egcd_2Elcm,type,
% 1.17/1.38 fo__c_2Egcd_2Elcm: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Egcd_2Elcm,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Egcd_2Elcm @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Egcd_2Eis__gcd__def,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) )
% 1.17/1.38 <=> ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V2c ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 & ! [V3d: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V3d ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V3d ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V3d ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__UNIQUE,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum,V3d: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) )
% 1.17/1.38 => ( V2c = V3d ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__REF,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__SYM,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__0R,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__0L,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EPRIME__IS__GCD,axiom,
% 1.17/1.38 ! [V0p: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 | ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__MINUS__L,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EIS__GCD__MINUS__R,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2Egcd__ind,axiom,
% 1.17/1.38 ! [V0P: $i] :
% 1.17/1.38 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
% 1.17/1.38 => ( ( ! [V1y: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.38 & ! [V2x: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 & ! [V3x: tp__ty_2Enum_2Enum,V4y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( ~ ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4y ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V4y ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) )
% 1.17/1.38 & ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4y ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V4y ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4y ) ) ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4y ) ) ) ) ) )
% 1.17/1.38 => ! [V5v: tp__ty_2Enum_2Enum,V6v1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V5v ) ) @ ( inj__ty_2Enum_2Enum @ V6v1 ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2Egcd__def,axiom,
% 1.17/1.38 ( ! [V0y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.38 = V0y )
% 1.17/1.38 & ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.38 & ! [V2y: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2Egcd__def__compute,axiom,
% 1.17/1.38 ( ! [V0y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) )
% 1.17/1.38 = V0y )
% 1.17/1.38 & ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) )
% 1.17/1.38 & ! [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) )
% 1.17/1.38 & ! [V3y: tp__ty_2Enum_2Enum,V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
% 1.17/1.38 & ! [V5y: tp__ty_2Enum_2Enum,V6x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V6x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6x ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V6x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6x ) ) ) ) ) ) ) )
% 1.17/1.38 & ! [V7y: tp__ty_2Enum_2Enum,V8x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V7y ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7y ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7y ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V7y ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7y ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
% 1.17/1.38 & ! [V9y: tp__ty_2Enum_2Enum,V10x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__IS__GCD,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ c_2Egcd_2Eis__gcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__IS__GREATEST__COMMON__DIVISOR,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 & ! [V2d: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V2d ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V2d ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V2d ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__REF,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 = V0a ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__SYM,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__0R,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = V0a ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__0L,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 = V0a ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__ADD__R,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__ADD__R__THM,axiom,
% 1.17/1.38 ( ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 & ! [V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3b ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__ADD__L,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__ADD__L__THM,axiom,
% 1.17/1.38 ( ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 & ! [V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3b ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__EQ__0,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 <=> ( ( V0n = fo__c_2Enum_2E0 )
% 1.17/1.38 & ( V1m = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__1,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EPRIME__GCD,axiom,
% 1.17/1.38 ! [V0p: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 | ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EL__EUCLIDES,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2c: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2c ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EP__EUCLIDES,axiom,
% 1.17/1.38 ! [V0p: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ c_2Edivides_2Eprime @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 | ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EFACTOR__OUT__GCD,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( V0n != fo__c_2Enum_2E0 )
% 1.17/1.38 & ( V1m != fo__c_2Enum_2E0 ) )
% 1.17/1.38 => ? [V2p: tp__ty_2Enum_2Enum,V3q: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0n
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.38 & ( V1m
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V3q ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__SUCfree__ind,axiom,
% 1.17/1.38 ! [V0P: $i] :
% 1.17/1.38 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
% 1.17/1.38 => ( ( ! [V1y: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.38 & ! [V2x: tp__ty_2Enum_2Enum,V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.38 & ! [V4x: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.38 & ! [V5x: tp__ty_2Enum_2Enum,V6y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V5x ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V6y ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V5x ) ) @ ( inj__ty_2Enum_2Enum @ V6y ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V5x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5x ) ) @ ( inj__ty_2Enum_2Enum @ V6y ) ) ) ) ) )
% 1.17/1.38 => ! [V7m: tp__ty_2Enum_2Enum,V8n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V7m ) ) @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELINEAR__GCD,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0n != fo__c_2Enum_2E0 )
% 1.17/1.38 => ? [V2p: tp__ty_2Enum_2Enum,V3q: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V3q ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__EFFICIENTLY,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Egcd_2Elcm__def,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELCM__IS__LEAST__COMMON__MULTIPLE,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 & ! [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELCM__0,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELCM__1,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.38 = V0x )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = V0x ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELCM__COMM,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELCM__LE,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2ELCM__LEAST,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 => ! [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Egcd_2Elcm @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.38 => ( ~ ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) )
% 1.17/1.38 | ~ ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2p ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__COMMON__FACTOR,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EGCD__CANCEL__MULT,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Egcd_2EBINARY__GCD,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 & ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
% 1.17/1.38 & ( ( ( p @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 & ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 thf(tp_c_2Enumpair_2Einvtri,type,
% 1.17/1.38 c_2Enumpair_2Einvtri: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Einvtri,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Einvtri @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Einvtri,type,
% 1.17/1.38 fo__c_2Enumpair_2Einvtri: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Einvtri,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Einvtri @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Einvtri0,type,
% 1.17/1.38 c_2Enumpair_2Einvtri0: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Einvtri0,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Einvtri0 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enapp,type,
% 1.17/1.38 c_2Enumpair_2Enapp: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enapp,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Enapp @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Enapp,type,
% 1.17/1.38 fo__c_2Enumpair_2Enapp: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Enapp,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Enapp @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Enumpair_2Enapp @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Encons,type,
% 1.17/1.38 c_2Enumpair_2Encons: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Encons,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Encons @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Encons,type,
% 1.17/1.38 fo__c_2Enumpair_2Encons: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Encons,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Encons @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enfoldl,type,
% 1.17/1.38 c_2Enumpair_2Enfoldl: del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enfoldl,axiom,
% 1.17/1.38 ! [A_27a: del] : ( mem @ ( c_2Enumpair_2Enfoldl @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) @ ( arr @ A_27a @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enfst,type,
% 1.17/1.38 c_2Enumpair_2Enfst: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enfst,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Enfst @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Enfst,type,
% 1.17/1.38 fo__c_2Enumpair_2Enfst: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Enfst,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Enfst @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Enumpair_2Enfst @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enlen,type,
% 1.17/1.38 c_2Enumpair_2Enlen: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enlen,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Enlen @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Enlen,type,
% 1.17/1.38 fo__c_2Enumpair_2Enlen: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Enlen,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Enlen @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Enumpair_2Enlen @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enlistrec,type,
% 1.17/1.38 c_2Enumpair_2Enlistrec: del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enlistrec,axiom,
% 1.17/1.38 ! [A_27a: del] : ( mem @ ( c_2Enumpair_2Enlistrec @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enmap,type,
% 1.17/1.38 c_2Enumpair_2Enmap: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enmap,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Enmap @ ( arr @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Enpair,type,
% 1.17/1.38 c_2Enumpair_2Enpair: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Enpair,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Enpair @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Enpair,type,
% 1.17/1.38 fo__c_2Enumpair_2Enpair: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Enpair,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Enpair @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Ensnd,type,
% 1.17/1.38 c_2Enumpair_2Ensnd: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Ensnd,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Ensnd @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Ensnd,type,
% 1.17/1.38 fo__c_2Enumpair_2Ensnd: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Ensnd,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Ensnd @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Enumpair_2Ensnd @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Enumpair_2Etri,type,
% 1.17/1.38 c_2Enumpair_2Etri: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Enumpair_2Etri,axiom,
% 1.17/1.38 mem @ c_2Enumpair_2Etri @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Enumpair_2Etri,type,
% 1.17/1.38 fo__c_2Enumpair_2Etri: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Enumpair_2Etri,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumpair_2Etri @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Etri__def,axiom,
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__def__compute,axiom,
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
% 1.17/1.38 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etwotri__formula,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__formula,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__eq__0,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 <=> ( V0n = fo__c_2Enum_2E0 ) )
% 1.17/1.38 & ( ( fo__c_2Enum_2E0
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 <=> ( V0n = fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__LT__I,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__LT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__11,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 <=> ( V0m = V1n ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__LE,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri0__ind,axiom,
% 1.17/1.38 ! [V0P: $i] :
% 1.17/1.38 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
% 1.17/1.38 => ( ! [V1n: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ~ ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) )
% 1.17/1.38 => ! [V3v: tp__ty_2Enum_2Enum,V4v1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3v ) ) @ ( inj__ty_2Enum_2Enum @ V4v1 ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri0__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Einvtri__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri0__thm,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumpair_2Etri @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ) @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2ESND__invtri0,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Epair_2EFST @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Epair_2ESND @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumpair_2Einvtri0 @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri__lower,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri__upper,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enumpair_2Etri @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri__linverse,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Einvtri @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = V0n ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri__unique,axiom,
% 1.17/1.38 ! [V0y: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Enumpair_2Etri @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0y ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = V0y ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri__linverse__r,axiom,
% 1.17/1.38 ! [V0y: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0y ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Einvtri @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) )
% 1.17/1.38 = V1x ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Etri__le,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enumpair_2Etri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Einvtri__le,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Enpair__def,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumpair_2Etri @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Enfst__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Enfst @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Ensnd__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Ensnd @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Enumpair_2Etri @ ( ap @ c_2Enumpair_2Einvtri @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enfst__npair,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Enfst @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.38 = V0x ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Ensnd__npair,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Ensnd @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.38 = V1y ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enpair__cases,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ? [V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( V0n
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enpair,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( ap @ c_2Enumpair_2Enfst @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enumpair_2Ensnd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = V0n ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enpair__11,axiom,
% 1.17/1.38 ! [V0x1: tp__ty_2Enum_2Enum,V1y1: tp__ty_2Enum_2Enum,V2x2: tp__ty_2Enum_2Enum,V3y2: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V0x1 ) ) @ ( inj__ty_2Enum_2Enum @ V1y1 ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V2x2 ) ) @ ( inj__ty_2Enum_2Enum @ V3y2 ) ) ) )
% 1.17/1.38 <=> ( ( V0x1 = V2x2 )
% 1.17/1.38 & ( V1y1 = V3y2 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enfst__le,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enumpair_2Enfst @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Ensnd__le,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enumpair_2Ensnd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Encons__def,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Encons__11,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum,V2h: tp__ty_2Enum_2Enum,V3t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) )
% 1.17/1.38 <=> ( ( V0x = V2h )
% 1.17/1.38 & ( V1y = V3t ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Encons__not__nnil,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.38 != fo__c_2Enum_2E0 ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enlistrec__ind,axiom,
% 1.17/1.38 ! [A_27a: del,V0P: $i] :
% 1.17/1.38 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) )
% 1.17/1.38 => ( ! [V1n: $i] :
% 1.17/1.38 ( ( mem @ V1n @ A_27a )
% 1.17/1.38 => ! [V2f: $i] :
% 1.17/1.38 ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) )
% 1.17/1.38 => ! [V3l: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( V3l != fo__c_2Enum_2E0 )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1n ) @ V2f ) @ ( ap @ c_2Enumpair_2Ensnd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1n ) @ V2f ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) ) ) )
% 1.17/1.38 => ! [V4v: $i] :
% 1.17/1.38 ( ( mem @ V4v @ A_27a )
% 1.17/1.38 => ! [V5v1: $i] :
% 1.17/1.38 ( ( mem @ V5v1 @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) )
% 1.17/1.38 => ! [V6v2: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ V0P @ V4v ) @ V5v1 ) @ ( inj__ty_2Enum_2Enum @ V6v2 ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enlistrec__def,axiom,
% 1.17/1.38 ! [A_27a: del,V0n: $i] :
% 1.17/1.38 ( ( mem @ V0n @ A_27a )
% 1.17/1.38 => ! [V1l: tp__ty_2Enum_2Enum,V2f: $i] :
% 1.17/1.38 ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) )
% 1.17/1.38 => ( ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ A_27a ) @ V0n ) @ V2f ) @ ( inj__ty_2Enum_2Enum @ V1l ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0n ) @ ( ap @ ( ap @ ( ap @ V2f @ ( ap @ c_2Enumpair_2Enfst @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Enumpair_2Ensnd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ A_27a ) @ V0n ) @ V2f ) @ ( ap @ c_2Enumpair_2Ensnd @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enlistrec__thm,axiom,
% 1.17/1.38 ! [A_27a: del,V0n: $i] :
% 1.17/1.38 ( ( mem @ V0n @ A_27a )
% 1.17/1.38 => ! [V1f: $i] :
% 1.17/1.38 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) ) )
% 1.17/1.38 => ! [V2h: tp__ty_2Enum_2Enum,V3t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ A_27a ) @ V0n ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.38 = V0n )
% 1.17/1.38 & ( ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ A_27a ) @ V0n ) @ V1f ) @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ V3t ) ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ A_27a ) @ V0n ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enlist__ind,axiom,
% 1.17/1.38 ! [V0P: $i] :
% 1.17/1.38 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.38 => ( ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 & ! [V1h: tp__ty_2Enum_2Enum,V2t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2t ) ) )
% 1.17/1.38 => ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) ) ) )
% 1.17/1.38 => ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Enlen__def,axiom,
% 1.17/1.38 ( c_2Enumpair_2Enlen
% 1.17/1.38 = ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V0n: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V1t: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2r: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2r ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enlen__thm,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Enlen @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumpair_2Enlen @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Enumpair_2Enlen @ ( inj__ty_2Enum_2Enum @ V1t ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Enmap__def,axiom,
% 1.17/1.38 ! [V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ( ( ap @ c_2Enumpair_2Enmap @ V0f )
% 1.17/1.38 = ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V1n: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2t: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V3r: $i] : ( ap @ ( ap @ c_2Enumpair_2Encons @ ( ap @ V0f @ V1n ) ) @ V3r ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enmap__thm,axiom,
% 1.17/1.38 ! [V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.38 => ! [V1h: tp__ty_2Enum_2Enum,V2t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enmap @ V0f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enmap @ V0f ) @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) @ ( ap @ ( ap @ c_2Enumpair_2Enmap @ V0f ) @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Enfoldl__def,axiom,
% 1.17/1.38 ! [A_27a: del,V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) )
% 1.17/1.38 => ! [V1a: $i] :
% 1.17/1.38 ( ( mem @ V1a @ A_27a )
% 1.17/1.38 => ! [V2l: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enfoldl @ A_27a ) @ V0f ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ V2l ) )
% 1.17/1.38 = ( ap
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Enumpair_2Enlistrec @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.38 @ ( lam @ A_27a
% 1.17/1.38 @ ^ [V3a: $i] : V3a ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V4n: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V5t: $i] :
% 1.17/1.38 ( lam @ ( arr @ A_27a @ A_27a )
% 1.17/1.38 @ ^ [V6r: $i] :
% 1.17/1.38 ( lam @ A_27a
% 1.17/1.38 @ ^ [V7a: $i] : ( ap @ V6r @ ( ap @ ( ap @ V0f @ V4n ) @ V7a ) ) ) ) ) ) )
% 1.17/1.38 @ ( inj__ty_2Enum_2Enum @ V2l ) )
% 1.17/1.38 @ V1a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enfoldl__thm,axiom,
% 1.17/1.38 ! [A_27a: del,V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ A_27a ) ) )
% 1.17/1.38 => ! [V1a: $i] :
% 1.17/1.38 ( ( mem @ V1a @ A_27a )
% 1.17/1.38 => ! [V2h: tp__ty_2Enum_2Enum,V3t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enfoldl @ A_27a ) @ V0f ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.38 = V1a )
% 1.17/1.38 & ( ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enfoldl @ A_27a ) @ V0f ) @ V1a ) @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ V3t ) ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ ( c_2Enumpair_2Enfoldl @ A_27a ) @ V0f ) @ ( ap @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V3t ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Enumpair_2Enapp__def,axiom,
% 1.17/1.38 ! [V0l1: tp__ty_2Enum_2Enum,V1l2: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enapp @ ( inj__ty_2Enum_2Enum @ V0l1 ) ) @ ( inj__ty_2Enum_2Enum @ V1l2 ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( ap @ ( c_2Enumpair_2Enlistrec @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1l2 ) )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V2n: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V3t: $i] :
% 1.17/1.38 ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V4r: $i] : ( ap @ ( ap @ c_2Enumpair_2Encons @ V2n ) @ V4r ) ) ) ) )
% 1.17/1.38 @ ( inj__ty_2Enum_2Enum @ V0l1 ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enapp__thm,axiom,
% 1.17/1.38 ! [V0nlist: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enapp @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0nlist ) ) )
% 1.17/1.38 = V0nlist )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enapp @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) @ ( inj__ty_2Enum_2Enum @ V0nlist ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( ap @ ( ap @ c_2Enumpair_2Enapp @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V0nlist ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Enumpair_2Enlist__cases,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0n = fo__c_2Enum_2E0 )
% 1.17/1.38 | ? [V1h: tp__ty_2Enum_2Enum,V2t: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( V0n
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Encons @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2t ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 thf(tp_c_2Ebit_2EBIT,type,
% 1.17/1.38 c_2Ebit_2EBIT: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EBIT,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EBIT @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EBITS,type,
% 1.17/1.38 c_2Ebit_2EBITS: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EBITS,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EBITS @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2EBITS,type,
% 1.17/1.38 fo__c_2Ebit_2EBITS: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2EBITS,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2EBITS @ X0 @ X1 @ X2 ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EBITV,type,
% 1.17/1.38 c_2Ebit_2EBITV: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EBITV,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EBITV @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2EBITV,type,
% 1.17/1.38 fo__c_2Ebit_2EBITV: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2EBITV,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2EBITV @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Ebit_2EBITV @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EBITWISE,type,
% 1.17/1.38 c_2Ebit_2EBITWISE: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EBITWISE,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EBITWISE @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EBIT__MODIFY,type,
% 1.17/1.38 c_2Ebit_2EBIT__MODIFY: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EBIT__MODIFY,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EBIT__MODIFY @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EBIT__REVERSE,type,
% 1.17/1.38 c_2Ebit_2EBIT__REVERSE: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EBIT__REVERSE,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EBIT__REVERSE @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2EBIT__REVERSE,type,
% 1.17/1.38 fo__c_2Ebit_2EBIT__REVERSE: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2EBIT__REVERSE,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2EBIT__REVERSE @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EDIVMOD__2EXP,type,
% 1.17/1.38 c_2Ebit_2EDIVMOD__2EXP: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EDIVMOD__2EXP,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EDIVMOD__2EXP @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EDIV__2EXP,type,
% 1.17/1.38 c_2Ebit_2EDIV__2EXP: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EDIV__2EXP,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EDIV__2EXP @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2EDIV__2EXP,type,
% 1.17/1.38 fo__c_2Ebit_2EDIV__2EXP: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2EDIV__2EXP,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2EDIV__2EXP @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2ELOG2,type,
% 1.17/1.38 c_2Ebit_2ELOG2: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2ELOG2,axiom,
% 1.17/1.38 mem @ c_2Ebit_2ELOG2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2ELOG2,type,
% 1.17/1.38 fo__c_2Ebit_2ELOG2: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2ELOG2,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2ELOG2 @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2ELOWEST__SET__BIT,type,
% 1.17/1.38 c_2Ebit_2ELOWEST__SET__BIT: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2ELOWEST__SET__BIT,axiom,
% 1.17/1.38 mem @ c_2Ebit_2ELOWEST__SET__BIT @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2ELOWEST__SET__BIT,type,
% 1.17/1.38 fo__c_2Ebit_2ELOWEST__SET__BIT: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2ELOWEST__SET__BIT,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2ELOWEST__SET__BIT @ X0 ) )
% 1.17/1.38 = ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EMOD__2EXP,type,
% 1.17/1.38 c_2Ebit_2EMOD__2EXP: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EMOD__2EXP,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EMOD__2EXP @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2EMOD__2EXP,type,
% 1.17/1.38 fo__c_2Ebit_2EMOD__2EXP: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2EMOD__2EXP,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2EMOD__2EXP @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EMOD__2EXP__EQ,type,
% 1.17/1.38 c_2Ebit_2EMOD__2EXP__EQ: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EMOD__2EXP__EQ,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EMOD__2EXP__EQ @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2EMOD__2EXP__MAX,type,
% 1.17/1.38 c_2Ebit_2EMOD__2EXP__MAX: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2EMOD__2EXP__MAX,axiom,
% 1.17/1.38 mem @ c_2Ebit_2EMOD__2EXP__MAX @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2ESBIT,type,
% 1.17/1.38 c_2Ebit_2ESBIT: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2ESBIT,axiom,
% 1.17/1.38 mem @ c_2Ebit_2ESBIT @ ( arr @ bool @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2ESIGN__EXTEND,type,
% 1.17/1.38 c_2Ebit_2ESIGN__EXTEND: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2ESIGN__EXTEND,axiom,
% 1.17/1.38 mem @ c_2Ebit_2ESIGN__EXTEND @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2ESIGN__EXTEND,type,
% 1.17/1.38 fo__c_2Ebit_2ESIGN__EXTEND: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2ESIGN__EXTEND,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2ESIGN__EXTEND @ X0 @ X1 @ X2 ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ c_2Ebit_2ESIGN__EXTEND @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2ESLICE,type,
% 1.17/1.38 c_2Ebit_2ESLICE: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2ESLICE,axiom,
% 1.17/1.38 mem @ c_2Ebit_2ESLICE @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2ESLICE,type,
% 1.17/1.38 fo__c_2Ebit_2ESLICE: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2ESLICE,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2ESLICE @ X0 @ X1 @ X2 ) )
% 1.17/1.38 = ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Ebit_2ETIMES__2EXP,type,
% 1.17/1.38 c_2Ebit_2ETIMES__2EXP: $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Ebit_2ETIMES__2EXP,axiom,
% 1.17/1.38 mem @ c_2Ebit_2ETIMES__2EXP @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(stp_fo_c_2Ebit_2ETIMES__2EXP,type,
% 1.17/1.38 fo__c_2Ebit_2ETIMES__2EXP: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.38
% 1.17/1.38 thf(stp_eq_fo_c_2Ebit_2ETIMES__2EXP,axiom,
% 1.17/1.38 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebit_2ETIMES__2EXP @ X0 @ X1 ) )
% 1.17/1.38 = ( ap @ ( ap @ c_2Ebit_2ETIMES__2EXP @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EMOD__2EXP__def,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EDIV__2EXP__def,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2ETIMES__2EXP__def,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ETIMES__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EDIVMOD__2EXP__def,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EDIVMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2ESBIT__def,axiom,
% 1.17/1.38 ! [V0b: $i] :
% 1.17/1.38 ( ( mem @ V0b @ bool )
% 1.17/1.38 => ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EBITS__def,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EBITV__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBITV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EBIT__def,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2ESLICE__def,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2ELOG2__def,axiom,
% 1.17/1.38 ( c_2Ebit_2ELOG2
% 1.17/1.38 = ( ap @ c_2Elogroot_2ELOG @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2ELOWEST__SET__BIT__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum
% 1.17/1.38 @ ( ap @ c_2Ewhile_2ELEAST
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V1i: $i] : ( ap @ ( ap @ c_2Ebit_2EBIT @ V1i ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EBIT__REVERSE__def,axiom,
% 1.17/1.38 ( ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ! [V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EBITWISE__def,axiom,
% 1.17/1.38 ( ! [V0op: $i] :
% 1.17/1.38 ( ( mem @ V0op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0op ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) )
% 1.17/1.38 & ! [V3n: tp__ty_2Enum_2Enum,V4op: $i] :
% 1.17/1.38 ( ( mem @ V4op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V5x: tp__ty_2Enum_2Enum,V6y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V4op ) @ ( inj__ty_2Enum_2Enum @ V5x ) ) @ ( inj__ty_2Enum_2Enum @ V6y ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V4op ) @ ( inj__ty_2Enum_2Enum @ V5x ) ) @ ( inj__ty_2Enum_2Enum @ V6y ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ V4op @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V5x ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V6y ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EBIT__MODIFY__def,axiom,
% 1.17/1.38 ( ! [V0f: $i] :
% 1.17/1.38 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) )
% 1.17/1.38 & ! [V2n: tp__ty_2Enum_2Enum,V3f: $i] :
% 1.17/1.38 ( ( mem @ V3f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3f ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V3f ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ V3f @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2ESIGN__EXTEND__def,axiom,
% 1.17/1.38 ! [V0l: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESIGN__EXTEND @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.38 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.38 @ ^ [V3m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0l ) ) ) ) @ V3m ) ) @ V3m ) ) )
% 1.17/1.38 @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0l ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EMOD__2EXP__EQ__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__EQ @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(ax_thm_2Ebit_2EMOD__2EXP__MAX__def,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__MAX @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELESS__MULT__MONO2,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum,V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELOG2__UNIQUE,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = V1p ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELOG2__TWOEXP,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = V0n ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIVMOD__2EXP,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EDIVMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESUC__SUB,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIV__MULT__1,axiom,
% 1.17/1.38 ! [V0r: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0r ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0r ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__ZERO__ADD1,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0m != fo__c_2Enum_2E0 )
% 1.17/1.38 => ? [V1p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( V0m
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EZERO__LT__TWOEXP,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EONE__LE__TWOEXP,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ETWOEXP__NOT__ZERO,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 != fo__c_2Enum_2E0 ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__2EXP__LT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ETWOEXP__DIVISION,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( V1k
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ETWOEXP__MONO,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ETWOEXP__MONO2,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EEXP__SUB__LESS__EQ,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__LEQ,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITSLT__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITSLT__THM2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__THM2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__LEQ,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__COMP__THM,axiom,
% 1.17/1.38 ! [V0h1: tp__ty_2Enum_2Enum,V1l1: tp__ty_2Enum_2Enum,V2h2: tp__ty_2Enum_2Enum,V3l2: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) @ ( inj__ty_2Enum_2Enum @ V0h1 ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V3l2 ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h1 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3l2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__DIV__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__LT__HIGH,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__ZERO,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__ZERO2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__ZERO3,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__ZERO4,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__ZEROL,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = V1a ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__LOG2__ZERO__ID,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = V0n ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__LT__LOW,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__ZERO,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__B,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__TWO__POW,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.38 <=> ( V1m = V0n ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__B__NEQ,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0a != V1b )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__COMP__THM2,axiom,
% 1.17/1.38 ! [V0h1: tp__ty_2Enum_2Enum,V1l1: tp__ty_2Enum_2Enum,V2h2: tp__ty_2Enum_2Enum,V3l2: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V3l2 ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h1 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3l2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__MOD2__LEM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 != fo__c_2Enum_2E0 )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__MOD2__LEM2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 != ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EODD__MOD2__LEM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIV__MULT__THM,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIV__MULT__THM2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELESS__EQ__EXP__MULT,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 => ? [V2p: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2p ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__THM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICELT__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SLICE__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SLICE__THM2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1h2: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1h2 ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V1h2 ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__ZERO__THM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__2EXP__MONO,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__COMP__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__COMP__RWT,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1m_27: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum,V3l: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
% 1.17/1.38 & ( V1m_27
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__ZERO,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__ZERO2,axiom,
% 1.17/1.38 ! [V0l: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SUM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SUM2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESLICE__COMP__THM2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum,V3y: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SUM3,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__MUL,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__COMP__THM3,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__BIT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__BITS,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 != fo__c_2Enum_2E0 )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__BITS2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 != ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SLICE,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SLICE__LEM,axiom,
% 1.17/1.38 ! [V0y: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0y ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SLICE__THM,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SLICE__THM2,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SLICE__THM3,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SLICE__THM4,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 1.17/1.38 <=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESBIT__DIV,axiom,
% 1.17/1.38 ! [V0b: $i] :
% 1.17/1.38 ( ( mem @ V0b @ bool )
% 1.17/1.38 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SUC,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__SUC__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__BITS__THM,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ! [V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITS__ZERO5,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ! [V2i: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT0__ODD,axiom,
% 1.17/1.38 ( ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.38 = c_2Earithmetic_2EODD ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITV__THM,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBITV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EADD__BIT0,axiom,
% 1.17/1.38 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 <=> ~ ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EADD__BITS__SUC,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EADD__BIT__SUC,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__LT__2EXP,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1op: $i] :
% 1.17/1.38 ( ( mem @ V1op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1op ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__THM,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2op: $i] :
% 1.17/1.38 ( ( mem @ V2op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V3a: tp__ty_2Enum_2Enum,V4b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2op ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ V2op @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__COR,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2op: $i] :
% 1.17/1.38 ( ( mem @ V2op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V3a: tp__ty_2Enum_2Enum,V4b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ V2op @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2op ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__NOT__COR,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2op: $i] :
% 1.17/1.38 ( ( mem @ V2op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V3a: tp__ty_2Enum_2Enum,V4b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( ~ ( p @ ( ap @ ( ap @ V2op @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2op ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__BITS,axiom,
% 1.17/1.38 ! [V0wl: tp__ty_2Enum_2Enum,V1op: $i] :
% 1.17/1.38 ( ( mem @ V1op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0wl ) ) ) @ V1op ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0wl ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0wl ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0wl ) ) ) @ V1op ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__BIT__GT__TWOEXP,axiom,
% 1.17/1.38 ! [V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__IMP__GE__TWOEXP,axiom,
% 1.17/1.38 ! [V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__ONE__COMP__LEM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap
% 1.17/1.38 @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 @ ( lam @ bool
% 1.17/1.38 @ ^ [V3x: $i] :
% 1.17/1.38 ( lam @ bool
% 1.17/1.38 @ ^ [V4y: $i] : ( ap @ c_2Ebool_2E_7E @ V3x ) ) ) )
% 1.17/1.38 @ ( inj__ty_2Enum_2Enum @ V1a ) )
% 1.17/1.38 @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__COMPLEMENT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
% 1.17/1.38 <=> ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 & ( V1i = V0n ) )
% 1.17/1.38 | ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 != fo__c_2Enum_2E0 )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 & ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__OF__BITS__THM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SHIFT__THM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2s: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2s ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2s ) ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SHIFT__THM2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2s: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2s ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2s ) ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2s ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SHIFT__THM3,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum,V2s: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2s ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2s ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__OF__BITS__THM2,axiom,
% 1.17/1.38 ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__DIV2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SHIFT__THM4,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIV__LT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__ZERO__GT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( V1a != fo__c_2Enum_2E0 )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIV__GT0,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EDIV__SUB1,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.38 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__EXP__SUB1,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SHIFT__THM5,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum,V3a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ESBIT__MULT,axiom,
% 1.17/1.38 ! [V0b: $i] :
% 1.17/1.38 ( ( mem @ V0b @ bool )
% 1.17/1.38 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ V0b ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBITWISE__EVAL,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1op: $i] :
% 1.17/1.38 ( ( mem @ V1op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V2a: tp__ty_2Enum_2Enum,V3b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1op ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V3b ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1op ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V3b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ V1op @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V3b ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__PLUS__RIGHT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ! [V1j: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1j ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__PLUS__LEFT,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ! [V1j: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V1j ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__PLUS__1,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = fo__c_2Enum_2E0 )
% 1.17/1.38 <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.38 = V0n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EMOD__ADD__1,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 != fo__c_2Enum_2E0 )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__REVERSE__THM,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELOG2__LE__MONO,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2,axiom,
% 1.17/1.38 ( ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) )
% 1.17/1.38 & ! [V2y: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__BIT__GT__LOG2,axiom,
% 1.17/1.38 ! [V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ENOT__BIT__GT__BITWISE,axiom,
% 1.17/1.38 ! [V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2op: $i] :
% 1.17/1.38 ( ( mem @ V2op @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V3a: tp__ty_2Enum_2Enum,V4b: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2op ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELT__TWOEXP,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.38 <=> ( ( V0x = fo__c_2Enum_2E0 )
% 1.17/1.38 | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__MODIFY__THM,axiom,
% 1.17/1.38 ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2f: $i] :
% 1.17/1.38 ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.38 => ! [V3a: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2f ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ V2f @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__SIGN__EXTEND,axiom,
% 1.17/1.38 ! [V0l: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3i: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0l != fo__c_2Enum_2E0 )
% 1.17/1.38 => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESIGN__EXTEND @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.38 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V0l ) ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0l ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EBIT__LOG2,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( V0n != fo__c_2Enum_2E0 )
% 1.17/1.38 => ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EEXISTS__BIT__IN__RANGE,axiom,
% 1.17/1.38 ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( V2n != fo__c_2Enum_2E0 )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) )
% 1.17/1.38 => ? [V3i: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2EEXISTS__BIT__LT,axiom,
% 1.17/1.38 ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( ( V1n != fo__c_2Enum_2E0 )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) )
% 1.17/1.38 => ? [V2i: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
% 1.17/1.38 & ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(conj_thm_2Ebit_2ELEAST__THM,axiom,
% 1.17/1.38 ! [V0n: tp__ty_2Enum_2Enum,V1P: $i] :
% 1.17/1.38 ( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.38 => ( ( ! [V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.38 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.38 => ~ ( p @ ( ap @ V1P @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
% 1.17/1.38 & ( p @ ( ap @ V1P @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.38 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ewhile_2ELEAST @ V1P ) )
% 1.17/1.38 = V0n ) ) ) ).
% 1.17/1.38
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 %------------------------------------------------------------------------------
% 1.17/1.38 thf(tp_c_2Epred__set_2EBIGINTER,type,
% 1.17/1.38 c_2Epred__set_2EBIGINTER: del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Epred__set_2EBIGINTER,axiom,
% 1.17/1.38 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.38
% 1.17/1.38 thf(tp_c_2Epred__set_2EBIGUNION,type,
% 1.17/1.38 c_2Epred__set_2EBIGUNION: del > $i ).
% 1.17/1.38
% 1.17/1.38 thf(mem_c_2Epred__set_2EBIGUNION,axiom,
% 1.17/1.38 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.38
% 1.17/1.39 thf(tp_c_2Epred__set_2EBIJ,type,
% 1.17/1.39 c_2Epred__set_2EBIJ: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EBIJ,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ECARD,type,
% 1.17/1.39 c_2Epred__set_2ECARD: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ECARD,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Enum_2Enum ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ECHOICE,type,
% 1.17/1.39 c_2Epred__set_2ECHOICE: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ECHOICE,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ECOMPL,type,
% 1.17/1.39 c_2Epred__set_2ECOMPL: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ECOMPL,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ECROSS,type,
% 1.17/1.39 c_2Epred__set_2ECROSS: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ECROSS,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EDELETE,type,
% 1.17/1.39 c_2Epred__set_2EDELETE: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EDELETE,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EDFUNSET,type,
% 1.17/1.39 c_2Epred__set_2EDFUNSET: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EDFUNSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EDFUNSET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EDIFF,type,
% 1.17/1.39 c_2Epred__set_2EDIFF: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EDIFF,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EDISJOINT,type,
% 1.17/1.39 c_2Epred__set_2EDISJOINT: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EDISJOINT,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EEMPTY,type,
% 1.17/1.39 c_2Epred__set_2EEMPTY: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EEMPTY,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EEMPTY @ A_27a ) @ ( arr @ A_27a @ bool ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EFINITE,type,
% 1.17/1.39 c_2Epred__set_2EFINITE: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EFINITE,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EFUNSET,type,
% 1.17/1.39 c_2Epred__set_2EFUNSET: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EFUNSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EGSPEC,type,
% 1.17/1.39 c_2Epred__set_2EGSPEC: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EGSPEC,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EIMAGE,type,
% 1.17/1.39 c_2Epred__set_2EIMAGE: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EIMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EINJ,type,
% 1.17/1.39 c_2Epred__set_2EINJ: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EINJ,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EINSERT,type,
% 1.17/1.39 c_2Epred__set_2EINSERT: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EINSERT,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EINSERT @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EINTER,type,
% 1.17/1.39 c_2Epred__set_2EINTER: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EINTER,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EITSET,type,
% 1.17/1.39 c_2Epred__set_2EITSET: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EITSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ A_27b ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ELINV,type,
% 1.17/1.39 c_2Epred__set_2ELINV: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ELINV,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2ELINV @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ELINV__OPT,type,
% 1.17/1.39 c_2Epred__set_2ELINV__OPT: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ELINV__OPT,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2ELINV__OPT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EMAX__SET,type,
% 1.17/1.39 c_2Epred__set_2EMAX__SET: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EMAX__SET,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2EMAX__SET @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ty_2Enum_2Enum ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EMIN__SET,type,
% 1.17/1.39 c_2Epred__set_2EMIN__SET: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EMIN__SET,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2EMIN__SET @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ty_2Enum_2Enum ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EPOW,type,
% 1.17/1.39 c_2Epred__set_2EPOW: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EPOW,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EPOW @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EPREIMAGE,type,
% 1.17/1.39 c_2Epred__set_2EPREIMAGE: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EPREIMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EPROD__IMAGE,type,
% 1.17/1.39 c_2Epred__set_2EPROD__IMAGE: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EPROD__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EPROD__IMAGE @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EPROD__SET,type,
% 1.17/1.39 c_2Epred__set_2EPROD__SET: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EPROD__SET,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2EPROD__SET @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ty_2Enum_2Enum ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EPSUBSET,type,
% 1.17/1.39 c_2Epred__set_2EPSUBSET: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EPSUBSET,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EREL__RESTRICT,type,
% 1.17/1.39 c_2Epred__set_2EREL__RESTRICT: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EREL__RESTRICT,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EREST,type,
% 1.17/1.39 c_2Epred__set_2EREST: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EREST,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EREST @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ERINV,type,
% 1.17/1.39 c_2Epred__set_2ERINV: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ERINV,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2ERINV @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ESING,type,
% 1.17/1.39 c_2Epred__set_2ESING: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ESING,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2ESING @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ESUBSET,type,
% 1.17/1.39 c_2Epred__set_2ESUBSET: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ESUBSET,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ESUM__IMAGE,type,
% 1.17/1.39 c_2Epred__set_2ESUM__IMAGE: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ESUM__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ESUM__SET,type,
% 1.17/1.39 c_2Epred__set_2ESUM__SET: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ESUM__SET,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2ESUM__SET @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ty_2Enum_2Enum ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2ESURJ,type,
% 1.17/1.39 c_2Epred__set_2ESURJ: del > del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2ESURJ,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EUNION,type,
% 1.17/1.39 c_2Epred__set_2EUNION: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EUNION,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2EUNIV,type,
% 1.17/1.39 c_2Epred__set_2EUNIV: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2EUNIV,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2EUNIV @ A_27a ) @ ( arr @ A_27a @ bool ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Echooser,type,
% 1.17/1.39 c_2Epred__set_2Echooser: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Echooser,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Echooser @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Ecount,type,
% 1.17/1.39 c_2Epred__set_2Ecount: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Ecount,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2Ecount @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Ecountable,type,
% 1.17/1.39 c_2Epred__set_2Ecountable: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Ecountable,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Eenumerate,type,
% 1.17/1.39 c_2Epred__set_2Eenumerate: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Eenumerate,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Eenumerate @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ty_2Enum_2Enum @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Eequiv__on,type,
% 1.17/1.39 c_2Epred__set_2Eequiv__on: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Eequiv__on,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Eis__measure__maximal,type,
% 1.17/1.39 c_2Epred__set_2Eis__measure__maximal: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Eis__measure__maximal,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Eis__measure__maximal @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Enum__to__pair,type,
% 1.17/1.39 c_2Epred__set_2Enum__to__pair: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Enum__to__pair,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2Enum__to__pair @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Epair__to__num,type,
% 1.17/1.39 c_2Epred__set_2Epair__to__num: $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Epair__to__num,axiom,
% 1.17/1.39 mem @ c_2Epred__set_2Epair__to__num @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).
% 1.17/1.39
% 1.17/1.39 thf(stp_fo_c_2Epred__set_2Epair__to__num,type,
% 1.17/1.39 fo__c_2Epred__set_2Epair__to__num: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.39
% 1.17/1.39 thf(stp_eq_fo_c_2Epred__set_2Epair__to__num,axiom,
% 1.17/1.39 ! [X0: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
% 1.17/1.39 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Epred__set_2Epair__to__num @ X0 ) )
% 1.17/1.39 = ( ap @ c_2Epred__set_2Epair__to__num @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Epairwise,type,
% 1.17/1.39 c_2Epred__set_2Epairwise: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Epairwise,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Epairwise @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Epartition,type,
% 1.17/1.39 c_2Epred__set_2Epartition: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Epartition,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Epartition @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(tp_c_2Epred__set_2Eschroeder__close,type,
% 1.17/1.39 c_2Epred__set_2Eschroeder__close: del > $i ).
% 1.17/1.39
% 1.17/1.39 thf(mem_c_2Epred__set_2Eschroeder__close,axiom,
% 1.17/1.39 ! [A_27a: del] : ( mem @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ ( arr @ ( arr @ A_27a @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESPECIFICATION,axiom,
% 1.17/1.39 ! [A_27a: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0P ) )
% 1.17/1.39 <=> ( p @ ( ap @ V0P @ V1x ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__APP,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1P: $i] :
% 1.17/1.39 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1P ) )
% 1.17/1.39 <=> ( p @ ( ap @ V1P @ V0x ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__ABS,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1P: $i] :
% 1.17/1.39 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2x: $i] : ( ap @ V1P @ V2x ) ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ V1P @ V0x ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEXTENSION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s = V1t )
% 1.17/1.39 <=> ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__EQUAL__SETS,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s != V1t )
% 1.17/1.39 <=> ? [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 & ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) )
% 1.17/1.39 <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENUM__SET__WOP,axiom,
% 1.17/1.39 ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.39 => ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0s ) )
% 1.17/1.39 <=> ? [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.39 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V0s ) )
% 1.17/1.39 & ! [V3m: tp__ty_2Enum_2Enum] :
% 1.17/1.39 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ V0s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) )
% 1.17/1.39 => ! [V1v: $i] :
% 1.17/1.39 ( ( mem @ V1v @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1v ) @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27b ) @ V0f ) ) )
% 1.17/1.39 <=> ? [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27b )
% 1.17/1.39 & ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1v ) @ c_2Ebool_2ET )
% 1.17/1.39 = ( ap @ V0f @ V2x ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EGSPECIFICATION__applied,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) )
% 1.17/1.39 => ! [V1v: $i] :
% 1.17/1.39 ( ( mem @ V1v @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27b ) @ V0f ) @ V1v ) )
% 1.17/1.39 <=> ? [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27b )
% 1.17/1.39 & ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1v ) @ c_2Ebool_2ET )
% 1.17/1.39 = ( ap @ V0f @ V2x ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EGSPEC__ETA,axiom,
% 1.17/1.39 ! [A_27a: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x ) @ ( ap @ V0P @ V1x ) ) ) )
% 1.17/1.39 = V0P ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EGSPEC__PAIR__ETA,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.39 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.39 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V1x: $i] :
% 1.17/1.39 ( lam @ A_27b
% 1.17/1.39 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) ) ) )
% 1.17/1.39 = ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool ) @ V0P ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__GSPEC__IFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0y: $i] :
% 1.17/1.39 ( ( mem @ V0y @ A_27a )
% 1.17/1.39 => ! [V1P: $i] :
% 1.17/1.39 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0y )
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ V1P @ V2x ) ) ) ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ V1P @ V0y ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__IFF,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27b )
% 1.17/1.39 => ! [V2P: $i] :
% 1.17/1.39 ( ( mem @ V2P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.39 => ( ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y ) )
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.39 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V3x: $i] :
% 1.17/1.39 ( lam @ A_27b
% 1.17/1.39 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V3x ) @ V4y ) ) @ ( ap @ ( ap @ V2P @ V3x ) @ V4y ) ) ) ) ) ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ V2P @ V0x ) @ V1y ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__GSPEC,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27b )
% 1.17/1.39 => ! [V3P: $i] :
% 1.17/1.39 ( ( mem @ V3P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ V3P @ V1y ) )
% 1.17/1.39 & ( V2x
% 1.17/1.39 = ( ap @ V0f @ V1y ) ) )
% 1.17/1.39 => ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2x )
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V4x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ ( ap @ V0f @ V4x ) ) @ ( ap @ V3P @ V4x ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__1,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0a: $i] :
% 1.17/1.39 ( ( mem @ V0a @ A_27a )
% 1.17/1.39 => ! [V1b: $i] :
% 1.17/1.39 ( ( mem @ V1b @ A_27b )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27b )
% 1.17/1.39 => ! [V3P: $i] :
% 1.17/1.39 ( ( mem @ V3P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0a ) @ V1b ) )
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V4y ) @ V2x ) ) @ ( ap @ V3P @ V4y ) ) ) ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ V3P @ V0a ) )
% 1.17/1.39 & ( V1b = V2x ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__2,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0a: $i] :
% 1.17/1.39 ( ( mem @ V0a @ A_27a )
% 1.17/1.39 => ! [V1b: $i] :
% 1.17/1.39 ( ( mem @ V1b @ A_27b )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ! [V3P: $i] :
% 1.17/1.39 ( ( mem @ V3P @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0a ) @ V1b ) )
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b )
% 1.17/1.39 @ ( lam @ A_27b
% 1.17/1.39 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V4y ) ) @ ( ap @ V3P @ V4y ) ) ) ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ V3P @ V1b ) )
% 1.17/1.39 & ( V0a = V2x ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__same,axiom,
% 1.17/1.39 ! [A_27a: del,V0a: $i] :
% 1.17/1.39 ( ( mem @ V0a @ A_27a )
% 1.17/1.39 => ! [V1b: $i] :
% 1.17/1.39 ( ( mem @ V1b @ A_27a )
% 1.17/1.39 => ! [V2P: $i] :
% 1.17/1.39 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p
% 1.17/1.39 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V0a ) @ V1b ) )
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3x ) @ V3x ) ) @ ( ap @ V2P @ V3x ) ) ) ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ V2P @ V0a ) )
% 1.17/1.39 & ( V0a = V1b ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESET__MINIMUM,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1M: $i] :
% 1.17/1.39 ( ( mem @ V1M @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.39 => ( ? [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) )
% 1.17/1.39 <=> ? [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) )
% 1.17/1.39 & ! [V4y: $i] :
% 1.17/1.39 ( ( mem @ V4y @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V0s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V1M @ V3x ) ) @ ( ap @ V1M @ V4y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EEMPTY__DEF,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ( c_2Epred__set_2EEMPTY @ A_27a )
% 1.17/1.39 = ( lam @ A_27a
% 1.17/1.39 @ ^ [V0x: $i] : c_2Ebool_2EF ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__IN__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EMEMBER__NOT__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ? [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEMPTY__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( c_2Epred__set_2EEMPTY @ A_27a ) @ V0x ) )
% 1.17/1.39 <=> $false ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EUNIV__DEF,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ( c_2Epred__set_2EUNIV @ A_27a )
% 1.17/1.39 = ( lam @ A_27a
% 1.17/1.39 @ ^ [V0x: $i] : c_2Ebool_2ET ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNIV__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( p @ ( ap @ ( c_2Epred__set_2EUNIV @ A_27a ) @ V0x ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNIV__NOT__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ( c_2Epred__set_2EUNIV @ A_27a )
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEMPTY__NOT__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ( c_2Epred__set_2EEMPTY @ A_27a )
% 1.17/1.39 != ( c_2Epred__set_2EUNIV @ A_27a ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEQ__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__EQ__UNIV__IMP,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.39 => ! [V1v: $i] :
% 1.17/1.39 ( ( mem @ V1v @ A_27a )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1v ) @ V0s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__THM,axiom,
% 1.17/1.39 ! [A_27a: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1Q: $i] :
% 1.17/1.39 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0P ) @ V1Q ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0P ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1Q ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ V0s @ V2x ) )
% 1.17/1.39 => ( p @ ( ap @ V1t @ V2x ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__TRANS,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V2u ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__REFL,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__ANTISYM,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) ) )
% 1.17/1.39 => ( V0s = V1t ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEMPTY__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNIV__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ V0s ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEQ__SUBSET__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s = V1t )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__SUBSET__EQ,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) ) )
% 1.17/1.39 <=> ( V0s = V1t ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__ADD,axiom,
% 1.17/1.39 ! [A_27a: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.39 => ! [V1n: tp__ty_2Enum_2Enum,V2d: tp__ty_2Enum_2Enum] :
% 1.17/1.39 ( ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ V0f @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2d ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EK__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ bool )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ A_27a ) @ V0x ) ) @ V1y ) )
% 1.17/1.39 <=> ( ~ ( p @ V0x )
% 1.17/1.39 | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ V1y ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__K,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ bool )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0x ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ A_27a ) @ V1y ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 | ( p @ V1y ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EPSUBSET__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( V0s != V1t ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPSUBSET__TRANS,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V1t ) @ V2u ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPSUBSET__IRREFL,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__PSUBSET__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__UNIV__PSUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPSUBSET__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.39 <=> ? [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EUNION__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) @ V2x ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__ASSOC,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1t ) @ V2u ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ V2u ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__IDEMPOT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V0s )
% 1.17/1.39 = V0s ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__COMM,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1t ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__UNION,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) ) ) )
% 1.17/1.39 & ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V3t ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ V2u ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V2u ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V2u ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__UNION__ABSORPTION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = V1t ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0s )
% 1.17/1.39 = V0s ) )
% 1.17/1.39 & ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 = V1s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ V0s )
% 1.17/1.39 = ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.39 & ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.39 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEMPTY__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 <=> ( ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 & ( V1t
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EFORALL__IN__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ V3x ) ) ) )
% 1.17/1.39 <=> ( ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ V4x ) ) ) )
% 1.17/1.39 & ! [V5x: $i] :
% 1.17/1.39 ( ( mem @ V5x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V2t ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ V5x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EINTER__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) @ V2x ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__ASSOC,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1t ) @ V2u ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) @ V2u ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__IDEMPOT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V0s )
% 1.17/1.39 = V0s ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__COMM,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1t ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) @ V0s ) ) ) )
% 1.17/1.39 & ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V3t ) @ V2s ) ) @ V2s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1t ) @ V2u ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__INTER__ABSORPTION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__INTER1,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__INTER2,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1t ) @ V0s )
% 1.17/1.39 = V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0s )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 & ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ! [V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ V0s )
% 1.17/1.39 = V0s ) )
% 1.17/1.39 & ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.39 = V1s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__OVER__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1t ) @ V2u ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINTER__OVER__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1t ) @ V2u ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EDISJOINT__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__DISJOINT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ~ ? [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__SYM,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__ALT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V0s ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ V2u ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V2u ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1t ) @ V2u ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__UNION__BOTH,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) @ V2u ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V2u ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1t ) @ V2u ) ) ) )
% 1.17/1.39 & ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V2u ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V2u ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1t ) @ V2u ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2u ) @ V1t ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EDIFF__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.39 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__DIFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) @ V2x ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 = V0s ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEMPTY__DIFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0s )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__DIFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) @ V1t )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__EQ__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V0s )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNION__DIFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.39 = V1t )
% 1.17/1.39 & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1t ) @ V0s ) ) @ V0s )
% 1.17/1.39 = V1t ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__DIFF__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 = V1t ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2z: $i] :
% 1.17/1.39 ( ( mem @ V2z @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1y ) @ V2z ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0x ) @ V1y ) ) @ V2z ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__COMM,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2z: $i] :
% 1.17/1.39 ( ( mem @ V2z @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0x ) @ V1y ) ) @ V2z )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0x ) @ V2z ) ) @ V1y ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__SAME__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0x ) @ V1y ) ) @ V0x )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1y ) @ V0x ) )
% 1.17/1.39 & ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0x ) @ V1y ) ) @ V1y )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2g: $i] :
% 1.17/1.39 ( ( mem @ V2g @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) @ V2g )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V2g ) ) @ V1t ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__INTER2,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__DIFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1t ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) @ V1t ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__DIFFS,axiom,
% 1.17/1.39 ! [A_27a: del,V0g: $i] :
% 1.17/1.39 ( ( mem @ V0g @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.39 => ! [V1f: $i] :
% 1.17/1.39 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.39 => ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.39 ( ( ! [V4n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( ap @ V1f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) )
% 1.17/1.39 & ! [V5n: tp__ty_2Enum_2Enum] :
% 1.17/1.39 ( ( ap @ V0g @ ( inj__ty_2Enum_2Enum @ V5n ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ V1f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) )
% 1.17/1.39 & ( V2m != V3n ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ V0g @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ V0g @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EINSERT__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s )
% 1.17/1.39 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2y ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2y ) @ V0x ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ V2s ) ) )
% 1.17/1.39 <=> ( ( V0x = V1y )
% 1.17/1.39 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ V2s ) @ V0x ) )
% 1.17/1.39 <=> ( ( V0x = V1y )
% 1.17/1.39 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ECOMPONENT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESET__CASES,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 | ? [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 & ? [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 & ( V0s
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V2t ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDECOMPOSITION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.39 <=> ? [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 & ( V0s
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V2t ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EABSORPTION,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 <=> ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s )
% 1.17/1.39 = V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EABSORPTION__RWT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s )
% 1.17/1.39 = V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__COMM,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ V2s ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__UNIV,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.39 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__INSERT__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s )
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__EMPTY__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( c_2Epred__set_2EEMPTY @ A_27a )
% 1.17/1.39 != ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V2t )
% 1.17/1.39 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__UNION__EQ,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V2t )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V2t )
% 1.17/1.39 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V2t ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1s ) @ V2t ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__INSERT_27,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V2t ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V2t ) @ V1s ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) @ V2t ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V2t ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__DIFF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V0s ) ) @ V1t )
% 1.17/1.39 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EUNIV__BOOL,axiom,
% 1.17/1.39 ( ( c_2Epred__set_2EUNIV @ bool )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ bool ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ bool ) @ c_2Ebool_2EF ) @ ( c_2Epred__set_2EEMPTY @ bool ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EFORALL__IN__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1a: $i] :
% 1.17/1.39 ( ( mem @ V1a @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ V2s ) ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ V3x ) ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ V0P @ V1a ) )
% 1.17/1.39 & ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ V4x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEXISTS__IN__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1a: $i] :
% 1.17/1.39 ( ( mem @ V1a @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ? [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1a ) @ V2s ) ) )
% 1.17/1.39 & ( p @ ( ap @ V0P @ V3x ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ V0P @ V1a ) )
% 1.17/1.39 | ? [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
% 1.17/1.39 & ( p @ ( ap @ V0P @ V4x ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EDELETE__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V1x )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2y: $i] :
% 1.17/1.39 ( ( mem @ V2y @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2y ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.39 & ( V1x != V2y ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2y: $i] :
% 1.17/1.39 ( ( mem @ V2y @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2y ) @ V1x ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.39 & ( V1x != V2y ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 <=> ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x )
% 1.17/1.39 = V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V1x )
% 1.17/1.39 = V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__DELETE__EQ,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2x_27: $i] :
% 1.17/1.39 ( ( mem @ V2x_27 @ A_27a )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x_27 ) @ V0s ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2x_27 ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x_27 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V1x ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEMPTY__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0x )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EELT__IN__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) ) @ V0x )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__COMM,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V0x ) ) @ V1y )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1y ) ) @ V0x ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) ) @ V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2t ) @ V0x ) ) )
% 1.17/1.39 <=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__INSERT__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V2t ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESUBSET__OF__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDIFF__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V1t ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2x ) ) @ V1t ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPSUBSET__INSERT__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ? [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V0s ) ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EPSUBSET__MEMBER,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 & ? [V2y: $i] :
% 1.17/1.39 ( ( mem @ V2y @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ V1t ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ V0s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V2s ) ) @ V1y )
% 1.17/1.39 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0x ) @ V1y ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1y ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1y ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) )
% 1.17/1.39 = V1s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2x ) ) @ V1t )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) @ V2x ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__DELETE__SYM,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2x: $i] :
% 1.17/1.39 ( ( mem @ V2x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V2x ) ) @ V1t ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1t ) @ V2x ) ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2ECHOICE__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EREST__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__REST,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V1s ) ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 & ( V0x
% 1.17/1.39 != ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EREST__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V1s ) @ V0x ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 & ( V0x
% 1.17/1.39 != ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ECHOICE__NOT__IN__REST,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ECHOICE__INSERT__REST,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) )
% 1.17/1.39 = V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EREST__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EREST__PSUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( V0s
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2ESING__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V0s ) )
% 1.17/1.39 <=> ? [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 & ( V0s
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 <=> $false ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) )
% 1.17/1.39 <=> ( ( V1s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 | ( V1s
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 <=> ( ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V0s ) )
% 1.17/1.39 & ( V1t
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 | ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V1t ) )
% 1.17/1.39 & ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 | ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V0s ) )
% 1.17/1.39 & ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V1t ) )
% 1.17/1.39 & ( V0s = V1t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__SING,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) )
% 1.17/1.39 <=> ( V0x = V1y ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING__applied,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0x ) )
% 1.17/1.39 <=> ( V0x = V1y ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__SING__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ENOT__EMPTY__SING,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( c_2Epred__set_2EEMPTY @ A_27a )
% 1.17/1.39 != ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEQUAL__SING,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1y: $i] :
% 1.17/1.39 ( ( mem @ V1y @ A_27a )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 <=> ( V0x = V1y ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__SING__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINSERT__SING__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V0s )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V0s ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V0x )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDELETE__EQ__SING,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V1x )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ECHOICE__SING,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 = V0x ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EREST__SING,axiom,
% 1.17/1.39 ! [A_27a: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ( ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESING__IFF__EMPTY__REST,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V0s ) )
% 1.17/1.39 <=> ( ( V0s
% 1.17/1.39 != ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 & ( ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EIMAGE__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s )
% 1.17/1.39 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ ( ap @ V0f @ V2x ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIN__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0y: $i] :
% 1.17/1.39 ( ( mem @ V0y @ A_27b )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V0y ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V1s ) ) )
% 1.17/1.39 <=> ? [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 & ( V0y
% 1.17/1.39 = ( ap @ V2f @ V3x ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__applied,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0y: $i] :
% 1.17/1.39 ( ( mem @ V0y @ A_27b )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V1s ) @ V0y ) )
% 1.17/1.39 <=> ? [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 & ( V0y
% 1.17/1.39 = ( ap @ V2f @ V3x ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__IN,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.39 ( ( mem @ V0x @ A_27a )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V0x ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__ID,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V1x: $i] : V1x ) )
% 1.17/1.39 @ V0s )
% 1.17/1.39 = V0s ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__I,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a ) @ ( c_2Ecombin_2EI @ A_27a ) ) @ V0s )
% 1.17/1.39 = V0s ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__II,axiom,
% 1.17/1.39 ! [A_27a: del] :
% 1.17/1.39 ( ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a ) @ ( c_2Ecombin_2EI @ A_27a ) )
% 1.17/1.39 = ( c_2Ecombin_2EI @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__COMPOSE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.39 => ! [V1g: $i] :
% 1.17/1.39 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V0f ) @ V1g ) ) @ V2s )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1g ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V2s ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ ( ap @ V0f @ V1x ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__EQ__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1f: $i] :
% 1.17/1.39 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1f ) @ V0s )
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.39 <=> ( V0s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V2s ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1x ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__UNION,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__INTER,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__11,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s1: $i] :
% 1.17/1.39 ( ( mem @ V1s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2s2: $i] :
% 1.17/1.39 ( ( mem @ V2s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ! [V4y: $i] :
% 1.17/1.39 ( ( mem @ V4y @ A_27a )
% 1.17/1.39 => ( ( ( ap @ V0f @ V3x )
% 1.17/1.39 = ( ap @ V0f @ V4y ) )
% 1.17/1.39 <=> ( V3x = V4y ) ) ) )
% 1.17/1.39 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s1 )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s2 ) )
% 1.17/1.39 <=> ( V1s1 = V2s2 ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EDISJOINT__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s1: $i] :
% 1.17/1.39 ( ( mem @ V1s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2s2: $i] :
% 1.17/1.39 ( ( mem @ V2s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ! [V4y: $i] :
% 1.17/1.39 ( ( mem @ V4y @ A_27a )
% 1.17/1.39 => ( ( ( ap @ V0f @ V3x )
% 1.17/1.39 = ( ap @ V0f @ V4y ) )
% 1.17/1.39 <=> ( V3x = V4y ) ) ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s1 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s2 ) ) )
% 1.17/1.39 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1s1 ) @ V2s2 ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__CONG,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2f_27: $i] :
% 1.17/1.39 ( ( mem @ V2f_27 @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V3s_27: $i] :
% 1.17/1.39 ( ( mem @ V3s_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( ( V1s = V3s_27 )
% 1.17/1.39 & ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3s_27 ) )
% 1.17/1.39 => ( ( ap @ V0f @ V4x )
% 1.17/1.39 = ( ap @ V2f_27 @ V4x ) ) ) ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f_27 ) @ V3s_27 ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EGSPEC__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) )
% 1.17/1.39 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27b ) @ V0f )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ A_27a @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) @ ( c_2Epair_2EFST @ A_27a @ bool ) ) @ V0f ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ bool @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) @ ( c_2Epair_2ESND @ A_27a @ bool ) ) @ V0f ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1g: $i] :
% 1.17/1.39 ( ( mem @ V1g @ ( arr @ A_27c @ A_27a ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27c @ bool ) )
% 1.17/1.39 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27c @ A_27a ) @ V1g ) @ V2s ) )
% 1.17/1.39 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ A_27b @ A_27a ) @ V0f ) @ V1g ) ) @ V2s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EFORALL__IN__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1f: $i] :
% 1.17/1.39 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ! [V3y: $i] :
% 1.17/1.39 ( ( mem @ V3y @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27a ) @ V1f ) @ V2s ) ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ V3y ) ) ) )
% 1.17/1.39 <=> ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27b )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4x ) @ V2s ) )
% 1.17/1.39 => ( p @ ( ap @ V0P @ ( ap @ V1f @ V4x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EEXISTS__IN__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.39 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1f: $i] :
% 1.17/1.39 ( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ? [V3y: $i] :
% 1.17/1.39 ( ( mem @ V3y @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27a ) @ V1f ) @ V2s ) ) )
% 1.17/1.39 & ( p @ ( ap @ V0P @ V3y ) ) )
% 1.17/1.39 <=> ? [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27b )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4x ) @ V2s ) )
% 1.17/1.39 & ( p @ ( ap @ V0P @ ( ap @ V1f @ V4x ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EINJ__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 <=> ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2t ) ) ) )
% 1.17/1.39 & ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27a )
% 1.17/1.39 => ! [V5y: $i] :
% 1.17/1.39 ( ( mem @ V5y @ A_27a )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V1s ) ) )
% 1.17/1.39 => ( ( ( ap @ V0f @ V4x )
% 1.17/1.39 = ( ap @ V0f @ V5y ) )
% 1.17/1.39 => ( V4x = V5y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__IFF,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 <=> ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2t ) ) ) )
% 1.17/1.39 & ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27a )
% 1.17/1.39 => ! [V5y: $i] :
% 1.17/1.39 ( ( mem @ V5y @ A_27a )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V1s ) ) )
% 1.17/1.39 => ( ( ( ap @ V0f @ V4x )
% 1.17/1.39 = ( ap @ V0f @ V5y ) )
% 1.17/1.39 <=> ( V4x = V5y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__ID,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p
% 1.17/1.39 @ ( ap
% 1.17/1.39 @ ( ap
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V1x: $i] : V1x ) )
% 1.17/1.39 @ V0s )
% 1.17/1.39 @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__COMPOSE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1g: $i] :
% 1.17/1.39 ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V4u: $i] :
% 1.17/1.39 ( ( mem @ V4u @ ( arr @ A_27c @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V3t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27b @ A_27c ) @ V1g ) @ V3t ) @ V4u ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V1g ) @ V0f ) ) @ V2s ) @ V4u ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1s ) ) )
% 1.17/1.39 & ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
% 1.17/1.39 <=> ( V2s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) )
% 1.17/1.39 => ! [V3e: $i] :
% 1.17/1.39 ( ( mem @ V3e @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3e ) @ V0s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V2f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V3e ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27b ) @ V1t ) @ ( ap @ V2f @ V3e ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__INSERT,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V2s ) ) @ V3t ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V3t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V1x ) ) @ V3t ) )
% 1.17/1.39 & ! [V4y: $i] :
% 1.17/1.39 ( ( mem @ V4y @ A_27a )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V2s ) )
% 1.17/1.39 & ( ( ap @ V0f @ V1x )
% 1.17/1.39 = ( ap @ V0f @ V4y ) ) )
% 1.17/1.39 => ( V1x = V4y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__EXTEND,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0b: $i] :
% 1.17/1.39 ( ( mem @ V0b @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ! [V4y: $i] :
% 1.17/1.39 ( ( mem @ V4y @ A_27b )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0b ) @ V1s ) @ V2t ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.39 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V2t ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EUPDATE @ A_27a @ A_27b ) @ V3x ) @ V4y ) @ V0b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V3x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V4y ) @ V2t ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V3s0: $i] :
% 1.17/1.39 ( ( mem @ V3s0 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V4t0: $i] :
% 1.17/1.39 ( ( mem @ V4t0 @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V3s0 ) @ V1s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V2t ) @ V4t0 ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V3s0 ) @ V4t0 ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__IMAGE__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2ESURJ__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 <=> ( ! [V3x: $i] :
% 1.17/1.39 ( ( mem @ V3x @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2t ) ) ) )
% 1.17/1.39 & ! [V4x: $i] :
% 1.17/1.39 ( ( mem @ V4x @ A_27b )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4x ) @ V2t ) )
% 1.17/1.39 => ? [V5y: $i] :
% 1.17/1.39 ( ( mem @ V5y @ A_27a )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5y ) @ V1s ) )
% 1.17/1.39 & ( ( ap @ V0f @ V5y )
% 1.17/1.39 = V4x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESURJ__ID,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p
% 1.17/1.39 @ ( ap
% 1.17/1.39 @ ( ap
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V1x: $i] : V1x ) )
% 1.17/1.39 @ V0s )
% 1.17/1.39 @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESURJ__COMPOSE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1g: $i] :
% 1.17/1.39 ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V4u: $i] :
% 1.17/1.39 ( ( mem @ V4u @ ( arr @ A_27c @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V3t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27b @ A_27c ) @ V1g ) @ V3t ) @ V4u ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V1g ) @ V0f ) ) @ V2s ) @ V4u ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESURJ__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1s ) )
% 1.17/1.39 <=> ( V1s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) )
% 1.17/1.39 & ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
% 1.17/1.39 <=> ( V2s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EIMAGE__SURJ,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 <=> ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s )
% 1.17/1.39 = V2t ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESURJ__IMAGE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2ESURJ__IMP__INJ,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ? [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 => ? [V3g: $i] :
% 1.17/1.39 ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27b @ A_27a ) @ V3g ) @ V1t ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(ax_thm_2Epred__set_2EBIJ__DEF,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 <=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__ID,axiom,
% 1.17/1.39 ! [A_27a: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( p
% 1.17/1.39 @ ( ap
% 1.17/1.39 @ ( ap
% 1.17/1.39 @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27a )
% 1.17/1.39 @ ( lam @ A_27a
% 1.17/1.39 @ ^ [V1x: $i] : V1x ) )
% 1.17/1.39 @ V0s )
% 1.17/1.39 @ V0s ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__IMP__11,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) )
% 1.17/1.39 => ! [V1x: $i] :
% 1.17/1.39 ( ( mem @ V1x @ A_27a )
% 1.17/1.39 => ! [V2y: $i] :
% 1.17/1.39 ( ( mem @ V2y @ A_27a )
% 1.17/1.39 => ( ( ( ap @ V0f @ V1x )
% 1.17/1.39 = ( ap @ V0f @ V2y ) )
% 1.17/1.39 <=> ( V1x = V2y ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__EMPTY,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1s ) )
% 1.17/1.39 <=> ( V1s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) )
% 1.17/1.39 & ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
% 1.17/1.39 <=> ( V2s
% 1.17/1.39 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__COMPOSE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.39 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V1g: $i] :
% 1.17/1.39 ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.39 => ! [V2s: $i] :
% 1.17/1.39 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V4u: $i] :
% 1.17/1.39 ( ( mem @ V4u @ ( arr @ A_27c @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V3t ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27b @ A_27c ) @ V1g ) @ V3t ) @ V4u ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V1g ) @ V0f ) ) @ V2s ) @ V4u ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__DELETE,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) )
% 1.17/1.39 => ! [V3e: $i] :
% 1.17/1.39 ( ( mem @ V3e @ A_27a )
% 1.17/1.39 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3e ) @ V0s ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V3e ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27b ) @ V1t ) @ ( ap @ V2f @ V3e ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__IMAGE__BIJ,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1f: $i] :
% 1.17/1.39 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ( ? [V2t: $i] :
% 1.17/1.39 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ V2t ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1f ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EINJ__BIJ__SUBSET,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s0: $i] :
% 1.17/1.39 ( ( mem @ V0s0 @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1s: $i] :
% 1.17/1.39 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 => ! [V3t: $i] :
% 1.17/1.39 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s0 ) @ V1s ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V2f ) @ V1s ) @ V3t ) ) )
% 1.17/1.39 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0s0 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V2f ) @ V0s0 ) ) ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__SYM__IMP,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ? [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 => ? [V3g: $i] :
% 1.17/1.39 ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27b @ A_27a ) @ V3g ) @ V1t ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__SYM,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ? [V2f: $i] :
% 1.17/1.39 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 <=> ? [V3g: $i] :
% 1.17/1.39 ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27b @ A_27a ) @ V3g ) @ V1t ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.39
% 1.17/1.39 thf(conj_thm_2Epred__set_2EBIJ__TRANS,axiom,
% 1.17/1.39 ! [A_27a: del,A_27b: del,A_27c: del,V0s: $i] :
% 1.17/1.39 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.39 => ! [V1t: $i] :
% 1.17/1.39 ( ( mem @ V1t @ ( arr @ A_27c @ bool ) )
% 1.17/1.39 => ! [V2u: $i] :
% 1.17/1.39 ( ( mem @ V2u @ ( arr @ A_27b @ bool ) )
% 1.17/1.39 => ( ( ? [V3f: $i] :
% 1.17/1.39 ( ( mem @ V3f @ ( arr @ A_27a @ A_27c ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27c ) @ V3f ) @ V0s ) @ V1t ) ) )
% 1.17/1.39 & ? [V4g: $i] :
% 1.17/1.39 ( ( mem @ V4g @ ( arr @ A_27c @ A_27b ) )
% 1.17/1.39 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27c @ A_27b ) @ V4g ) @ V1t ) @ V2u ) ) ) )
% 1.17/1.39 => ? [V5h: $i] :
% 1.17/1.40 ( ( mem @ V5h @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V5h ) @ V0s ) @ V2u ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__INV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ? [V3g: $i] :
% 1.17/1.40 ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27b @ A_27a ) @ V3g ) @ V2t ) @ V1s ) )
% 1.17/1.40 & ! [V4x: $i] :
% 1.17/1.40 ( ( mem @ V4x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27a @ A_27b ) @ V3g ) @ V0f ) @ V4x )
% 1.17/1.40 = V4x ) ) )
% 1.17/1.40 & ! [V5x: $i] :
% 1.17/1.40 ( ( mem @ V5x @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5x ) @ V2t ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ A_27b @ A_27a ) @ V0f ) @ V3g ) @ V5x )
% 1.17/1.40 = V5x ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EFUNSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0P ) @ V1Q )
% 1.17/1.40 = ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.40 @ ^ [V2f: $i] :
% 1.17/1.40 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0P ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ V1Q ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EDFUNSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDFUNSET @ A_27a @ A_27b ) @ V0P ) @ V1Q )
% 1.17/1.40 = ( lam @ ( arr @ A_27a @ A_27b )
% 1.17/1.40 @ ^ [V2f: $i] :
% 1.17/1.40 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0P ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__FUNSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2Q: $i] :
% 1.17/1.40 ( ( mem @ V2Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ A_27b ) ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V1P ) @ V2Q ) ) )
% 1.17/1.40 <=> ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2Q ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFUNSET__applied,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2Q: $i] :
% 1.17/1.40 ( ( mem @ V2Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V1P ) @ V2Q ) @ V0f ) )
% 1.17/1.40 <=> ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2Q ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__DFUNSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2Q: $i] :
% 1.17/1.40 ( ( mem @ V2Q @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ A_27b ) ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDFUNSET @ A_27a @ A_27b ) @ V1P ) @ V2Q ) ) )
% 1.17/1.40 <=> ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ ( ap @ V2Q @ V3x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EDFUNSET__applied,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2Q: $i] :
% 1.17/1.40 ( ( mem @ V2Q @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EDFUNSET @ A_27a @ A_27b ) @ V1P ) @ V2Q ) @ V0f ) )
% 1.17/1.40 <=> ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ ( ap @ V2Q @ V3x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFUNSET__THM,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ A_27b ) ) @ V2f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V0s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V2f @ V3x ) ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EUNIV__FUNSET__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del] :
% 1.17/1.40 ( ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( c_2Epred__set_2EUNIV @ A_27b ) )
% 1.17/1.40 = ( c_2Epred__set_2EUNIV @ ( arr @ A_27a @ A_27b ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFUNSET__DFUNSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1y: $i] :
% 1.17/1.40 ( ( mem @ V1y @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EDFUNSET @ A_27a @ A_27b ) @ V0x ) @ ( ap @ ( c_2Ecombin_2EK @ ( arr @ A_27b @ bool ) @ A_27a ) @ V1y ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EEMPTY__FUNSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V0s )
% 1.17/1.40 = ( c_2Epred__set_2EUNIV @ ( arr @ A_27a @ A_27b ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFUNSET__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ A_27b ) ) @ V1f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) )
% 1.17/1.40 <=> ( V0s
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFUNSET__INTER,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0a: $i] :
% 1.17/1.40 ( ( mem @ V0a @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1b: $i] :
% 1.17/1.40 ( ( mem @ V1b @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2c: $i] :
% 1.17/1.40 ( ( mem @ V2c @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27b ) @ V1b ) @ V2c ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ ( arr @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V0a ) @ V2c ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2Eschroeder__close__def,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ V0f ) @ V1s ) @ V2x ) )
% 1.17/1.40 <=> ? [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a ) @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESCHROEDER__CLOSE,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ V1f ) @ V2s ) ) )
% 1.17/1.40 <=> ? [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a ) @ V1f ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESCHROEDER__CLOSED,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ V0f ) @ V1s ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESCHROEDER__CLOSE__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESCHROEDER__CLOSE__SET,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ A_27a ) ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27a ) @ V1s ) @ V1s ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2Eschroeder__close @ A_27a ) @ V0f ) @ V2t ) ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESCHROEDER__BERNSTEIN__AUTO,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.40 & ? [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27a ) @ V2f ) @ V0s ) @ V1t ) ) ) )
% 1.17/1.40 => ? [V3g: $i] :
% 1.17/1.40 ( ( mem @ V3g @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27a ) @ V3g ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESCHROEDER__BERNSTEIN,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ? [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 & ? [V3g: $i] :
% 1.17/1.40 ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27b @ A_27a ) @ V3g ) @ V1t ) @ V0s ) ) ) )
% 1.17/1.40 => ? [V4h: $i] :
% 1.17/1.40 ( ( mem @ V4h @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V4h ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__INJ__SURJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ? [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 & ? [V3g: $i] :
% 1.17/1.40 ( ( mem @ V3g @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V3g ) @ V0s ) @ V1t ) ) ) )
% 1.17/1.40 => ? [V4h: $i] :
% 1.17/1.40 ( ( mem @ V4h @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V4h ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__ALT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ A_27b ) ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EFUNSET @ A_27a @ A_27b ) @ V1s ) @ V2t ) ) )
% 1.17/1.40 & ! [V3y: $i] :
% 1.17/1.40 ( ( mem @ V3y @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3y ) @ V2t ) )
% 1.17/1.40 => ( p
% 1.17/1.40 @ ( ap @ ( c_2Ebool_2E_3F_21 @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V4x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V3y ) @ ( ap @ V0f @ V4x ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__INSERT__IMP,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ A_27a )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V3t: $i] :
% 1.17/1.40 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1e ) @ V2s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ V2s ) ) @ V3t ) ) )
% 1.17/1.40 => ? [V4u: $i] :
% 1.17/1.40 ( ( mem @ V4u @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 & ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ ( ap @ V0f @ V1e ) ) @ V4u )
% 1.17/1.40 = V3t )
% 1.17/1.40 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V1e ) ) @ V4u ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V4u ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ( V2t
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ELINV__OPT__def,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV__OPT @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2y )
% 1.17/1.40 = ( ap
% 1.17/1.40 @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2y ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
% 1.17/1.40 @ ( ap @ ( c_2Eoption_2ESOME @ A_27a )
% 1.17/1.40 @ ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2y ) ) ) ) ) )
% 1.17/1.40 @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ELINV__OPT__THM,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27b )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV__OPT @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2y )
% 1.17/1.40 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 & ( ( ap @ V0f @ V3x )
% 1.17/1.40 = V2y ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__LINV__OPT__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV__OPT @ A_27b @ A_27a ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27a ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Eoption_2ESOME @ A_27b ) ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__LINV__OPT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ! [V4y: $i] :
% 1.17/1.40 ( ( mem @ V4y @ A_27b )
% 1.17/1.40 => ( ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV__OPT @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V4y )
% 1.17/1.40 = ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) )
% 1.17/1.40 <=> ( ( V4y
% 1.17/1.40 = ( ap @ V0f @ V3x ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V2t ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ELINV__LO,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2y )
% 1.17/1.40 = ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV__OPT @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ELINV__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ ( ap @ V0f @ V3x ) )
% 1.17/1.40 = V3x ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__LINV__INV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3x ) @ V2t ) )
% 1.17/1.40 => ( ( ap @ V0f @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V3x ) )
% 1.17/1.40 = V3x ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__LINV__BIJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ V2t ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__IFF__INV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 <=> ( ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2t ) ) ) )
% 1.17/1.40 & ? [V4g: $i] :
% 1.17/1.40 ( ( mem @ V4g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.40 & ! [V5x: $i] :
% 1.17/1.40 ( ( mem @ V5x @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V5x ) @ V2t ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V4g @ V5x ) ) @ V1s ) ) ) )
% 1.17/1.40 & ! [V6x: $i] :
% 1.17/1.40 ( ( mem @ V6x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6x ) @ V1s ) )
% 1.17/1.40 => ( ( ap @ V4g @ ( ap @ V0f @ V6x ) )
% 1.17/1.40 = V6x ) ) )
% 1.17/1.40 & ! [V7x: $i] :
% 1.17/1.40 ( ( mem @ V7x @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V7x ) @ V2t ) )
% 1.17/1.40 => ( ( ap @ V0f @ ( ap @ V4g @ V7x ) )
% 1.17/1.40 = V7x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ A_27a )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V3t: $i] :
% 1.17/1.40 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ V2s ) ) @ V3t ) )
% 1.17/1.40 <=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1e ) @ V2s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V1e ) ) @ V3t ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27b ) @ V3t ) @ ( ap @ V0f @ V1e ) ) ) ) )
% 1.17/1.40 | ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1e ) @ V2s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V3t ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ERINV__LO,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ERINV @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2y )
% 1.17/1.40 = ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ELINV__OPT @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ERINV__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3x ) @ V2t ) )
% 1.17/1.40 => ( ( ap @ V0f @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ERINV @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V3x ) )
% 1.17/1.40 = V3x ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESURJ__INJ__INV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ? [V3g: $i] :
% 1.17/1.40 ( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27b @ A_27a ) @ V3g ) @ V2t ) @ V1s ) )
% 1.17/1.40 & ! [V4y: $i] :
% 1.17/1.40 ( ( mem @ V4y @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V4y ) @ V2t ) )
% 1.17/1.40 => ( ( ap @ V0f @ ( ap @ V3g @ V4y ) )
% 1.17/1.40 = V4y ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EFINITE__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 <=> ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ V1P @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 & ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ V1P @ V2s ) )
% 1.17/1.40 => ! [V3e: $i] :
% 1.17/1.40 ( ( mem @ V3e @ A_27a )
% 1.17/1.40 => ( p @ ( ap @ V1P @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V3e ) @ V2s ) ) ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ V1P @ V0s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del] : ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__INDUCT,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ V0P @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 & ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ V0P @ V1s ) ) )
% 1.17/1.40 => ! [V2e: $i] :
% 1.17/1.40 ( ( mem @ V2e @ A_27a )
% 1.17/1.40 => ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2e ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2e ) @ V1s ) ) ) ) ) ) ) )
% 1.17/1.40 => ! [V3s: $i] :
% 1.17/1.40 ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ V3s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__DELETE,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V0x ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__REST,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__REST__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__UNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINTER__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__FINITE__I,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPSUBSET__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__DIFF,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__DIFF__down,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0P ) @ V1Q ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1Q ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0P ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__SING,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESING__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIMAGE__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V1f ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27b )
% 1.17/1.40 => ( p
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2y ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1x ) @ ( ap @ V0f @ V2y ) ) ) ) ) ) ) )
% 1.17/1.40 => ! [V3s: $i] :
% 1.17/1.40 ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V3s ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27a )
% 1.17/1.40 => ( ( ( ap @ V0f @ V1x )
% 1.17/1.40 = ( ap @ V0f @ V2y ) )
% 1.17/1.40 <=> ( V1x = V2y ) ) ) )
% 1.17/1.40 => ! [V3s: $i] :
% 1.17/1.40 ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V3s ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__INJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EREL__RESTRICT__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,V0R: $i] :
% 1.17/1.40 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ! [V3y: $i] :
% 1.17/1.40 ( ( mem @ V3y @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ V1s ) @ V2x ) @ V3y ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V3y ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EREL__RESTRICT__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del,V0R: $i] :
% 1.17/1.40 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 = ( c_2Erelation_2EEMPTY__REL @ A_27a ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EREL__RESTRICT__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0s1: $i] :
% 1.17/1.40 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s2: $i] :
% 1.17/1.40 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2R: $i] :
% 1.17/1.40 ( ( mem @ V2R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V2R ) @ V0s1 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V2R ) @ V1s2 ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ECARD__DEF,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 & ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V0s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V0s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__EQ__0,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 <=> ( V0s
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__DELETE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V1x ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__INTER__LESS__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__UNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__UNION__EQN,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__PSUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__EQ__CARD,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) )
% 1.17/1.40 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 => ( V0s = V1t ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__SING,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESING__IFF__CARD1,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2ESING @ A_27a ) @ V0s ) )
% 1.17/1.40 <=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__DIFF,axiom,
% 1.17/1.40 ! [A_27a: del,V0t: $i] :
% 1.17/1.40 ( ( mem @ V0t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0t ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s ) @ V0t ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V0t ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__DIFF__EQN,axiom,
% 1.17/1.40 ! [A_27a: del,V0t: $i] :
% 1.17/1.40 ( ( mem @ V0t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s ) @ V0t ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V0t ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ELESS__CARD__DIFF,axiom,
% 1.17/1.40 ! [A_27a: del,V0t: $i] :
% 1.17/1.40 ( ( mem @ V0t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0t ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0t ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s ) @ V0t ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIJ__FINITE__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ V0f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) ) )
% 1.17/1.40 => ? [V3N: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3N ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) )
% 1.17/1.40 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
% 1.17/1.40 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIJ__CARD,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIJ__CARD__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0S: $i] :
% 1.17/1.40 ( ( mem @ V0S @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0S ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0S ) @ V1t ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1t ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0S ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__INJ__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ! [V3y: $i] :
% 1.17/1.40 ( ( mem @ V3y @ A_27a )
% 1.17/1.40 => ( ( ( ap @ V0f @ V2x )
% 1.17/1.40 = ( ap @ V0f @ V3y ) )
% 1.17/1.40 <=> ( V2x = V3y ) ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESURJ__CARD,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__SURJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ V2t ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__SURJ__BIJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ V2t ) )
% 1.17/1.40 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__COMPLETE__INDUCTION,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V2y ) @ V1x ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ V2y ) ) ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1x ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ V1x ) ) ) ) )
% 1.17/1.40 => ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3x ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ V3x ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__CARD__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V2s ) @ V1t ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V2s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__CARD,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPHP,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V2t ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) )
% 1.17/1.40 => ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__CARD__IMAGE__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2Ecount__def,axiom,
% 1.17/1.40 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.40 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.40 @ ^ [V1m: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1m ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V1m ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__COUNT,axiom,
% 1.17/1.40 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOUNT__applied,axiom,
% 1.17/1.40 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOUNT__ZERO,axiom,
% 1.17/1.40 ( ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOUNT__SUC,axiom,
% 1.17/1.40 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ap @ c_2Epred__set_2Ecount @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__COUNT,axiom,
% 1.17/1.40 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__COUNT,axiom,
% 1.17/1.40 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.40 = V0n ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOUNT__11,axiom,
% 1.17/1.40 ! [V0n1: tp__ty_2Enum_2Enum,V1n2: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n1 ) )
% 1.17/1.40 = ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1n2 ) ) )
% 1.17/1.40 <=> ( V0n1 = V1n2 ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ENOT__IN__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.40 <=> ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ? [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__INHAB,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0P ) )
% 1.17/1.40 => ? [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0P ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIMAGE__11__INFINITE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27a )
% 1.17/1.40 => ( ( ( ap @ V0f @ V1x )
% 1.17/1.40 = ( ap @ V0f @ V2y ) )
% 1.17/1.40 => ( V1x = V2y ) ) ) )
% 1.17/1.40 => ! [V3s: $i] :
% 1.17/1.40 ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V3s ) )
% 1.17/1.40 => ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V3s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.40 => ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__INFINITE__NOT__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
% 1.17/1.40 => ? [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.40 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__INJ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.40 & ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__INJ__NOT__SURJ,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 <=> ? [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27a ) @ V1f ) @ V0s ) @ V0s ) )
% 1.17/1.40 & ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ A_27a ) @ V1f ) @ V0s ) @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.40 <=> ? [V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 & ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27a )
% 1.17/1.40 => ( ( ( ap @ V0f @ V1x )
% 1.17/1.40 = ( ap @ V0f @ V2y ) )
% 1.17/1.40 => ( V1x = V2y ) ) ) )
% 1.17/1.40 & ? [V3y: $i] :
% 1.17/1.40 ( ( mem @ V3y @ A_27a )
% 1.17/1.40 & ! [V4x: $i] :
% 1.17/1.40 ( ( mem @ V4x @ A_27a )
% 1.17/1.40 => ( ( ap @ V0f @ V4x )
% 1.17/1.40 != V3y ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__NUM__UNIV,axiom,
% 1.17/1.40 ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__PSUBSET__INFINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 <=> ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V1t ) @ V0s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__PSUBSET__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.40 <=> ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__DIFF__FINITE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIJ__COUNT__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 <=> ? [V1c: $i] :
% 1.17/1.40 ( ( mem @ V1c @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.40 & ? [V2n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ V1c ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIJ__COUNT,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ? [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.40 & ? [V2b: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V2b ) ) ) @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__ISO__NUM,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ? [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.40 & ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) )
% 1.17/1.40 => ( ( ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V2n ) )
% 1.17/1.40 = ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V3m ) ) )
% 1.17/1.40 => ( V2n = V3m ) ) )
% 1.17/1.40 & ( V0s
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ ty_2Enum_2Enum )
% 1.17/1.40 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.40 @ ^ [V4n: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ ( ap @ V1f @ V4n ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V4n ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__WEAK__ENUMERATE,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 <=> ? [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.40 & ? [V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ! [V3e: $i] :
% 1.17/1.40 ( ( mem @ V3e @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3e ) @ V0s ) )
% 1.17/1.40 <=> ? [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.40 & ( V3e
% 1.17/1.40 = ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__WF__noloops,axiom,
% 1.17/1.40 ! [A_27a: del,V0R: $i] :
% 1.17/1.40 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( c_2Erelation_2Eirreflexive @ A_27a ) @ ( ap @ ( c_2Erelation_2ETC @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__StrongOrder__WF,axiom,
% 1.17/1.40 ! [A_27a: del,V0R: $i] :
% 1.17/1.40 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Erelation_2EStrongOrder @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ V1s ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EBIGUNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0P )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V1x: $i] :
% 1.17/1.40 ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x )
% 1.17/1.40 @ ( ap @ ( c_2Ebool_2E_3F @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.40 @ ^ [V2s: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2s ) @ V0P ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V2s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__BIGUNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1sos: $i] :
% 1.17/1.40 ( ( mem @ V1sos @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1sos ) ) )
% 1.17/1.40 <=> ? [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2s ) @ V1sos ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__applied,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1sos: $i] :
% 1.17/1.40 ( ( mem @ V1sos @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1sos ) @ V0x ) )
% 1.17/1.40 <=> ? [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2s ) @ V1sos ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__BIGUNION__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2y: $i] :
% 1.17/1.40 ( ( mem @ V2y @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2y ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ ( arr @ A_27b @ bool ) ) @ V0f ) @ V1s ) ) ) )
% 1.17/1.40 <=> ? [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2y ) @ ( ap @ V0f @ V3x ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__EQ__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0P )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 <=> ( ( V0P
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 | ( V0P
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) ) ) )
% 1.17/1.40 & ( ( ( c_2Epred__set_2EEMPTY @ A_27a )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0P ) )
% 1.17/1.40 <=> ( ( V0P
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 | ( V0P
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__SING,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.40 = V0x ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__PAIR,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V1t ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__UNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0s1: $i] :
% 1.17/1.40 ( ( mem @ V0s1 @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ! [V1s2: $i] :
% 1.17/1.40 ( ( mem @ V1s2 @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( arr @ A_27a @ bool ) ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0s1 ) ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1s2 ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EDISJOINT__BIGUNION,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0s ) ) @ V1t ) )
% 1.17/1.40 <=> ! [V2s_27: $i] :
% 1.17/1.40 ( ( mem @ V2s_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2s_27 ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V2s_27 ) @ V1t ) ) ) ) ) ) )
% 1.17/1.40 & ! [V3s: $i] :
% 1.17/1.40 ( ( mem @ V3s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ! [V4t: $i] :
% 1.17/1.40 ( ( mem @ V4t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V4t ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V3s ) ) )
% 1.17/1.40 <=> ! [V5s_27: $i] :
% 1.17/1.40 ( ( mem @ V5s_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V5s_27 ) @ V3s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V4t ) @ V5s_27 ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V0s ) @ V1P ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1P ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0X: $i] :
% 1.17/1.40 ( ( mem @ V0X @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1P ) ) @ V0X ) )
% 1.17/1.40 <=> ! [V2Y: $i] :
% 1.17/1.40 ( ( mem @ V2Y @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2Y ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2Y ) @ V0X ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGUNION__IMAGE__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ! [V1N: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1N ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.40 => ( ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2n ) )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ V0f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ V0f ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1N ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIGUNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V0P ) )
% 1.17/1.40 & ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1s ) @ V0P ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0P ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIGUNION__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0P ) ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V0P ) )
% 1.17/1.40 & ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1s ) @ V0P ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__BIGUNION__I,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V0x ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1P ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__BIGUNION__SAME__SIZED__SETS,axiom,
% 1.17/1.40 ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ V1s ) )
% 1.17/1.40 & ! [V2e: $i] :
% 1.17/1.40 ( ( mem @ V2e @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2e ) @ V1s ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2e ) )
% 1.17/1.40 & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V2e ) )
% 1.17/1.40 = V0n ) ) ) )
% 1.17/1.40 & ! [V3e1: $i] :
% 1.17/1.40 ( ( mem @ V3e1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V4e2: $i] :
% 1.17/1.40 ( ( mem @ V4e2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3e1 ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V4e2 ) @ V1s ) )
% 1.17/1.40 & ( V3e1 != V4e2 ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V3e1 ) @ V4e2 ) ) ) ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ ( arr @ A_27a @ bool ) ) @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EDISJOINT__COUNT,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ( ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( V1m != V2n )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
% 1.17/1.40 => ! [V3n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ ( arr @ A_27a @ bool ) ) @ V0f ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFORALL__IN__BIGUNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ V2x ) ) ) )
% 1.17/1.40 <=> ! [V3t: $i] :
% 1.17/1.40 ( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V4x: $i] :
% 1.17/1.40 ( ( mem @ V4x @ A_27a )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3t ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V3t ) ) )
% 1.17/1.40 => ( p @ ( ap @ V0P @ V4x ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EBIGINTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V0P )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V1x: $i] :
% 1.17/1.40 ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x )
% 1.17/1.40 @ ( ap @ ( c_2Ebool_2E_21 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.40 @ ^ [V2s: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2s ) @ V0P ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V2s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__BIGINTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1B: $i] :
% 1.17/1.40 ( ( mem @ V1B @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1B ) ) )
% 1.17/1.40 <=> ! [V2P: $i] :
% 1.17/1.40 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2P ) @ V1B ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2P ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__applied,axiom,
% 1.17/1.40 ! [A_27a: del,V0B: $i] :
% 1.17/1.40 ( ( mem @ V0B @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ! [V1x: $i] :
% 1.17/1.40 ( ( mem @ V1x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V0B ) @ V1x ) )
% 1.17/1.40 <=> ! [V2P: $i] :
% 1.17/1.40 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2P ) @ V0B ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V2P ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__BIGINTER__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ ( arr @ A_27a @ bool ) ) @ V1f ) @ V2s ) ) ) )
% 1.17/1.40 <=> ! [V3y: $i] :
% 1.17/1.40 ( ( mem @ V3y @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3y ) @ V2s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ V1f @ V3y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1B: $i] :
% 1.17/1.40 ( ( mem @ V1B @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V0P ) @ V1B ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0P ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1B ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.40 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__INTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V0P ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V1Q ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0P ) @ V1Q ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__SING,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ V0P ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.40 = V0P ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__BIGINTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0X: $i] :
% 1.17/1.40 ( ( mem @ V0X @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0X ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1P ) ) )
% 1.17/1.40 <=> ! [V2Y: $i] :
% 1.17/1.40 ( ( mem @ V2Y @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2Y ) @ V1P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0X ) @ V2Y ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EDISJOINT__BIGINTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0X: $i] :
% 1.17/1.40 ( ( mem @ V0X @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Y: $i] :
% 1.17/1.40 ( ( mem @ V1Y @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2P: $i] :
% 1.17/1.40 ( ( mem @ V2P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1Y ) @ V2P ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V1Y ) @ V0X ) ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0X ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V2P ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V2P ) ) @ V0X ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__UNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0s1: $i] :
% 1.17/1.40 ( ( mem @ V0s1 @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ! [V1s2: $i] :
% 1.17/1.40 ( ( mem @ V1s2 @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( arr @ A_27a @ bool ) ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V0s1 ) ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1s2 ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EBIGINTER__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,V0sp: $i] :
% 1.17/1.40 ( ( mem @ V0sp @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V0sp ) ) ) )
% 1.17/1.40 & ( V1s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1s ) ) @ V0sp ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EDIFF__BIGINTER1,axiom,
% 1.17/1.40 ! [A_27a: del,V0sp: $i] :
% 1.17/1.40 ( ( mem @ V0sp @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0sp ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1s ) )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a )
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.40 @ ^ [V2u: $i] : ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0sp ) @ V2u ) ) )
% 1.17/1.40 @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EDIFF__BIGINTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0sp: $i] :
% 1.17/1.40 ( ( mem @ V0sp @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ( ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V0sp ) ) ) )
% 1.17/1.40 & ( V1s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V1s )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0sp )
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a )
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.40 @ ^ [V3u: $i] : ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0sp ) @ V3u ) ) )
% 1.17/1.40 @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__BIGINTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 => ( ? [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1s ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a ) @ V0P ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ECROSS__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.40 @ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
% 1.17/1.40 @ ^ [V2p: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ V2p ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V2p ) ) @ V0P ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V2p ) ) @ V1Q ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__CROSS,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2x ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V2x ) ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V2x ) ) @ V1Q ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__applied,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) @ V2x ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V2x ) ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V2x ) ) @ V1Q ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,A_27c: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
% 1.17/1.40 & ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27c @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27c ) ) @ V0P )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27c @ A_27a ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__EMPTY__EQN,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0s ) @ V1t )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
% 1.17/1.40 <=> ( ( V0s
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 | ( V1t
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__INSERT__LEFT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V0P ) ) @ V1Q )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V1Q ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__INSERT__RIGHT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V2x ) @ V1Q ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V2x ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__CROSS,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1Q ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__SINGS,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1y: $i] :
% 1.17/1.40 ( ( mem @ V1y @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27b ) @ V1y ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__SING__CROSS,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1P ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V1P ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1P ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__CROSS,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1Q ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0P ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27b ) @ V1Q ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__SUBSET,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ! [V2P0: $i] :
% 1.17/1.40 ( ( mem @ V2P0 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V3Q0: $i] :
% 1.17/1.40 ( ( mem @ V3Q0 @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V2P0 ) @ V3Q0 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) )
% 1.17/1.40 <=> ( ( V2P0
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 | ( V3Q0
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.40 | ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2P0 ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V3Q0 ) @ V1Q ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__CROSS__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0P ) @ V1Q ) ) )
% 1.17/1.40 <=> ( ( V0P
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 | ( V1Q
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.40 | ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0P ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V1Q ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECROSS__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del] :
% 1.17/1.40 ( ( c_2Epred__set_2EUNIV @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINFINITE__PAIR__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del] :
% 1.17/1.40 ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
% 1.17/1.40 <=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__UNIV,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del] :
% 1.17/1.40 ( ( c_2Epred__set_2EUNIV @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2EINL @ A_27a @ A_27b ) ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2EINR @ A_27a @ A_27b ) ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__INL,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.40 => ( ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V2x ) ) @ V1t ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2EINL @ A_27a @ A_27b ) ) @ V0s ) @ V1t ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINJ__INR,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ ( ty_2Esum_2Esum @ A_27b @ A_27a ) @ bool ) )
% 1.17/1.40 => ( ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Esum_2Esum @ A_27b @ A_27a ) ) @ ( ap @ ( c_2Esum_2EINR @ A_27b @ A_27a ) @ V2x ) ) @ V1t ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ ( ty_2Esum_2Esum @ A_27b @ A_27a ) ) @ ( c_2Esum_2EINR @ A_27b @ A_27a ) ) @ V0s ) @ V1t ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ECOMPL__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0P )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) @ V0P ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__COMPL,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V1s ) ) )
% 1.17/1.40 <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__applied,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ A_27a )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V1s ) @ V0x ) )
% 1.17/1.40 <=> ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__COMPL,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0s ) )
% 1.17/1.40 = V0s ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__CLAUSES,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0s ) ) @ V0s )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 & ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0s ) ) @ V0s )
% 1.17/1.40 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__SPLITS,axiom,
% 1.17/1.40 ! [A_27a: del,V0p: $i] :
% 1.17/1.40 ( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1q: $i] :
% 1.17/1.40 ( ( mem @ V1q @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0p ) @ V1q ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0p ) ) @ V1q ) )
% 1.17/1.40 = V1q ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EINTER__UNION__COMPL,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__INTER,axiom,
% 1.17/1.40 ! [A_27a: del,V0x: $i] :
% 1.17/1.40 ( ( mem @ V0x @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0x ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0x ) )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0x ) ) @ V0x )
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMPL__UNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V1t ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EITSET__ind,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.40 => ( ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V3b: $i] :
% 1.17/1.40 ( ( mem @ V3b @ A_27b )
% 1.17/1.40 => ( ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 & ( V2s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ V1P @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V2s ) ) @ ( ap @ ( ap @ V0f @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V2s ) ) @ V3b ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ V1P @ V2s ) @ V3b ) ) ) ) )
% 1.17/1.40 => ! [V4v: $i] :
% 1.17/1.40 ( ( mem @ V4v @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V5v1: $i] :
% 1.17/1.40 ( ( mem @ V5v1 @ A_27b )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ V1P @ V4v ) @ V5v1 ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EITSET__def,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V2b: $i] :
% 1.17/1.40 ( ( mem @ V2b @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ V2b )
% 1.17/1.40 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V2b ) @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V1f ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) @ ( ap @ ( ap @ V1f @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) @ V2b ) ) ) ) @ ( c_2Ebool_2EARB @ A_27b ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EITSET__IND,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V1P: $i] :
% 1.17/1.40 ( ( mem @ V1P @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.40 => ( ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V3b: $i] :
% 1.17/1.40 ( ( mem @ V3b @ A_27b )
% 1.17/1.40 => ( ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 & ( V2s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ V1P @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V2s ) ) @ ( ap @ ( ap @ V0f @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V2s ) ) @ V3b ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ V1P @ V2s ) @ V3b ) ) ) ) )
% 1.17/1.40 => ! [V4v: $i] :
% 1.17/1.40 ( ( mem @ V4v @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V5v1: $i] :
% 1.17/1.40 ( ( mem @ V5v1 @ A_27b )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ V1P @ V4v ) @ V5v1 ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EITSET__THM,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V2b: $i] :
% 1.17/1.40 ( ( mem @ V2b @ A_27b )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V1f ) @ V0s ) @ V2b )
% 1.17/1.40 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V2b ) @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V1f ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) @ ( ap @ ( ap @ V1f @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) @ V2b ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EITSET__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V1b: $i] :
% 1.17/1.40 ( ( mem @ V1b @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V1b )
% 1.17/1.40 = V1b ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EITSET__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ! [V3b: $i] :
% 1.17/1.40 ( ( mem @ V3b @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V1f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V0s ) ) @ V3b )
% 1.17/1.40 = ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V1f ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V0s ) ) ) @ ( ap @ ( ap @ V1f @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V0s ) ) ) @ V3b ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMMUTING__ITSET__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ! [V3y: $i] :
% 1.17/1.40 ( ( mem @ V3y @ A_27a )
% 1.17/1.40 => ! [V4z: $i] :
% 1.17/1.40 ( ( mem @ V4z @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ ( ap @ V0f @ V3y ) @ V4z ) )
% 1.17/1.40 = ( ap @ ( ap @ V0f @ V3y ) @ ( ap @ ( ap @ V0f @ V2x ) @ V4z ) ) ) ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
% 1.17/1.40 => ! [V5x: $i] :
% 1.17/1.40 ( ( mem @ V5x @ A_27a )
% 1.17/1.40 => ! [V6b: $i] :
% 1.17/1.40 ( ( mem @ V6b @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V5x ) @ V1s ) ) @ V6b )
% 1.17/1.40 = ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V5x ) ) @ ( ap @ ( ap @ V0f @ V5x ) @ V6b ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECOMMUTING__ITSET__RECURSES,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
% 1.17/1.40 => ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ A_27a )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V3b: $i] :
% 1.17/1.40 ( ( mem @ V3b @ A_27b )
% 1.17/1.40 => ( ( ! [V4x: $i] :
% 1.17/1.40 ( ( mem @ V4x @ A_27a )
% 1.17/1.40 => ! [V5y: $i] :
% 1.17/1.40 ( ( mem @ V5y @ A_27a )
% 1.17/1.40 => ! [V6z: $i] :
% 1.17/1.40 ( ( mem @ V6z @ A_27b )
% 1.17/1.40 => ( ( ap @ ( ap @ V0f @ V4x ) @ ( ap @ ( ap @ V0f @ V5y ) @ V6z ) )
% 1.17/1.40 = ( ap @ ( ap @ V0f @ V5y ) @ ( ap @ ( ap @ V0f @ V4x ) @ V6z ) ) ) ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) ) )
% 1.17/1.40 => ( ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ V2s ) ) @ V3b )
% 1.17/1.40 = ( ap @ ( ap @ V0f @ V1e ) @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1e ) ) @ V3b ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ESUM__IMAGE__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ ty_2Enum_2Enum )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V2e: $i] :
% 1.17/1.40 ( lam @ ty_2Enum_2Enum
% 1.17/1.40 @ ^ [V3acc: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V2e ) ) @ V3acc ) ) ) )
% 1.17/1.40 @ V1s )
% 1.17/1.40 @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__THM,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 & ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ A_27a )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ V2s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V0f @ V1e ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1e ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__SING,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ A_27a )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V1e ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__SUBSET__LE,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V2t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__IN__LE,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2e: $i] :
% 1.17/1.40 ( ( mem @ V2e @ A_27a )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2e ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V2e ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__DELETE,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ! [V2e: $i] :
% 1.17/1.40 ( ( mem @ V2e @ A_27a )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s ) @ V2e ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2e ) @ V1s ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) @ ( ap @ V0f @ V2e ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__UNION,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2t: $i] :
% 1.17/1.40 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s ) @ V2t ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V2t ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__lower__bound,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ V0f @ V3x ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__upper__bound,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SAME__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0P ) )
% 1.17/1.40 => ! [V1f: $i] :
% 1.17/1.40 ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V2p: $i] :
% 1.17/1.40 ( ( mem @ V2p @ A_27a )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2p ) @ V0P ) )
% 1.17/1.40 & ! [V3q: $i] :
% 1.17/1.40 ( ( mem @ V3q @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3q ) @ V0P ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ V1f @ V2p ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ V1f @ V3q ) ) ) ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V1f ) @ V0P ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0P ) ) @ ( ap @ V1f @ V2p ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__CONG,axiom,
% 1.17/1.40 ! [A_27a: del,V0s1: $i] :
% 1.17/1.40 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s2: $i] :
% 1.17/1.40 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2f1: $i] :
% 1.17/1.40 ( ( mem @ V2f1 @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V3f2: $i] :
% 1.17/1.40 ( ( mem @ V3f2 @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( ( V0s1 = V1s2 )
% 1.17/1.40 & ! [V4x: $i] :
% 1.17/1.40 ( ( mem @ V4x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V1s2 ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ V2f1 @ V4x ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ V3f2 @ V4x ) ) ) ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V2f1 ) @ V0s1 ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V3f2 ) @ V1s2 ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__ZERO,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.40 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V1s ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 <=> ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ V0f @ V2x ) )
% 1.17/1.40 = fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EABS__DIFF__SUM__IMAGE,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1g: $i] :
% 1.17/1.40 ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 => ( p
% 1.17/1.40 @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V1g ) @ V2s ) ) )
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Earithmetic_2EABS__DIFF @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) )
% 1.17/1.40 @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__MONO__LESS__EQ,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1g: $i] :
% 1.17/1.40 ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 => ( ! [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V1g ) @ V2s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__MONO__LESS,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1g: $i] :
% 1.17/1.40 ( ( mem @ V1g @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 => ( ( ? [V3x: $i] :
% 1.17/1.40 ( ( mem @ V3x @ A_27a )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V0f @ V3x ) ) @ ( ap @ V1g @ V3x ) ) ) )
% 1.17/1.40 & ! [V4x: $i] :
% 1.17/1.40 ( ( mem @ V4x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4x ) @ V2s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0f @ V4x ) ) @ ( ap @ V1g @ V4x ) ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V0f ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V1g ) @ V2s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__INJ__o,axiom,
% 1.17/1.40 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27b @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ V0s ) )
% 1.17/1.40 => ! [V1g: $i] :
% 1.17/1.40 ( ( mem @ V1g @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27b @ A_27a ) @ V1g ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.40 => ! [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V2f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27a ) @ V1g ) @ V0s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ ty_2Enum_2Enum @ A_27a ) @ V2f ) @ V1g ) ) @ V0s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__IMAGE__PERMUTES,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ! [V1g: $i] :
% 1.17/1.40 ( ( mem @ V1g @ ( arr @ A_27a @ A_27a ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27a ) @ V1g ) @ V0s ) @ V0s ) )
% 1.17/1.40 => ! [V2f: $i] :
% 1.17/1.40 ( ( mem @ V2f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ ty_2Enum_2Enum @ A_27a ) @ V2f ) @ V1g ) ) @ V0s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ A_27a ) @ V2f ) @ V0s ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2ESUM__SET__DEF,axiom,
% 1.17/1.40 ( c_2Epred__set_2ESUM__SET
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ ty_2Enum_2Enum ) @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__THM,axiom,
% 1.17/1.40 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2ESUM__SET @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 & ! [V0x: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2ESUM__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Epred__set_2ESUM__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ ty_2Enum_2Enum ) @ V1s ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__EMPTY,axiom,
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2ESUM__SET @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__SING,axiom,
% 1.17/1.40 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2ESUM__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) )
% 1.17/1.40 = V0n ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__SUBSET__LE,axiom,
% 1.17/1.40 ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1t ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Enum_2Enum ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Epred__set_2ESUM__SET @ V0s ) ) @ ( ap @ c_2Epred__set_2ESUM__SET @ V1t ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__IN__LE,axiom,
% 1.17/1.40 ! [V0x: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1s ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Epred__set_2ESUM__SET @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__DELETE,axiom,
% 1.17/1.40 ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) )
% 1.17/1.40 => ! [V1e: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2ESUM__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ ty_2Enum_2Enum ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) @ V0s ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Epred__set_2ESUM__SET @ V0s ) ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) ) @ ( ap @ c_2Epred__set_2ESUM__SET @ V0s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUM__SET__UNION,axiom,
% 1.17/1.40 ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1t: $i] :
% 1.17/1.40 ( ( mem @ V1t @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1t ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2ESUM__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ V0s ) @ V1t ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Epred__set_2ESUM__SET @ V0s ) ) @ ( ap @ c_2Epred__set_2ESUM__SET @ V1t ) ) ) @ ( ap @ c_2Epred__set_2ESUM__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ ty_2Enum_2Enum ) @ V0s ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EPROD__IMAGE__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2EPROD__IMAGE @ A_27a ) @ V0f ) @ V1s ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EITSET @ A_27a @ ty_2Enum_2Enum )
% 1.17/1.40 @ ( lam @ A_27a
% 1.17/1.40 @ ^ [V2e: $i] :
% 1.17/1.40 ( lam @ ty_2Enum_2Enum
% 1.17/1.40 @ ^ [V3acc: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ V0f @ V2e ) ) @ V3acc ) ) ) )
% 1.17/1.40 @ V1s )
% 1.17/1.40 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPROD__IMAGE__THM,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2EPROD__IMAGE @ A_27a ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.40 & ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ A_27a )
% 1.17/1.40 => ! [V2s: $i] :
% 1.17/1.40 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2EPROD__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ V2s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ V0f @ V1e ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPROD__IMAGE @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V2s ) @ V1e ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EPROD__SET__DEF,axiom,
% 1.17/1.40 ( c_2Epred__set_2EPROD__SET
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EPROD__IMAGE @ ty_2Enum_2Enum ) @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPROD__SET__THM,axiom,
% 1.17/1.40 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EPROD__SET @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.40 & ! [V0x: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EPROD__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Epred__set_2EPROD__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ ty_2Enum_2Enum ) @ V1s ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPROD__SET__EMPTY,axiom,
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EPROD__SET @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPROD__SET__IMAGE__REDUCTION,axiom,
% 1.17/1.40 ! [A_27a: del,V0f: $i] :
% 1.17/1.40 ( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ V1s ) ) )
% 1.17/1.40 & ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( ap @ V0f @ V2x ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ V1s ) ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EPROD__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2x ) @ V1s ) ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ V0f @ V2x ) ) @ ( ap @ c_2Epred__set_2EPROD__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ V1s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EMAX__SET__DEF,axiom,
% 1.17/1.40 ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) )
% 1.17/1.40 => ( ( ( V0s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V0s ) ) @ V0s ) )
% 1.17/1.40 & ! [V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V0s ) ) ) ) ) )
% 1.17/1.40 & ( ( V0s
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMAX__SET @ V0s ) )
% 1.17/1.40 = fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMAX__SET__THM,axiom,
% 1.17/1.40 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMAX__SET @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 & ! [V0e: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMAX__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ V1s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMAX__SET__REWRITES,axiom,
% 1.17/1.40 ! [V0e: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMAX__SET @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 = fo__c_2Enum_2E0 )
% 1.17/1.40 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMAX__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) )
% 1.17/1.40 = V0e ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMAX__SET__ELIM,axiom,
% 1.17/1.40 ! [V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0P ) )
% 1.17/1.40 & ( ( V0P
% 1.17/1.40 = ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( p @ ( ap @ V1Q @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
% 1.17/1.40 & ! [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ! [V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ V0P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ V0P ) ) )
% 1.17/1.40 => ( p @ ( ap @ V1Q @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ V1Q @ ( ap @ c_2Epred__set_2EMAX__SET @ V0P ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EMIN__SET__DEF,axiom,
% 1.17/1.40 c_2Epred__set_2EMIN__SET = c_2Ewhile_2ELEAST ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMIN__SET__ELIM,axiom,
% 1.17/1.40 ! [V0P: $i] :
% 1.17/1.40 ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1Q: $i] :
% 1.17/1.40 ( ( mem @ V1Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( V0P
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 & ! [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( ! [V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) @ V0P ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ V0P ) ) )
% 1.17/1.40 => ( p @ ( ap @ V1Q @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) )
% 1.17/1.40 => ( p @ ( ap @ V1Q @ ( ap @ c_2Epred__set_2EMIN__SET @ V0P ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMIN__SET__THM,axiom,
% 1.17/1.40 ( ! [V0e: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMIN__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0e ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) )
% 1.17/1.40 = V0e )
% 1.17/1.40 & ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V2e1: tp__ty_2Enum_2Enum,V3e2: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMIN__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2e1 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3e2 ) ) @ V1s ) ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V2e1 ) ) @ ( ap @ c_2Epred__set_2EMIN__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3e2 ) ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMIN__SET__LEM,axiom,
% 1.17/1.40 ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( V0s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2EMIN__SET @ V0s ) ) @ V0s ) )
% 1.17/1.40 & ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.40 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Epred__set_2EMIN__SET @ V0s ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__MIN__SET,axiom,
% 1.17/1.40 ! [A_27a: del,V0I: $i] :
% 1.17/1.40 ( ( mem @ V0I @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1J: $i] :
% 1.17/1.40 ( ( mem @ V1J @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V2n: $i] :
% 1.17/1.40 ( ( mem @ V2n @ A_27a )
% 1.17/1.40 => ( ( ( V0I
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 & ( V1J
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Enum_2Enum ) @ V0I ) @ V1J ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Epred__set_2EMIN__SET @ V1J ) ) @ ( ap @ c_2Epred__set_2EMIN__SET @ V0I ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__MAX__SET,axiom,
% 1.17/1.40 ! [V0I: $i] :
% 1.17/1.40 ( ( mem @ V0I @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1J: $i] :
% 1.17/1.40 ( ( mem @ V1J @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0I ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1J ) )
% 1.17/1.40 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ty_2Enum_2Enum ) @ V0I ) @ V1J ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Epred__set_2EMAX__SET @ V0I ) ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V1J ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMIN__SET__LEQ__MAX__SET,axiom,
% 1.17/1.40 ! [V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( V0s
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Epred__set_2EMIN__SET @ V0s ) ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMIN__SET__UNION,axiom,
% 1.17/1.40 ! [V0A: $i] :
% 1.17/1.40 ( ( mem @ V0A @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1B: $i] :
% 1.17/1.40 ( ( mem @ V1B @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0A ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1B ) )
% 1.17/1.40 & ( V0A
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.40 & ( V1B
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMIN__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ V0A ) @ V1B ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ c_2Epred__set_2EMIN__SET @ V0A ) ) @ ( ap @ c_2Epred__set_2EMIN__SET @ V1B ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EMAX__SET__UNION,axiom,
% 1.17/1.40 ! [V0A: $i] :
% 1.17/1.40 ( ( mem @ V0A @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ! [V1B: $i] :
% 1.17/1.40 ( ( mem @ V1B @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.40 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0A ) )
% 1.17/1.40 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V1B ) ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2EMAX__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ V0A ) @ V1B ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ c_2Epred__set_2EMAX__SET @ V0A ) ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V1B ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(ax_thm_2Epred__set_2EPOW__DEF,axiom,
% 1.17/1.40 ! [A_27a: del,V0set: $i] :
% 1.17/1.40 ( ( mem @ V0set @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0set )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.40 @ ^ [V1s: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ bool ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V0set ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EIN__POW,axiom,
% 1.17/1.40 ! [A_27a: del,V0set: $i] :
% 1.17/1.40 ( ( mem @ V0set @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1e: $i] :
% 1.17/1.40 ( ( mem @ V1e @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1e ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0set ) ) )
% 1.17/1.40 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1e ) @ V0set ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EUNIV__FUN__TO__BOOL,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( c_2Epred__set_2EUNIV @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 = ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__POW,axiom,
% 1.17/1.40 ! [A_27a: del,V0s1: $i] :
% 1.17/1.40 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s2: $i] :
% 1.17/1.40 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s1 ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V1s2 ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__INSERT__RIGHT,axiom,
% 1.17/1.40 ! [A_27a: del,V0e: $i] :
% 1.17/1.40 ( ( mem @ V0e @ A_27a )
% 1.17/1.40 => ! [V1s1: $i] :
% 1.17/1.40 ( ( mem @ V1s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2s2: $i] :
% 1.17/1.40 ( ( mem @ V2s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s1 ) @ V2s2 ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s1 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) @ V2s2 ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ESUBSET__DELETE__BOTH,axiom,
% 1.17/1.40 ! [A_27a: del,V0s1: $i] :
% 1.17/1.40 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V1s2: $i] :
% 1.17/1.40 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ! [V2x: $i] :
% 1.17/1.40 ( ( mem @ V2x @ A_27a )
% 1.17/1.40 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.40 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s1 ) @ V2x ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1s2 ) @ V2x ) ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPOW__EMPTY,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s )
% 1.17/1.40 != ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPOW__INSERT,axiom,
% 1.17/1.40 ! [A_27a: del,V0e: $i] :
% 1.17/1.40 ( ( mem @ V0e @ A_27a )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) @ V1s ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V1s ) ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V1s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EPOW__EQNS,axiom,
% 1.17/1.40 ! [A_27a: del] :
% 1.17/1.40 ( ( ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.40 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( arr @ A_27a @ bool ) ) ) )
% 1.17/1.40 & ! [V0e: $i] :
% 1.17/1.40 ( ( mem @ V0e @ A_27a )
% 1.17/1.40 => ! [V1s: $i] :
% 1.17/1.40 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) @ V1s ) )
% 1.17/1.40 = ( ap
% 1.17/1.40 @ ( ap @ ( c_2Ebool_2ELET @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.40 @ ( lam @ ( arr @ ( arr @ A_27a @ bool ) @ bool )
% 1.17/1.40 @ ^ [V2ps: $i] : ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0e ) ) @ V2ps ) ) @ V2ps ) ) )
% 1.17/1.40 @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EFINITE__POW,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2ECARD__POW,axiom,
% 1.17/1.40 ! [A_27a: del,V0s: $i] :
% 1.17/1.40 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.40 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.40 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s ) ) )
% 1.17/1.40 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.40
% 1.17/1.40 thf(conj_thm_2Epred__set_2EGSPEC__F,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V0x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V0x ) @ c_2Ebool_2EF ) ) )
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__T,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V0x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V0x ) @ c_2Ebool_2ET ) ) )
% 1.17/1.41 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__ID,axiom,
% 1.17/1.41 ! [A_27a: del,V0y: $i] :
% 1.17/1.41 ( ( mem @ V0y @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0y ) ) ) )
% 1.17/1.41 = V0y ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__EQ,axiom,
% 1.17/1.41 ! [A_27a: del,V0y: $i] :
% 1.17/1.41 ( ( mem @ V0y @ A_27a )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V0y ) ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__EQ2,axiom,
% 1.17/1.41 ! [A_27a: del,V0y: $i] :
% 1.17/1.41 ( ( mem @ V0y @ A_27a )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0y ) @ V1x ) ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__F__COND,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ bool ) ) )
% 1.17/1.41 => ( ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ~ ( p @ ( ap @ ( c_2Epair_2ESND @ A_27b @ bool ) @ ( ap @ V0f @ V1x ) ) ) )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27a ) @ V0f )
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__AND,axiom,
% 1.17/1.41 ! [A_27a: del,V0P: $i] :
% 1.17/1.41 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1Q: $i] :
% 1.17/1.41 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V2x ) ) @ ( ap @ V1Q @ V2x ) ) ) ) )
% 1.17/1.41 = ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ V0P @ V3x ) ) ) ) )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V4x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V4x ) @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EGSPEC__OR,axiom,
% 1.17/1.41 ! [A_27a: del,V0P: $i] :
% 1.17/1.41 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1Q: $i] :
% 1.17/1.41 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0P @ V2x ) ) @ ( ap @ V1Q @ V2x ) ) ) ) )
% 1.17/1.41 = ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x ) @ ( ap @ V0P @ V3x ) ) ) ) )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V4x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V4x ) @ ( ap @ V1Q @ V4x ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Eequiv__on__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 <=> ( ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ V0R @ V2x ) @ V2x ) ) ) )
% 1.17/1.41 & ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27a )
% 1.17/1.41 => ! [V4y: $i] :
% 1.17/1.41 ( ( mem @ V4y @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V1s ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ V0R @ V4y ) @ V3x ) ) ) ) ) )
% 1.17/1.41 & ! [V5x: $i] :
% 1.17/1.41 ( ( mem @ V5x @ A_27a )
% 1.17/1.41 => ! [V6y: $i] :
% 1.17/1.41 ( ( mem @ V6y @ A_27a )
% 1.17/1.41 => ! [V7z: $i] :
% 1.17/1.41 ( ( mem @ V7z @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V5x ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V6y ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V7z ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ V0R @ V5x ) @ V6y ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ V0R @ V6y ) @ V7z ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ V0R @ V5x ) @ V7z ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Epartition__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.41 @ ^ [V2t: $i] :
% 1.17/1.41 ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ bool ) @ V2t )
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V3x: $i] :
% 1.17/1.41 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.41 @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V2t )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V4y ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V1s ) ) @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EBIGUNION__partition,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 = V1s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EEMPTY__NOT__IN__partition,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epartition__elements__disjoint,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 => ! [V2t1: $i] :
% 1.17/1.41 ( ( mem @ V2t1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V3t2: $i] :
% 1.17/1.41 ( ( mem @ V3t2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t1 ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V3t2 ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.41 & ( V2t1 != V3t2 ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V2t1 ) @ V3t2 ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epartition__elements__interrelate,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.41 => ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27a )
% 1.17/1.41 => ! [V4y: $i] :
% 1.17/1.41 ( ( mem @ V4y @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V2t ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V2t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epartition__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2t ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EFINITE__partition,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.41 & ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V2t ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V2t ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epartition__CARD,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Eequiv__on @ A_27a ) @ V0R ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) ) )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1s ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ESUM__IMAGE @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2ECARD @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2Epartition @ A_27a ) @ V0R ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Epairwise__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0P: $i] :
% 1.17/1.41 ( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Epairwise @ A_27a ) @ V0P ) @ V1s ) )
% 1.17/1.41 <=> ! [V2e1: $i] :
% 1.17/1.41 ( ( mem @ V2e1 @ A_27a )
% 1.17/1.41 => ! [V3e2: $i] :
% 1.17/1.41 ( ( mem @ V3e2 @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2e1 ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3e2 ) @ V1s ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ V0P @ V2e1 ) @ V3e2 ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epairwise__UNION,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s1: $i] :
% 1.17/1.41 ( ( mem @ V1s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2s2: $i] :
% 1.17/1.41 ( ( mem @ V2s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Epairwise @ A_27a ) @ V0R ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1s1 ) @ V2s2 ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Epairwise @ A_27a ) @ V0R ) @ V1s1 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Epairwise @ A_27a ) @ V0R ) @ V2s2 ) )
% 1.17/1.41 & ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27a )
% 1.17/1.41 => ! [V4y: $i] :
% 1.17/1.41 ( ( mem @ V4y @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s1 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V2s2 ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ V0R @ V3x ) @ V4y ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ V0R @ V4y ) @ V3x ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epairwise__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Epairwise @ A_27a ) @ V0R ) @ V2t ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V2t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2Epairwise @ A_27a ) @ V0R ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EKoenigsLemma,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ( p
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2y ) @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) )
% 1.17/1.41 => ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27a )
% 1.17/1.41 => ( ~ ( p
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V4y ) @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3x ) @ V4y ) ) ) ) ) )
% 1.17/1.41 => ? [V5f: $i] :
% 1.17/1.41 ( ( mem @ V5f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ( ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.41 = V3x )
% 1.17/1.41 & ! [V6n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0R @ ( ap @ V5f @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ V5f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EKoenigsLemma__WF,axiom,
% 1.17/1.41 ! [A_27a: del,V0R: $i] :
% 1.17/1.41 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ( p
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2y ) @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Erelation_2EWF @ A_27a ) @ ( ap @ ( c_2Erelation_2Einv @ A_27a @ A_27a ) @ V0R ) ) ) )
% 1.17/1.41 => ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27a )
% 1.17/1.41 => ( p
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V4y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V4y ) @ ( ap @ ( ap @ ( ap @ ( c_2Erelation_2ERTC @ A_27a ) @ V0R ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ESET__EQ__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0s1: $i] :
% 1.17/1.41 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1s2: $i] :
% 1.17/1.41 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( V0s1 = V1s2 )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s2 ) @ V0s1 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPSUBSET__EQN,axiom,
% 1.17/1.41 ! [A_27a: del,V0s1: $i] :
% 1.17/1.41 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1s2: $i] :
% 1.17/1.41 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.41 & ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s2 ) @ V0s1 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPSUBSET__SUBSET__TRANS,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2u: $i] :
% 1.17/1.41 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V2u ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ESUBSET__PSUBSET__TRANS,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2u: $i] :
% 1.17/1.41 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V1t ) @ V2u ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V0s ) @ V2u ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECROSS__EQNS,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0a: $i] :
% 1.17/1.41 ( ( mem @ V0a @ A_27a )
% 1.17/1.41 => ! [V1s1: $i] :
% 1.17/1.41 ( ( mem @ V1s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2s2: $i] :
% 1.17/1.41 ( ( mem @ V2s2 @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) @ V2s2 )
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
% 1.17/1.41 & ( ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0a ) @ V1s1 ) ) @ V2s2 )
% 1.17/1.41 = ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.41 @ ( lam @ A_27b
% 1.17/1.41 @ ^ [V3y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0a ) @ V3y ) ) )
% 1.17/1.41 @ V2s2 ) )
% 1.17/1.41 @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V1s1 ) @ V2s2 ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecount__EQN,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) )
% 1.17/1.41 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) )
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V1p: $i] : ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ V1p ) @ ( ap @ c_2Epred__set_2Ecount @ V1p ) ) ) )
% 1.17/1.41 @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EUNIQUE__MEMBER__SING,axiom,
% 1.17/1.41 ! [A_27a: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.41 & ! [V2y: $i] :
% 1.17/1.41 ( ( mem @ V2y @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ V1s ) )
% 1.17/1.41 => ( V0x = V2y ) ) ) )
% 1.17/1.41 <=> ( V1s
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einj__surj,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) )
% 1.17/1.41 => ( ( V1s
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.41 | ? [V3f_27: $i] :
% 1.17/1.41 ( ( mem @ V3f_27 @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27b @ A_27a ) @ V3f_27 ) @ V2t ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einfinite__rest,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 => ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Echooser__def,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) )
% 1.17/1.41 & ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ V1s ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V1s ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Echooser__def__compute,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V0s ) ) )
% 1.17/1.41 & ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ V1s ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V1s ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
% 1.17/1.41 & ! [V3s: $i] :
% 1.17/1.41 ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ V3s ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2Echooser @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V3s ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einfinite__num__inj,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 <=> ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Ecountable__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 <=> ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ ty_2Enum_2Enum ) @ V1f ) @ V0s ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecountable__image__nats,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ A_27a ) @ V0f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecountable__surj,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 <=> ( ( V0s
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.41 | ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Enum__countable,axiom,
% 1.17/1.41 p @ ( ap @ ( c_2Epred__set_2Ecountable @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Esubset__countable,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1t ) @ V0s ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1t ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Eimage__countable,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1s ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__ALT,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 <=> ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0s ) )
% 1.17/1.41 => ? [V3n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V3n ) )
% 1.17/1.41 = V2x ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Efinite__countable,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__COUNT,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__NUM,axiom,
% 1.17/1.41 ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ty_2Enum_2Enum ) @ V0s ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__IMAGE__NUM,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ A_27a ) @ V0f ) @ V1s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Enum__to__pair__def,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2Enum__to__pair @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.41 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Enumpair_2Enfst @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Enumpair_2Ensnd @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Epair__to__num__def,axiom,
% 1.17/1.41 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2Epair__to__num @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumpair_2Enpair @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epair__to__num__formula,axiom,
% 1.17/1.41 ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2Epair__to__num @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epair__to__num__inv,axiom,
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2Epair__to__num @ ( ap @ c_2Epred__set_2Enum__to__pair @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) )
% 1.17/1.41 = V0x )
% 1.17/1.41 & ! [V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ c_2Epred__set_2Enum__to__pair @ ( ap @ c_2Epred__set_2Epair__to__num @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) )
% 1.17/1.41 = ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecross__countable,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ V1t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einter__countable,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 | ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einj__countable,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ V2t ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ebigunion__countable,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ( arr @ A_27a @ bool ) ) @ V0s ) )
% 1.17/1.41 & ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ A_27a @ bool ) ) @ V1x ) @ V0s ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1x ) ) ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Eunion__countable,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Eunion__countable__IFF,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einj__image__countable__IFF,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EINJ @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Epow__no__surj,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ~ ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2ESURJ @ A_27a @ ( arr @ A_27a @ bool ) ) @ V1f ) @ V0s ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Einfinite__pow__uncountable,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 => ~ ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EPOW @ A_27a ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecountable__Usum,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] :
% 1.17/1.41 ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecountable__EMPTY,axiom,
% 1.17/1.41 ! [A_27a: del] : ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecountable__INSERT,axiom,
% 1.17/1.41 ! [A_27a: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ V1s ) ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V1s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecross__countable__IFF,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ V0s ) @ V1t ) ) )
% 1.17/1.41 <=> ( ( V0s
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.41 | ( V1t
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.41 | ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecountable__Uprod,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] :
% 1.17/1.41 ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EEXPLICIT__ENUMERATE__MONO,axiom,
% 1.17/1.41 ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EREST @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1s ) ) @ V1s ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EEXPLICIT__ENUMERATE__NOT__EMPTY,axiom,
% 1.17/1.41 ! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EREST @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1s )
% 1.17/1.41 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EINFINITE__EXPLICIT__ENUMERATE,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 => ( p
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EINJ @ ty_2Enum_2Enum @ A_27a )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V1n: $i] : ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( arr @ A_27a @ bool ) ) @ ( c_2Epred__set_2EREST @ A_27a ) ) @ V1n ) @ V0s ) ) ) )
% 1.17/1.41 @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) )
% 1.17/1.41 @ V0s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EBIJ__NUM__COUNTABLE,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Eenumerate__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2Eenumerate @ A_27a ) @ V0s )
% 1.17/1.41 = ( ap @ ( c_2Emin_2E_40 @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 @ ( lam @ ( arr @ ty_2Enum_2Enum @ A_27a )
% 1.17/1.41 @ ^ [V1f: $i] : ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EENUMERATE,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ ( ap @ ( c_2Epred__set_2Eenumerate @ A_27a ) @ V0s ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__ALT__BIJ,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0s ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 | ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ A_27a ) @ ( ap @ ( c_2Epred__set_2Eenumerate @ A_27a ) @ V0s ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECOUNTABLE__ENUM,axiom,
% 1.17/1.41 ! [A_27a: del,V0c: $i] :
% 1.17/1.41 ( ( mem @ V0c @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2Ecountable @ A_27a ) @ V0c ) )
% 1.17/1.41 <=> ( ( V0c
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.41 | ? [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
% 1.17/1.41 & ( V0c
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EIMAGE__BIGUNION,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1M: $i] :
% 1.17/1.41 ( ( mem @ V1M @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ V1M ) )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) ) @ V1M ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ESUBSET__DIFF,axiom,
% 1.17/1.41 ! [A_27a: del,V0s1: $i] :
% 1.17/1.41 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1s2: $i] :
% 1.17/1.41 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2s3: $i] :
% 1.17/1.41 ( ( mem @ V2s3 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V1s2 ) @ V2s3 ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s1 ) @ V1s2 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ V0s1 ) @ V2s3 ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EINTER__SUBSET__EQN,axiom,
% 1.17/1.41 ! [A_27a: del,V0A: $i] :
% 1.17/1.41 ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1B: $i] :
% 1.17/1.41 ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0A ) @ V1B )
% 1.17/1.41 = V0A )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0A ) @ V1B ) ) )
% 1.17/1.41 & ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0A ) @ V1B )
% 1.17/1.41 = V1B )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1B ) @ V0A ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPSUBSET__SING,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ A_27a )
% 1.17/1.41 => ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EPSUBSET @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) )
% 1.17/1.41 <=> ( V1x
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EINTER__UNION,axiom,
% 1.17/1.41 ! [A_27a: del,V0A: $i] :
% 1.17/1.41 ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1B: $i] :
% 1.17/1.41 ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0A ) @ V1B ) ) @ V0A )
% 1.17/1.41 = V0A )
% 1.17/1.41 & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1B ) @ V0A ) ) @ V0A )
% 1.17/1.41 = V0A )
% 1.17/1.41 & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0A ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0A ) @ V1B ) )
% 1.17/1.41 = V0A )
% 1.17/1.41 & ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0A ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1B ) @ V0A ) )
% 1.17/1.41 = V0A ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EUNION__DELETE,axiom,
% 1.17/1.41 ! [A_27a: del,V0A: $i] :
% 1.17/1.41 ( ( mem @ V0A @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1B: $i] :
% 1.17/1.41 ( ( mem @ V1B @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0A ) @ V1B ) ) @ V2x )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0A ) @ V2x ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V1B ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EDELETE__SUBSET__INSERT,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1e: $i] :
% 1.17/1.41 ( ( mem @ V1e @ A_27a )
% 1.17/1.41 => ! [V2s2: $i] :
% 1.17/1.41 ( ( mem @ V2s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ V0s ) @ V1e ) ) @ V2s2 ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1e ) @ V2s2 ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EIN__INSERT__EXPAND,axiom,
% 1.17/1.41 ! [A_27a: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1y: $i] :
% 1.17/1.41 ( ( mem @ V1y @ A_27a )
% 1.17/1.41 => ! [V2P: $i] :
% 1.17/1.41 ( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1y ) @ V2P ) ) )
% 1.17/1.41 <=> ( ( V0x = V1y )
% 1.17/1.41 | ( ( V0x != V1y )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V2P ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EFINITE__INTER,axiom,
% 1.17/1.41 ! [A_27a: del,V0s1: $i] :
% 1.17/1.41 ( ( mem @ V0s1 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1s2: $i] :
% 1.17/1.41 ( ( mem @ V1s2 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s1 ) )
% 1.17/1.41 | ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s2 ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V0s1 ) @ V1s2 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EINSERT__EQ__SING,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ! [V2y: $i] :
% 1.17/1.41 ( ( mem @ V2y @ A_27a )
% 1.17/1.41 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V0s )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.41 <=> ( ( V1x = V2y )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2y ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECARD__UNION__LE,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ V1t ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V1t ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EIMAGE__SUBSET__gen,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2u: $i] :
% 1.17/1.41 ( ( mem @ V2u @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V3t: $i] :
% 1.17/1.41 ( ( mem @ V3t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ V2u ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2u ) ) @ V3t ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ V3t ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ECARD__REST,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V0s ) )
% 1.17/1.41 & ( V0s
% 1.17/1.41 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ ( ap @ ( c_2Epred__set_2EREST @ A_27a ) @ V0s ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Epred__set_2ECARD @ A_27a ) @ V0s ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2ESUBSET__DIFF__EMPTY,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t )
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0s ) @ V1t ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EDIFF__INTER__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0r ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1s ) @ V2t ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0r ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EUNION__DIFF__2,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V0s ) @ V1t ) )
% 1.17/1.41 = V0s ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecount__add,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ c_2Epred__set_2Ecount @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ty_2Enum_2Enum ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EIMAGE__EQ__SING,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2z: $i] :
% 1.17/1.41 ( ( mem @ V2z @ A_27a )
% 1.17/1.41 => ( ( ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27b @ A_27a ) @ V0f ) @ V1s )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V2z ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.41 <=> ( ( V1s
% 1.17/1.41 != ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.41 & ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27b )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V3x ) @ V1s ) )
% 1.17/1.41 => ( ( ap @ V0f @ V3x )
% 1.17/1.41 = V2z ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecount__add1,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ap @ c_2Epred__set_2Ecount @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ecompl__insert,axiom,
% 1.17/1.41 ! [A_27a: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ( ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ V0s ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ A_27a ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ V0s ) ) @ V1x ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Ein__max__set,axiom,
% 1.17/1.41 ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Enum_2Enum ) @ V0s ) )
% 1.17/1.41 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ V0s ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ c_2Epred__set_2EMAX__SET @ V0s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2EPREIMAGE__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V2x ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V2x ) ) @ V1s ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__ALT,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ A_27b ) @ V1s ) @ V0f ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EIN__PREIMAGE,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V2x ) ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__applied,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) @ V2x ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ ( ap @ V0f @ V2x ) ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__EMPTY,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) )
% 1.17/1.41 = ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__UNIV,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( c_2Epred__set_2EUNIV @ A_27b ) )
% 1.17/1.41 = ( c_2Epred__set_2EUNIV @ A_27a ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__COMPL,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27b ) @ V1s ) )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2ECOMPL @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__UNION,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27b ) @ V1s ) @ V2t ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__INTER,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27b ) @ V1s ) @ V2t ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__BIGUNION,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27b ) @ V1s ) )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( arr @ A_27b @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) ) @ V1s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__COMP,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1g: $i] :
% 1.17/1.41 ( ( mem @ V1g @ ( arr @ A_27b @ A_27c ) )
% 1.17/1.41 => ! [V2s: $i] :
% 1.17/1.41 ( ( mem @ V2s @ ( arr @ A_27c @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27b @ A_27c ) @ V1g ) @ V2s ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ A_27b ) @ V1g ) @ V0f ) ) @ V2s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__DIFF,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27b ) @ V1s ) @ V2t ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__I,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27a ) @ ( c_2Ecombin_2EI @ A_27a ) )
% 1.17/1.41 = ( c_2Ecombin_2EI @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__K,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27b @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ A_27a @ A_27b ) @ V0x ) ) @ V1s )
% 1.17/1.41 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ A_27b @ bool ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) @ ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__DISJOINT,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27b ) @ V1s ) @ V2t ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2t: $i] :
% 1.17/1.41 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V1s ) @ V2t ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__CROSS,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) )
% 1.17/1.41 => ! [V1a: $i] :
% 1.17/1.41 ( ( mem @ V1a @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2b: $i] :
% 1.17/1.41 ( ( mem @ V2b @ ( arr @ A_27c @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ A_27b @ A_27c ) @ V1a ) @ V2b ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( c_2Epair_2EFST @ A_27b @ A_27c ) ) @ V0f ) ) @ V1a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27c @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( c_2Epair_2ESND @ A_27b @ A_27c ) ) @ V0f ) ) @ V2b ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__COMPL__INTER,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2sp: $i] :
% 1.17/1.41 ( ( mem @ V2sp @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Epred__set_2ECOMPL @ A_27b ) @ V1t ) ) ) @ V2sp )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ V2sp ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1t ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EPREIMAGE__IMAGE,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EIMAGE__PREIMAGE,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2EPREIMAGE @ A_27a @ A_27b ) @ V0f ) @ V1s ) ) ) @ V1s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Epred__set_2Eis__measure__maximal__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0m: $i] :
% 1.17/1.41 ( ( mem @ V0m @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ A_27a ) @ V0m ) @ V1s ) @ V2x ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.41 & ! [V3y: $i] :
% 1.17/1.41 ( ( mem @ V3y @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ V0m @ V3y ) ) @ ( ap @ V0m @ V2x ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2EFINITE__is__measure__maximal,axiom,
% 1.17/1.41 ! [A_27a: del,V0m: $i] :
% 1.17/1.41 ( ( mem @ V0m @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ V1s ) )
% 1.17/1.41 & ( V1s
% 1.17/1.41 != ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
% 1.17/1.41 => ? [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ A_27a ) @ V0m ) @ V1s ) @ V2x ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Eis__measure__maximal__SING,axiom,
% 1.17/1.41 ! [A_27a: del,V0m: $i] :
% 1.17/1.41 ( ( mem @ V0m @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ! [V2y: $i] :
% 1.17/1.41 ( ( mem @ V2y @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ A_27a ) @ V0m ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V1x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ V2y ) )
% 1.17/1.41 <=> ( V2y = V1x ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Epred__set_2Eis__measure__maximal__INSERT,axiom,
% 1.17/1.41 ! [A_27a: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2m: $i] :
% 1.17/1.41 ( ( mem @ V2m @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V3e: $i] :
% 1.17/1.41 ( ( mem @ V3e @ A_27a )
% 1.17/1.41 => ! [V4y: $i] :
% 1.17/1.41 ( ( mem @ V4y @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V2m @ V3e ) ) @ ( ap @ V2m @ V0x ) ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ A_27a ) @ V2m ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V3e ) @ V1s ) ) @ V4y ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ A_27a ) @ V2m ) @ V1s ) @ V4y ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Eclosed,type,
% 1.17/1.41 c_2EfixedPoint_2Eclosed: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Eclosed,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2EfixedPoint_2Eclosed @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Edense,type,
% 1.17/1.41 c_2EfixedPoint_2Edense: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Edense,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2EfixedPoint_2Edense @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Eempty,type,
% 1.17/1.41 c_2EfixedPoint_2Eempty: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Eempty,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EfixedPoint_2Eempty @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Efnsum,type,
% 1.17/1.41 c_2EfixedPoint_2Efnsum: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Efnsum,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EfixedPoint_2Efnsum @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Egfp,type,
% 1.17/1.41 c_2EfixedPoint_2Egfp: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Egfp,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Elfp,type,
% 1.17/1.41 c_2EfixedPoint_2Elfp: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Elfp,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2EfixedPoint_2Emonotone,type,
% 1.17/1.41 c_2EfixedPoint_2Emonotone: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2EfixedPoint_2Emonotone,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) @ bool ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Emonotone__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27b ) @ V0f ) )
% 1.17/1.41 <=> ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2Y: $i] :
% 1.17/1.41 ( ( mem @ V2Y @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ V2Y ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ V0f @ V1X ) ) @ ( ap @ V0f @ V2Y ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Elfp__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EBIGINTER @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.41 @ ^ [V1X: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ bool ) @ V1X ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V0f @ V1X ) ) @ V1X ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Egfp__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EBIGUNION @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 @ ( lam @ ( arr @ A_27a @ bool )
% 1.17/1.41 @ ^ [V1X: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ bool ) @ bool ) @ V1X ) @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ V0f @ V1X ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Eclosed__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2EfixedPoint_2Eclosed @ A_27a ) @ V0f ) @ V1X ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V0f @ V1X ) ) @ V1X ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Edense__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2EfixedPoint_2Edense @ A_27a ) @ V0f ) @ V1X ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ V0f @ V1X ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__least__closed,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2EfixedPoint_2Eclosed @ A_27a ) @ V0f ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) )
% 1.17/1.41 & ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2EfixedPoint_2Eclosed @ A_27a ) @ V0f ) @ V1X ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) @ V1X ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Egfp__greatest__dense,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2EfixedPoint_2Edense @ A_27a ) @ V0f ) @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) )
% 1.17/1.41 & ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2EfixedPoint_2Edense @ A_27a ) @ V0f ) @ V1X ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__fixedpoint,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ( ( ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f )
% 1.17/1.41 = ( ap @ V0f @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) )
% 1.17/1.41 & ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( V1X
% 1.17/1.41 = ( ap @ V0f @ V1X ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) @ V1X ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Egfp__greatest__fixedpoint,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ( ( ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f )
% 1.17/1.41 = ( ap @ V0f @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) )
% 1.17/1.41 & ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( V1X
% 1.17/1.41 = ( ap @ V0f @ V1X ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__induction,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V0f @ V1X ) ) @ V1X ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) @ V1X ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Egfp__coinduction,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ V0f @ V1X ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__strong__induction,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ V0f @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) ) ) @ V1X ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) @ V1X ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Egfp__strong__coinduction,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ V0f @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Egfp @ A_27a ) @ V0f ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Efnsum__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f1: $i] :
% 1.17/1.41 ( ( mem @ V0f1 @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1f2: $i] :
% 1.17/1.41 ( ( mem @ V1f2 @ ( arr @ A_27b @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V2X: $i] :
% 1.17/1.41 ( ( mem @ V2X @ A_27b )
% 1.17/1.41 => ( ( ap @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27a @ A_27b ) @ V0f1 ) @ V1f2 ) @ V2X )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ V0f1 @ V2X ) ) @ ( ap @ V1f2 @ V2X ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Efnsum__monotone,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f1: $i] :
% 1.17/1.41 ( ( mem @ V0f1 @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ! [V1f2: $i] :
% 1.17/1.41 ( ( mem @ V1f2 @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27b ) @ V0f1 ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27b ) @ V1f2 ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ ( arr @ A_27a @ bool ) ) @ V0f1 ) @ V1f2 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2EfixedPoint_2Eempty__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] :
% 1.17/1.41 ( ( c_2EfixedPoint_2Eempty @ A_27a @ A_27b )
% 1.17/1.41 = ( lam @ A_27a
% 1.17/1.41 @ ^ [V0X: $i] : ( c_2Epred__set_2EEMPTY @ A_27b ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Eempty__monotone,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27b ) @ ( c_2EfixedPoint_2Eempty @ ( arr @ A_27a @ bool ) @ A_27b ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Efnsum__empty,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ( ( ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V0f ) @ ( c_2EfixedPoint_2Eempty @ A_27a @ A_27b ) )
% 1.17/1.41 = V0f )
% 1.17/1.41 & ( ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ ( c_2EfixedPoint_2Eempty @ A_27a @ A_27b ) ) @ V0f )
% 1.17/1.41 = V0f ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Efnsum__ASSOC,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ! [V1g: $i] :
% 1.17/1.41 ( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ! [V2h: $i] :
% 1.17/1.41 ( ( mem @ V2h @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V1g ) @ V2h ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V0f ) @ V1g ) ) @ V2h ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Efnsum__COMM,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ! [V1g: $i] :
% 1.17/1.41 ( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V0f ) @ V1g )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V1g ) @ V0f ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Efnsum__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ! [V1g: $i] :
% 1.17/1.41 ( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.41 => ! [V2X: $i] :
% 1.17/1.41 ( ( mem @ V2X @ A_27a )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ V0f @ V2X ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V0f ) @ V1g ) @ V2X ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ V1g @ V2X ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27b @ A_27a ) @ V0f ) @ V1g ) @ V2X ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__fnsum,axiom,
% 1.17/1.41 ! [A_27a: del,V0f1: $i] :
% 1.17/1.41 ( ( mem @ V0f1 @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1f2: $i] :
% 1.17/1.41 ( ( mem @ V1f2 @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f1 ) )
% 1.17/1.41 & ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V1f2 ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f1 ) ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27a @ ( arr @ A_27a @ bool ) ) @ V0f1 ) @ V1f2 ) ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V1f2 ) ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ ( ap @ ( ap @ ( c_2EfixedPoint_2Efnsum @ A_27a @ ( arr @ A_27a @ bool ) ) @ V0f1 ) @ V1f2 ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__rule__applied,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1X: $i] :
% 1.17/1.41 ( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2y: $i] :
% 1.17/1.41 ( ( mem @ V2y @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V1X ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ ( ap @ V0f @ V1X ) ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2EfixedPoint_2Elfp__empty,axiom,
% 1.17/1.41 ! [A_27a: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.41 => ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ A_27a )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( c_2EfixedPoint_2Emonotone @ A_27a @ A_27a ) @ V0f ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ V0f @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( c_2EfixedPoint_2Elfp @ A_27a ) @ V0f ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EBIT__MODF,type,
% 1.17/1.41 c_2Enumeral__bit_2EBIT__MODF: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EBIT__MODF,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EBIT__MODF @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EBIT__REV,type,
% 1.17/1.41 c_2Enumeral__bit_2EBIT__REV: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EBIT__REV,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EBIT__REV @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(stp_fo_c_2Enumeral__bit_2EBIT__REV,type,
% 1.17/1.41 fo__c_2Enumeral__bit_2EBIT__REV: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.41
% 1.17/1.41 thf(stp_eq_fo_c_2Enumeral__bit_2EBIT__REV,axiom,
% 1.17/1.41 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum,X2: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral__bit_2EBIT__REV @ X0 @ X1 @ X2 ) )
% 1.17/1.41 = ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) @ ( inj__ty_2Enum_2Enum @ X2 ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EFDUB,type,
% 1.17/1.41 c_2Enumeral__bit_2EFDUB: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EFDUB,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EFDUB @ ( arr @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2ESFUNPOW,type,
% 1.17/1.41 c_2Enumeral__bit_2ESFUNPOW: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2ESFUNPOW,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2ESFUNPOW @ ( arr @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EiBITWISE,type,
% 1.17/1.41 c_2Enumeral__bit_2EiBITWISE: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EiBITWISE,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EiBITWISE @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EiDIV2,type,
% 1.17/1.41 c_2Enumeral__bit_2EiDIV2: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EiDIV2,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EiDIV2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.41
% 1.17/1.41 thf(stp_fo_c_2Enumeral__bit_2EiDIV2,type,
% 1.17/1.41 fo__c_2Enumeral__bit_2EiDIV2: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.41
% 1.17/1.41 thf(stp_eq_fo_c_2Enumeral__bit_2EiDIV2,axiom,
% 1.17/1.41 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral__bit_2EiDIV2 @ X0 ) )
% 1.17/1.41 = ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EiLOG2,type,
% 1.17/1.41 c_2Enumeral__bit_2EiLOG2: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EiLOG2,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EiLOG2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.41
% 1.17/1.41 thf(stp_fo_c_2Enumeral__bit_2EiLOG2,type,
% 1.17/1.41 fo__c_2Enumeral__bit_2EiLOG2: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.41
% 1.17/1.41 thf(stp_eq_fo_c_2Enumeral__bit_2EiLOG2,axiom,
% 1.17/1.41 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral__bit_2EiLOG2 @ X0 ) )
% 1.17/1.41 = ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EiMOD__2EXP,type,
% 1.17/1.41 c_2Enumeral__bit_2EiMOD__2EXP: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EiMOD__2EXP,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EiMOD__2EXP @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(stp_fo_c_2Enumeral__bit_2EiMOD__2EXP,type,
% 1.17/1.41 fo__c_2Enumeral__bit_2EiMOD__2EXP: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.41
% 1.17/1.41 thf(stp_eq_fo_c_2Enumeral__bit_2EiMOD__2EXP,axiom,
% 1.17/1.41 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral__bit_2EiMOD__2EXP @ X0 @ X1 ) )
% 1.17/1.41 = ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Enumeral__bit_2EiSUC,type,
% 1.17/1.41 c_2Enumeral__bit_2EiSUC: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Enumeral__bit_2EiSUC,axiom,
% 1.17/1.41 mem @ c_2Enumeral__bit_2EiSUC @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ).
% 1.17/1.41
% 1.17/1.41 thf(stp_fo_c_2Enumeral__bit_2EiSUC,type,
% 1.17/1.41 fo__c_2Enumeral__bit_2EiSUC: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 1.17/1.41
% 1.17/1.41 thf(stp_eq_fo_c_2Enumeral__bit_2EiSUC,axiom,
% 1.17/1.41 ! [X0: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumeral__bit_2EiSUC @ X0 ) )
% 1.17/1.41 = ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EiMOD__2EXP,axiom,
% 1.17/1.41 c_2Enumeral__bit_2EiMOD__2EXP = c_2Ebit_2EMOD__2EXP ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2Enumeral__imod__2exp,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.41 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.41 & ! [V1x: tp__ty_2Enum_2Enum,V2n: $i] :
% 1.17/1.41 ( ( mem @ V2n @ A_27a )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.41 = fo__c_2Earithmetic_2EZERO ) )
% 1.17/1.41 & ! [V3x: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) )
% 1.17/1.41 & ! [V5x: tp__ty_2Enum_2Enum,V6n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V5x ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) )
% 1.17/1.41 & ! [V7x: tp__ty_2Enum_2Enum,V8n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7x ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V7x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) ) ) )
% 1.17/1.41 & ! [V9x: tp__ty_2Enum_2Enum,V10n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V9x ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9x ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EMOD__2EXP,axiom,
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V1x: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ c_2Enumeral__bit_2EiMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EDIV__2EXP,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ty_2Enum_2Enum ) @ c_2Earithmetic_2EDIV2 ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2Enumeral__mod2,axiom,
% 1.17/1.41 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EiDUB__NUMERAL,axiom,
% 1.17/1.41 ! [V0i: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EBIT__REV__def,axiom,
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.41 = V1y )
% 1.17/1.41 & ! [V2n: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum,V4y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( inj__ty_2Enum_2Enum @ V4y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V4y ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EBIT__REVERSE__EVAL,axiom,
% 1.17/1.41 ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EBIT__MODF__def,axiom,
% 1.17/1.41 ( ! [V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V1x: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum,V3e: tp__ty_2Enum_2Enum,V4y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V3e ) ) @ ( inj__ty_2Enum_2Enum @ V4y ) ) )
% 1.17/1.41 = V4y ) )
% 1.17/1.41 & ! [V5n: tp__ty_2Enum_2Enum,V6f: $i] :
% 1.17/1.41 ( ( mem @ V6f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V7x: tp__ty_2Enum_2Enum,V8b: tp__ty_2Enum_2Enum,V9e: tp__ty_2Enum_2Enum,V10y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) @ V6f ) @ ( inj__ty_2Enum_2Enum @ V7x ) ) @ ( inj__ty_2Enum_2Enum @ V8b ) ) @ ( inj__ty_2Enum_2Enum @ V9e ) ) @ ( inj__ty_2Enum_2Enum @ V10y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( inj__ty_2Enum_2Enum @ V5n ) ) @ V6f ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V7x ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V9e ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V6f @ ( inj__ty_2Enum_2Enum @ V8b ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V7x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V9e ) ) @ ( inj__ty_2Enum_2Enum @ V10y ) ) ) @ ( inj__ty_2Enum_2Enum @ V10y ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EBIT__MODIFY__EVAL,axiom,
% 1.17/1.41 ! [V0m: tp__ty_2Enum_2Enum,V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EiBITWISE__def,axiom,
% 1.17/1.41 c_2Enumeral__bit_2EiBITWISE = c_2Ebit_2EBITWISE ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EiBITWISE,axiom,
% 1.17/1.41 ( ! [V0opr: $i] :
% 1.17/1.41 ( ( mem @ V0opr @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V1a: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0opr ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
% 1.17/1.41 = fo__c_2Earithmetic_2EZERO ) )
% 1.17/1.41 & ! [V3x: tp__ty_2Enum_2Enum,V4opr: $i] :
% 1.17/1.41 ( ( mem @ V4opr @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V5a: tp__ty_2Enum_2Enum,V6b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) @ V4opr ) @ ( inj__ty_2Enum_2Enum @ V5a ) ) @ ( inj__ty_2Enum_2Enum @ V6b ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V7w: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V4opr @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V5a ) ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V6b ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ V7w ) ) @ ( ap @ c_2Enumeral_2EiDUB @ V7w ) ) ) )
% 1.17/1.41 @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V4opr ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V5a ) ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V6b ) ) ) ) ) ) )
% 1.17/1.41 & ! [V8x: tp__ty_2Enum_2Enum,V9opr: $i] :
% 1.17/1.41 ( ( mem @ V9opr @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V10a: tp__ty_2Enum_2Enum,V11b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ V9opr ) @ ( inj__ty_2Enum_2Enum @ V10a ) ) @ ( inj__ty_2Enum_2Enum @ V11b ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V12w: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V9opr @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V10a ) ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V11b ) ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ V12w ) ) @ ( ap @ c_2Enumeral_2EiDUB @ V12w ) ) ) )
% 1.17/1.41 @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8x ) ) ) ) @ V9opr ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V10a ) ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V11b ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__BITWISE,axiom,
% 1.17/1.41 ! [A_27a: del] :
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum,V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V2a: $i] :
% 1.17/1.41 ( ( mem @ V2a @ A_27a )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) )
% 1.17/1.41 & ! [V3x: tp__ty_2Enum_2Enum,V4f: $i] :
% 1.17/1.41 ( ( mem @ V4f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V5a: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ V4f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V5a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( inj__ty_2Enum_2Enum @ V3x ) ) @ V4f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V5a ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) )
% 1.17/1.41 & ! [V6x: tp__ty_2Enum_2Enum,V7f: $i] :
% 1.17/1.41 ( ( mem @ V7f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V8b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V6x ) ) @ V7f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V8b ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( inj__ty_2Enum_2Enum @ V6x ) ) @ V7f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V8b ) ) ) ) ) ) )
% 1.17/1.41 & ! [V9x: tp__ty_2Enum_2Enum,V10f: $i] :
% 1.17/1.41 ( ( mem @ V10f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V11a: tp__ty_2Enum_2Enum,V12b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( inj__ty_2Enum_2Enum @ V9x ) ) @ V10f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V11a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V12b ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EiBITWISE @ ( inj__ty_2Enum_2Enum @ V9x ) ) @ V10f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V11a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V12b ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REV,axiom,
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum,V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
% 1.17/1.41 = V1y )
% 1.17/1.41 & ! [V2n: tp__ty_2Enum_2Enum,V3y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V3y ) ) ) ) )
% 1.17/1.41 & ! [V4n: tp__ty_2Enum_2Enum,V5y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V5y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V5y ) ) ) ) )
% 1.17/1.41 & ! [V6n: tp__ty_2Enum_2Enum,V7x: tp__ty_2Enum_2Enum,V8y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V7x ) ) ) @ ( inj__ty_2Enum_2Enum @ V8y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V7x ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V7x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8y ) ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V8y ) ) ) ) ) )
% 1.17/1.41 & ! [V9n: tp__ty_2Enum_2Enum,V10x: tp__ty_2Enum_2Enum,V11y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V9n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) @ ( inj__ty_2Enum_2Enum @ V11y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9n ) ) ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V10x ) ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V11y ) ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V11y ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE,axiom,
% 1.17/1.41 ( ! [V0m: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__REV @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODF,axiom,
% 1.17/1.41 ( ! [V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V1x: tp__ty_2Enum_2Enum,V2b: tp__ty_2Enum_2Enum,V3e: tp__ty_2Enum_2Enum,V4y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V3e ) ) @ ( inj__ty_2Enum_2Enum @ V4y ) ) )
% 1.17/1.41 = V4y ) )
% 1.17/1.41 & ! [V5n: tp__ty_2Enum_2Enum,V6f: $i] :
% 1.17/1.41 ( ( mem @ V6f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V7b: tp__ty_2Enum_2Enum,V8e: tp__ty_2Enum_2Enum,V9y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) @ V6f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V7b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V8e ) ) ) @ ( inj__ty_2Enum_2Enum @ V9y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V6f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V8e ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V6f @ ( inj__ty_2Enum_2Enum @ V7b ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V8e ) ) ) @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) @ ( inj__ty_2Enum_2Enum @ V9y ) ) ) ) ) )
% 1.17/1.41 & ! [V10n: tp__ty_2Enum_2Enum,V11f: $i] :
% 1.17/1.41 ( ( mem @ V11f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V12b: tp__ty_2Enum_2Enum,V13e: tp__ty_2Enum_2Enum,V14y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) ) @ V11f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V12b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V13e ) ) ) @ ( inj__ty_2Enum_2Enum @ V14y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) ) @ V11f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V12b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V13e ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V11f @ ( inj__ty_2Enum_2Enum @ V12b ) ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V13e ) ) ) @ ( inj__ty_2Enum_2Enum @ V14y ) ) ) @ ( inj__ty_2Enum_2Enum @ V14y ) ) ) ) ) )
% 1.17/1.41 & ! [V15n: tp__ty_2Enum_2Enum,V16f: $i] :
% 1.17/1.41 ( ( mem @ V16f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V17x: tp__ty_2Enum_2Enum,V18b: tp__ty_2Enum_2Enum,V19e: tp__ty_2Enum_2Enum,V20y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) ) @ V16f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V17x ) ) ) @ ( inj__ty_2Enum_2Enum @ V18b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V19e ) ) ) @ ( inj__ty_2Enum_2Enum @ V20y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V16f ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V17x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V18b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V19e ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V16f @ ( inj__ty_2Enum_2Enum @ V18b ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V17x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V19e ) ) ) @ ( inj__ty_2Enum_2Enum @ V20y ) ) ) @ ( inj__ty_2Enum_2Enum @ V20y ) ) ) ) ) )
% 1.17/1.41 & ! [V21n: tp__ty_2Enum_2Enum,V22f: $i] :
% 1.17/1.41 ( ( mem @ V22f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V23x: tp__ty_2Enum_2Enum,V24b: tp__ty_2Enum_2Enum,V25e: tp__ty_2Enum_2Enum,V26y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V21n ) ) ) ) @ V22f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V23x ) ) ) @ ( inj__ty_2Enum_2Enum @ V24b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V25e ) ) ) @ ( inj__ty_2Enum_2Enum @ V26y ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V21n ) ) ) ) @ V22f ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V23x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V24b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V25e ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ V22f @ ( inj__ty_2Enum_2Enum @ V24b ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V23x ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V25e ) ) ) @ ( inj__ty_2Enum_2Enum @ V26y ) ) ) @ ( inj__ty_2Enum_2Enum @ V26y ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY,axiom,
% 1.17/1.41 ( ! [V0m: tp__ty_2Enum_2Enum,V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
% 1.17/1.41 & ! [V2m: tp__ty_2Enum_2Enum,V3f: $i] :
% 1.17/1.41 ( ( mem @ V3f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
% 1.17/1.41 => ! [V4n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ V3f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2EBIT__MODF @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ V3f ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EiSUC,axiom,
% 1.17/1.41 c_2Enumeral__bit_2EiSUC = c_2Enum_2ESUC ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EiDIV2,axiom,
% 1.17/1.41 c_2Enumeral__bit_2EiDIV2 = c_2Earithmetic_2EDIV2 ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2ESFUNPOW__def,axiom,
% 1.17/1.41 ( ! [V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ V0f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.41 = V1x ) )
% 1.17/1.41 & ! [V2f: $i] :
% 1.17/1.41 ( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V3n: tp__ty_2Enum_2Enum,V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ V2f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ V2f ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ V2f @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EFDUB__def,axiom,
% 1.17/1.41 ( ! [V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 ) )
% 1.17/1.41 & ! [V1f: $i] :
% 1.17/1.41 ( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ! [V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V1f ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ V1f @ ( ap @ V1f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP,axiom,
% 1.17/1.41 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ETIMES__2EXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2ETIMES__2EXP @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral_2EiDUB ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__iDIV2,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.41 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.41 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
% 1.17/1.41 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.41 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 = V0n )
% 1.17/1.41 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP,axiom,
% 1.17/1.41 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EDIV__2EXP @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral__bit_2EiDIV2 ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2,axiom,
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral__bit_2EiDIV2 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.41 = V0x )
% 1.17/1.41 & ! [V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral__bit_2EiDIV2 ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V2n: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral__bit_2EiDIV2 ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ c_2Enumeral__bit_2EiDIV2 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) )
% 1.17/1.41 & ! [V4n: tp__ty_2Enum_2Enum,V5x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral__bit_2EiDIV2 ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V5x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ c_2Enumeral__bit_2EiDIV2 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( inj__ty_2Enum_2Enum @ V5x ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB,axiom,
% 1.17/1.41 ( ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral_2EiDUB ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.41 = V0x )
% 1.17/1.41 & ! [V1y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral_2EiDUB ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V2n: tp__ty_2Enum_2Enum,V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral_2EiDUB ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ c_2Enumeral_2EiDUB ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) )
% 1.17/1.41 & ! [V4n: tp__ty_2Enum_2Enum,V5x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ c_2Enumeral_2EiDUB ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V5x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ c_2Enumeral_2EiDUB ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V5x ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB,axiom,
% 1.17/1.41 ! [V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ( ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
% 1.17/1.41 = V1x )
% 1.17/1.41 & ! [V2y: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V3n: tp__ty_2Enum_2Enum,V4x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) ) )
% 1.17/1.41 & ! [V5n: tp__ty_2Enum_2Enum,V6x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V6x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Enumeral__bit_2ESFUNPOW @ ( ap @ c_2Enumeral__bit_2EFDUB @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( inj__ty_2Enum_2Enum @ V6x ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EFDUB__iDIV2,axiom,
% 1.17/1.41 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ c_2Enumeral__bit_2EiDIV2 ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( ap @ c_2Enumeral__bit_2EiDIV2 @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EFDUB__iDUB,axiom,
% 1.17/1.41 ! [V0x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ c_2Enumeral_2EiDUB ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EFDUB__FDUB,axiom,
% 1.17/1.41 ! [V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
% 1.17/1.41 => ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.41 = fo__c_2Earithmetic_2EZERO )
% 1.17/1.41 & ! [V1x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ c_2Enumeral__bit_2EiSUC @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) )
% 1.17/1.41 & ! [V2x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) ) )
% 1.17/1.41 & ! [V3x: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ ( ap @ c_2Enumeral__bit_2EFDUB @ V0f ) @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3x ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ELOG__compute,axiom,
% 1.17/1.41 ! [V0base_20_3C_202_20or_20n_20_3D_200: $i] :
% 1.17/1.41 ( ( mem @ V0base_20_3C_202_20or_20n_20_3D_200 @ bool )
% 1.17/1.41 => ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ bool ) @ c_2Elogroot_2ELOG ) @ V0base_20_3C_202_20or_20n_20_3D_200 ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Enumeral__bit_2EiLOG2__def,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2Enumeral__ilog2,axiom,
% 1.17/1.41 ( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 )
% 1.17/1.41 & ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2Enumeral__log2,axiom,
% 1.17/1.41 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( ap @ c_2Enumeral_2EiDUB @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral__bit_2EiLOG2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EMOD__2EXP__EQ,axiom,
% 1.17/1.41 ( ! [V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__EQ @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 1.17/1.41 <=> $true )
% 1.17/1.41 & ! [V2n: tp__ty_2Enum_2Enum,V3a: tp__ty_2Enum_2Enum,V4b: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__EQ @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V3a ) ) @ ( inj__ty_2Enum_2Enum @ V4b ) ) )
% 1.17/1.41 <=> ( ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V3a ) ) )
% 1.17/1.41 <=> ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__EQ @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V3a ) ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V4b ) ) ) ) ) )
% 1.17/1.41 & ! [V5n: tp__ty_2Enum_2Enum,V6a: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__EQ @ ( inj__ty_2Enum_2Enum @ V5n ) ) @ ( inj__ty_2Enum_2Enum @ V6a ) ) @ ( inj__ty_2Enum_2Enum @ V6a ) ) )
% 1.17/1.41 <=> $true ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2EMOD__2EXP__MAX,axiom,
% 1.17/1.41 ( ! [V0a: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__MAX @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 1.17/1.41 <=> $true )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__MAX @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V2a ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__MAX @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ELOWEST__SET__BIT,axiom,
% 1.17/1.41 ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( V0n != fo__c_2Enum_2E0 )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute,axiom,
% 1.17/1.41 ( ! [V0n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) )
% 1.17/1.41 & ! [V1n: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOWEST__SET__BIT @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 ) ) ).
% 1.17/1.41
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 thf(tp_c_2Egcdset_2Egcdset,type,
% 1.17/1.41 c_2Egcdset_2Egcdset: $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Egcdset_2Egcdset,axiom,
% 1.17/1.41 mem @ c_2Egcdset_2Egcdset @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ty_2Enum_2Enum ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Egcdset_2Egcdset__def,axiom,
% 1.17/1.41 ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Egcdset_2Egcdset @ V0s ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum
% 1.17/1.41 @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ V0s ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
% 1.17/1.41 @ ( ap @ c_2Epred__set_2EMAX__SET
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EINTER @ ty_2Enum_2Enum )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V1n: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V1n ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V1n ) @ ( ap @ c_2Epred__set_2EMIN__SET @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ ty_2Enum_2Enum ) @ V0s ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V2d: $i] :
% 1.17/1.41 ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ bool ) @ V2d )
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
% 1.17/1.41 @ ( lam @ ty_2Enum_2Enum
% 1.17/1.41 @ ^ [V3e: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ V3e ) @ V0s ) ) @ ( ap @ ( ap @ c_2Edivides_2Edivides @ V2d ) @ V3e ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Egcdset_2Egcdset__divides,axiom,
% 1.17/1.41 ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ! [V1e: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) @ V0s ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( ap @ c_2Egcdset_2Egcdset @ V0s ) ) @ ( inj__ty_2Enum_2Enum @ V1e ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Egcdset_2Egcdset__greatest,axiom,
% 1.17/1.41 ! [V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ! [V1g: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ! [V2e: tp__ty_2Enum_2Enum] :
% 1.17/1.41 ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) @ V0s ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1g ) ) @ ( inj__ty_2Enum_2Enum @ V2e ) ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ c_2Edivides_2Edivides @ ( inj__ty_2Enum_2Enum @ V1g ) ) @ ( ap @ c_2Egcdset_2Egcdset @ V0s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Egcdset_2Egcdset__EMPTY,axiom,
% 1.17/1.41 ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Egcdset_2Egcdset @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) )
% 1.17/1.41 = fo__c_2Enum_2E0 ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Egcdset_2Egcdset__INSERT,axiom,
% 1.17/1.41 ! [V0x: tp__ty_2Enum_2Enum,V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ ty_2Enum_2Enum @ bool ) )
% 1.17/1.41 => ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Egcdset_2Egcdset @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1s ) ) )
% 1.17/1.41 = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Egcd_2Egcd @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Egcdset_2Egcdset @ V1s ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 %------------------------------------------------------------------------------
% 1.17/1.41 thf(tp_c_2Eset__relation_2ERREFL__EXP,type,
% 1.17/1.41 c_2Eset__relation_2ERREFL__EXP: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2ERREFL__EXP,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2ERREFL__EXP @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2ERRUNIV,type,
% 1.17/1.41 c_2Eset__relation_2ERRUNIV: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2ERRUNIV,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2ERRUNIV @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eacyclic,type,
% 1.17/1.41 c_2Eset__relation_2Eacyclic: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eacyclic,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ bool ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eall__choices,type,
% 1.17/1.41 c_2Eset__relation_2Eall__choices: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eall__choices,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eall__choices @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eantisym,type,
% 1.17/1.41 c_2Eset__relation_2Eantisym: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eantisym,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ bool ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Echain,type,
% 1.17/1.41 c_2Eset__relation_2Echain: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Echain,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Echain @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Edomain,type,
% 1.17/1.41 c_2Eset__relation_2Edomain: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Edomain,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Efchains,type,
% 1.17/1.41 c_2Eset__relation_2Efchains: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Efchains,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Efchains @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Efinite__prefixes,type,
% 1.17/1.41 c_2Eset__relation_2Efinite__prefixes: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Efinite__prefixes,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eget__min,type,
% 1.17/1.41 c_2Eset__relation_2Eget__min: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eget__min,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eget__min @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eirreflexive,type,
% 1.17/1.41 c_2Eset__relation_2Eirreflexive: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eirreflexive,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eirreflexive @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Elinear__order,type,
% 1.17/1.41 c_2Eset__relation_2Elinear__order: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Elinear__order,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Emaximal__elements,type,
% 1.17/1.41 c_2Eset__relation_2Emaximal__elements: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Emaximal__elements,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Emaximal__elements @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eminimal__elements,type,
% 1.17/1.41 c_2Eset__relation_2Eminimal__elements: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eminimal__elements,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eminimal__elements @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Enth__min,type,
% 1.17/1.41 c_2Eset__relation_2Enth__min: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Enth__min,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Enth__min @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Enum__order,type,
% 1.17/1.41 c_2Eset__relation_2Enum__order: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Enum__order,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Enum__order @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Epartial__order,type,
% 1.17/1.41 c_2Eset__relation_2Epartial__order: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Epartial__order,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eper,type,
% 1.17/1.41 c_2Eset__relation_2Eper: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eper,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eper @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eper__restrict,type,
% 1.17/1.41 c_2Eset__relation_2Eper__restrict: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eper__restrict,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Eper__restrict @ A_27a ) @ ( arr @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Erange,type,
% 1.17/1.41 c_2Eset__relation_2Erange: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Erange,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eset__relation_2Erange @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Ercomp,type,
% 1.17/1.41 c_2Eset__relation_2Ercomp: del > del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Ercomp,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Eset__relation_2Ercomp @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27c ) @ bool ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Ereflexive,type,
% 1.17/1.41 c_2Eset__relation_2Ereflexive: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Ereflexive,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Ereflexive @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Erel__to__reln,type,
% 1.17/1.41 c_2Eset__relation_2Erel__to__reln: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Erel__to__reln,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eset__relation_2Erel__to__reln @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Ereln__to__rel,type,
% 1.17/1.41 c_2Eset__relation_2Ereln__to__rel: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Ereln__to__rel,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eset__relation_2Ereln__to__rel @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Errestrict,type,
% 1.17/1.41 c_2Eset__relation_2Errestrict: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Errestrict,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Estrict,type,
% 1.17/1.41 c_2Eset__relation_2Estrict: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Estrict,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Estrict @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Estrict__linear__order,type,
% 1.17/1.41 c_2Eset__relation_2Estrict__linear__order: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Estrict__linear__order,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Estrict__linear__order @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Etc,type,
% 1.17/1.41 c_2Eset__relation_2Etc: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Etc,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Etransitive,type,
% 1.17/1.41 c_2Eset__relation_2Etransitive: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Etransitive,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ bool ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Euniv__reln,type,
% 1.17/1.41 c_2Eset__relation_2Euniv__reln: del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Euniv__reln,axiom,
% 1.17/1.41 ! [A_27a: del] : ( mem @ ( c_2Eset__relation_2Euniv__reln @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(tp_c_2Eset__relation_2Eupper__bounds,type,
% 1.17/1.41 c_2Eset__relation_2Eupper__bounds: del > del > $i ).
% 1.17/1.41
% 1.17/1.41 thf(mem_c_2Eset__relation_2Eupper__bounds,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eset__relation_2Eupper__bounds @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ bool ) @ ( arr @ A_27a @ bool ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Erextension,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0s: $i] :
% 1.17/1.41 ( ( mem @ V0s @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1t: $i] :
% 1.17/1.41 ( ( mem @ V1t @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( V0s = V1t )
% 1.17/1.41 <=> ! [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27a )
% 1.17/1.41 => ! [V3y: $i] :
% 1.17/1.41 ( ( mem @ V3y @ A_27b )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V3y ) ) @ V0s ) )
% 1.17/1.41 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V3y ) ) @ V1t ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Edomain__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27b ) @ V0r )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1x: $i] :
% 1.17/1.41 ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1x )
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
% 1.17/1.41 @ ( lam @ A_27b
% 1.17/1.41 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Erange__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27b ) @ V0r )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1y: $i] :
% 1.17/1.41 ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1y )
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
% 1.17/1.41 @ ( lam @ A_27b
% 1.17/1.41 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27a ) @ V2x ) @ V1y ) ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Ein__domain,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1r: $i] :
% 1.17/1.41 ( ( mem @ V1r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27b ) @ V1r ) ) )
% 1.17/1.41 <=> ? [V2y: $i] :
% 1.17/1.41 ( ( mem @ V2y @ A_27b )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V2y ) ) @ V1r ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Ein__range,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0y: $i] :
% 1.17/1.41 ( ( mem @ V0y @ A_27a )
% 1.17/1.41 => ! [V1r: $i] :
% 1.17/1.41 ( ( mem @ V1r @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0y ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27b ) @ V1r ) ) )
% 1.17/1.41 <=> ? [V2x: $i] :
% 1.17/1.41 ( ( mem @ V2x @ A_27b )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27a ) @ V2x ) @ V0y ) ) @ V1r ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Ein__dom__rg,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1y: $i] :
% 1.17/1.41 ( ( mem @ V1y @ A_27b )
% 1.17/1.41 => ! [V2r: $i] :
% 1.17/1.41 ( ( mem @ V2r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y ) ) @ V2r ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27b ) @ V2r ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V1y ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27b @ A_27a ) @ V2r ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Edomain__mono,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1r_27: $i] :
% 1.17/1.41 ( ( mem @ V1r_27 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0r ) @ V1r_27 ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27b ) @ V0r ) ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27b ) @ V1r_27 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Erange__mono,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1r_27: $i] :
% 1.17/1.41 ( ( mem @ V1r_27 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0r ) @ V1r_27 ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27b @ A_27a ) @ V0r ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27b @ A_27a ) @ V1r_27 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Errestrict__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1s )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
% 1.17/1.41 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27a @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2x: $i] :
% 1.17/1.41 ( lam @ A_27a
% 1.17/1.41 @ ^ [V3y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Ein__rrestrict,axiom,
% 1.17/1.41 ! [A_27a: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ A_27a )
% 1.17/1.41 => ! [V1y: $i] :
% 1.17/1.41 ( ( mem @ V1y @ A_27a )
% 1.17/1.41 => ! [V2r: $i] :
% 1.17/1.41 ( ( mem @ V2r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V3s: $i] :
% 1.17/1.41 ( ( mem @ V3s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V0x ) @ V1y ) ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V2r ) @ V3s ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V0x ) @ V1y ) ) @ V2r ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ V3s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1y ) @ V3s ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Ein__rrestrict__alt,axiom,
% 1.17/1.41 ! [A_27a: del,V0x: $i] :
% 1.17/1.41 ( ( mem @ V0x @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
% 1.17/1.41 => ! [V1r: $i] :
% 1.17/1.41 ( ( mem @ V1r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V2s: $i] :
% 1.17/1.41 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0x ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V1r ) @ V2s ) ) )
% 1.17/1.41 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0x ) @ V1r ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27a ) @ V0x ) ) @ V2s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27a ) @ V0x ) ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Errestrict__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1s ) ) @ V0r ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Errestrict__union,axiom,
% 1.17/1.41 ! [A_27a: del,V0r1: $i] :
% 1.17/1.41 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1r2: $i] :
% 1.17/1.41 ( ( mem @ V1r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V2s: $i] :
% 1.17/1.41 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0r1 ) @ V1r2 ) ) @ V2s )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r1 ) @ V2s ) ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V1r2 ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Errestrict__rrestrict,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1x: $i] :
% 1.17/1.41 ( ( mem @ V1x @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2y: $i] :
% 1.17/1.41 ( ( mem @ V2y @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1x ) ) @ V2y )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Edomain__rrestrict__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1s ) ) ) @ V1s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Erange__rrestrict__SUBSET,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1s ) ) ) @ V1s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Ercomp__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,A_27c: del,V0r1: $i] :
% 1.17/1.41 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27c ) @ bool ) )
% 1.17/1.41 => ! [V1r2: $i] :
% 1.17/1.41 ( ( mem @ V1r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) @ bool ) )
% 1.17/1.41 => ( ( ap @ ( ap @ ( c_2Eset__relation_2Ercomp @ A_27a @ A_27b @ A_27c ) @ V0r1 ) @ V1r2 )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.41 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V2x: $i] :
% 1.17/1.41 ( lam @ A_27b
% 1.17/1.41 @ ^ [V3y: $i] :
% 1.17/1.41 ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ V3y ) )
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2E_3F @ A_27c )
% 1.17/1.41 @ ( lam @ A_27c
% 1.17/1.41 @ ^ [V4z: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27c ) @ V2x ) @ V4z ) ) @ V0r1 ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27c @ A_27b ) @ V4z ) @ V3y ) ) @ V1r2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Estrict__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
% 1.17/1.41 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27a @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1x: $i] :
% 1.17/1.41 ( lam @ A_27a
% 1.17/1.41 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Estrict__rrestrict,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.41 = ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r ) ) @ V1s ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Euniv__reln__def,axiom,
% 1.17/1.41 ! [A_27a: del,V0xs: $i] :
% 1.17/1.41 ( ( mem @ V0xs @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ap @ ( c_2Eset__relation_2Euniv__reln @ A_27a ) @ V0xs )
% 1.17/1.41 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
% 1.17/1.41 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27a @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V1x1: $i] :
% 1.17/1.41 ( lam @ A_27a
% 1.17/1.41 @ ^ [V2x2: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x1 ) @ V2x2 ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x1 ) @ V0xs ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x2 ) @ V0xs ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(ax_thm_2Eset__relation_2Efinite__prefixes__def,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ V1s ) )
% 1.17/1.41 <=> ! [V2e: $i] :
% 1.17/1.41 ( ( mem @ V2e @ A_27b )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27b ) @ V2e ) @ V1s ) )
% 1.17/1.41 => ( p
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V3e_27: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3e_27 ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V3e_27 ) @ V2e ) ) @ V0r ) ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__subset__s,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2s_27: $i] :
% 1.17/1.41 ( ( mem @ V2s_27 @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V2s_27 ) @ V1s ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ V2s_27 ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__subset__r,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1r_27: $i] :
% 1.17/1.41 ( ( mem @ V1r_27 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V2s: $i] :
% 1.17/1.41 ( ( mem @ V2s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ V2s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1r_27 ) @ V0r ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V1r_27 ) @ V2s ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__subset__rs,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V2r_27: $i] :
% 1.17/1.41 ( ( mem @ V2r_27 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V3s_27: $i] :
% 1.17/1.41 ( ( mem @ V3s_27 @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ V1s ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_27 ) @ V0r ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b ) @ V3s_27 ) @ V1s ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V2r_27 ) @ V3s_27 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__subset,axiom,
% 1.17/1.41 ! [A_27a: del,V0r: $i] :
% 1.17/1.41 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V1s: $i] :
% 1.17/1.41 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ! [V2s_27: $i] :
% 1.17/1.41 ( ( mem @ V2s_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2s_27 ) @ V1s ) ) )
% 1.17/1.41 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27a ) @ V0r ) @ V2s_27 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V2s_27 ) ) @ V2s_27 ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__union,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0r1: $i] :
% 1.17/1.41 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1r2: $i] :
% 1.17/1.41 ( ( mem @ V1r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V2s1: $i] :
% 1.17/1.41 ( ( mem @ V2s1 @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V3s2: $i] :
% 1.17/1.41 ( ( mem @ V3s2 @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r1 ) @ V2s1 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V1r2 ) @ V3s2 ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0r1 ) @ V1r2 ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINTER @ A_27b ) @ V2s1 ) @ V3s2 ) ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__comp,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,A_27c: del,V0r1: $i] :
% 1.17/1.41 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.41 => ! [V1r2: $i] :
% 1.17/1.41 ( ( mem @ V1r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) @ bool ) )
% 1.17/1.41 => ! [V2s1: $i] :
% 1.17/1.41 ( ( mem @ V2s1 @ ( arr @ A_27b @ bool ) )
% 1.17/1.41 => ! [V3s2: $i] :
% 1.17/1.41 ( ( mem @ V3s2 @ ( arr @ A_27c @ bool ) )
% 1.17/1.41 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r1 ) @ V2s1 ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27b @ A_27c ) @ V1r2 ) @ V3s2 ) )
% 1.17/1.41 & ( p
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27b )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27b @ A_27b )
% 1.17/1.41 @ ( lam @ A_27b
% 1.17/1.41 @ ^ [V4x: $i] :
% 1.17/1.41 ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ bool ) @ V4x )
% 1.17/1.41 @ ( ap @ ( c_2Ebool_2E_3F @ A_27c )
% 1.17/1.41 @ ( lam @ A_27c
% 1.17/1.41 @ ^ [V5y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27c ) @ V5y ) @ V3s2 ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27c ) @ V4x ) @ V5y ) ) @ V1r2 ) ) ) ) ) ) ) )
% 1.17/1.41 @ V2s1 ) ) )
% 1.17/1.41 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Ercomp @ A_27a @ A_27c @ A_27b ) @ V0r1 ) @ V1r2 ) ) @ V3s2 ) ) ) ) ) ) ) ).
% 1.17/1.41
% 1.17/1.41 thf(conj_thm_2Eset__relation_2Efinite__prefixes__inj__image,axiom,
% 1.17/1.41 ! [A_27a: del,A_27b: del,V0f: $i] :
% 1.17/1.41 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 1.17/1.41 => ! [V1r: $i] :
% 1.17/1.41 ( ( mem @ V1r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.41 => ! [V2s: $i] :
% 1.17/1.41 ( ( mem @ V2s @ ( arr @ A_27a @ bool ) )
% 1.17/1.41 => ( ( ! [V3x: $i] :
% 1.17/1.41 ( ( mem @ V3x @ A_27a )
% 1.17/1.41 => ! [V4y: $i] :
% 1.17/1.41 ( ( mem @ V4y @ A_27a )
% 1.17/1.41 => ( ( ( ap @ V0f @ V3x )
% 1.17/1.41 = ( ap @ V0f @ V4y ) )
% 1.17/1.41 => ( V3x = V4y ) ) ) )
% 1.17/1.41 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27a ) @ V1r ) @ V2s ) ) )
% 1.17/1.41 => ( p
% 1.17/1.41 @ ( ap
% 1.17/1.41 @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27b @ A_27b )
% 1.17/1.41 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27b @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
% 1.17/1.41 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27a @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27b @ A_27b ) @ bool ) )
% 1.17/1.41 @ ( lam @ A_27a
% 1.17/1.41 @ ^ [V5x: $i] :
% 1.17/1.41 ( lam @ A_27a
% 1.17/1.41 @ ^ [V6y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27b @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27b @ A_27b ) @ ( ap @ V0f @ V5x ) ) @ ( ap @ V0f @ V6y ) ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V5x ) @ V6y ) ) @ V1r ) ) ) ) ) ) )
% 1.17/1.41 @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ A_27a @ A_27b ) @ V0f ) @ V2s ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Efinite__prefixes__range,axiom,
% 1.17/1.42 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27b @ bool ) )
% 1.17/1.42 => ! [V2t: $i] :
% 1.17/1.42 ( ( mem @ V2t @ ( arr @ A_27b @ bool ) )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27b ) @ V2t ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27b @ A_27a ) @ V0r ) ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27b ) @ V0r ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27b ) @ V1s ) @ V2t ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Etc__def,axiom,
% 1.17/1.42 ! [A_27a: del] :
% 1.17/1.42 ( ( c_2Eset__relation_2Etc @ A_27a )
% 1.17/1.42 = ( lam @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool )
% 1.17/1.42 @ ^ [V0r: $i] :
% 1.17/1.42 ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27a )
% 1.17/1.42 @ ^ [V1a0: $i] :
% 1.17/1.42 ( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 @ ( lam @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool )
% 1.17/1.42 @ ^ [V2tc_27: $i] :
% 1.17/1.42 ( ap
% 1.17/1.42 @ ( ap @ c_2Emin_2E_3D_3D_3E
% 1.17/1.42 @ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
% 1.17/1.42 @ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27a )
% 1.17/1.42 @ ^ [V3a0: $i] :
% 1.17/1.42 ( ap
% 1.17/1.42 @ ( ap @ c_2Emin_2E_3D_3D_3E
% 1.17/1.42 @ ( ap
% 1.17/1.42 @ ( ap @ c_2Ebool_2E_5C_2F
% 1.17/1.42 @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V4x: $i] :
% 1.17/1.42 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V5y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V3a0 ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V5y ) ) ) @ ( ap @ V0r @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V5y ) ) ) ) ) ) ) )
% 1.17/1.42 @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V6x: $i] :
% 1.17/1.42 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V7y: $i] :
% 1.17/1.42 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V3a0 ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6x ) @ V7y ) ) )
% 1.17/1.42 @ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V8z: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2tc_27 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6x ) @ V8z ) ) ) @ ( ap @ V2tc_27 @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V8z ) @ V7y ) ) ) ) ) ) ) ) ) ) ) )
% 1.17/1.42 @ ( ap @ V2tc_27 @ V3a0 ) ) ) ) )
% 1.17/1.42 @ ( ap @ V2tc_27 @ V1a0 ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__rules,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ) )
% 1.17/1.42 & ! [V3x: $i] :
% 1.17/1.42 ( ( mem @ V3x @ A_27a )
% 1.17/1.42 => ! [V4y: $i] :
% 1.17/1.42 ( ( mem @ V4y @ A_27a )
% 1.17/1.42 => ( ? [V5z: $i] :
% 1.17/1.42 ( ( mem @ V5z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3x ) @ V5z ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V5z ) @ V4y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3x ) @ V4y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__cases,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) )
% 1.17/1.42 | ? [V3z: $i] :
% 1.17/1.42 ( ( mem @ V3z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V3z ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3z ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__ind,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.42 & ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ? [V6z: $i] :
% 1.17/1.42 ( ( mem @ V6z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V6z ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V6z ) @ V5y ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.42 => ! [V7x: $i] :
% 1.17/1.42 ( ( mem @ V7x @ A_27a )
% 1.17/1.42 => ! [V8y: $i] :
% 1.17/1.42 ( ( mem @ V8y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V7x ) @ V8y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__closure,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0r ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V1s ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Esubset__tc,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0r ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__idemp,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) )
% 1.17/1.42 = ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__mono,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0r ) @ V1s ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__strongind,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.42 & ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ? [V6z: $i] :
% 1.17/1.42 ( ( mem @ V6z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V6z ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V6z ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6z ) @ V5y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V6z ) @ V5y ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.42 => ! [V7x: $i] :
% 1.17/1.42 ( ( mem @ V7x @ A_27a )
% 1.17/1.42 => ! [V8y: $i] :
% 1.17/1.42 ( ( mem @ V8y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V7x ) @ V8y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__cases__right,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) )
% 1.17/1.42 | ? [V3z: $i] :
% 1.17/1.42 ( ( mem @ V3z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V3z ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3z ) @ V2y ) ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__cases__left,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) )
% 1.17/1.42 | ? [V3z: $i] :
% 1.17/1.42 ( ( mem @ V3z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V3z ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3z ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__ind__left,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.42 & ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ? [V6z: $i] :
% 1.17/1.42 ( ( mem @ V6z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V6z ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V6z ) @ V5y ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.42 => ! [V7x: $i] :
% 1.17/1.42 ( ( mem @ V7x @ A_27a )
% 1.17/1.42 => ! [V8y: $i] :
% 1.17/1.42 ( ( mem @ V8y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V7x ) @ V8y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__strongind__left,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.42 & ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ? [V6z: $i] :
% 1.17/1.42 ( ( mem @ V6z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V6z ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6z ) @ V5y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V6z ) @ V5y ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.42 => ! [V7x: $i] :
% 1.17/1.42 ( ( mem @ V7x @ A_27a )
% 1.17/1.42 => ! [V8y: $i] :
% 1.17/1.42 ( ( mem @ V8y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V7x ) @ V8y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__ind__right,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.42 & ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ? [V6z: $i] :
% 1.17/1.42 ( ( mem @ V6z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V6z ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6z ) @ V5y ) ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.42 => ! [V7x: $i] :
% 1.17/1.42 ( ( mem @ V7x @ A_27a )
% 1.17/1.42 => ! [V8y: $i] :
% 1.17/1.42 ( ( mem @ V8y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V7x ) @ V8y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Ertc__ind__right,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0r ) ) )
% 1.17/1.42 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0r ) ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V2x ) ) ) )
% 1.17/1.42 & ! [V3x: $i] :
% 1.17/1.42 ( ( mem @ V3x @ A_27a )
% 1.17/1.42 => ! [V4y: $i] :
% 1.17/1.42 ( ( mem @ V4y @ A_27a )
% 1.17/1.42 => ( ? [V5z: $i] :
% 1.17/1.42 ( ( mem @ V5z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V3x ) @ V5z ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V5z ) @ V4y ) ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V3x ) @ V4y ) ) ) ) ) )
% 1.17/1.42 => ! [V6x: $i] :
% 1.17/1.42 ( ( mem @ V6x @ A_27a )
% 1.17/1.42 => ! [V7y: $i] :
% 1.17/1.42 ( ( mem @ V7y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6x ) @ V7y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V6x ) @ V7y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__strongind__right,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1tc_27: $i] :
% 1.17/1.42 ( ( mem @ V1tc_27 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V2x ) @ V3y ) ) ) ) )
% 1.17/1.42 & ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ? [V6z: $i] :
% 1.17/1.42 ( ( mem @ V6z @ A_27a )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V6z ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V6z ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V6z ) @ V5y ) ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V4x ) @ V5y ) ) ) ) ) )
% 1.17/1.42 => ! [V7x: $i] :
% 1.17/1.42 ( ( mem @ V7x @ A_27a )
% 1.17/1.42 => ! [V8y: $i] :
% 1.17/1.42 ( ( mem @ V8y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V7x ) @ V8y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ V1tc_27 @ V7x ) @ V8y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__union,axiom,
% 1.17/1.42 ! [A_27a: del,V0r1: $i] :
% 1.17/1.42 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r1 ) ) )
% 1.17/1.42 => ! [V3r2: $i] :
% 1.17/1.42 ( ( mem @ V3r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0r1 ) @ V3r2 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__implication,axiom,
% 1.17/1.42 ! [A_27a: del,V0r1: $i] :
% 1.17/1.42 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1r2: $i] :
% 1.17/1.42 ( ( mem @ V1r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r1 ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V1r2 ) ) ) ) )
% 1.17/1.42 => ! [V4x: $i] :
% 1.17/1.42 ( ( mem @ V4x @ A_27a )
% 1.17/1.42 => ! [V5y: $i] :
% 1.17/1.42 ( ( mem @ V5y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V5y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r1 ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4x ) @ V5y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V1r2 ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__empty,axiom,
% 1.17/1.42 ! [A_27a: del,V0x: $i] :
% 1.17/1.42 ( ( mem @ V0x @ A_27a )
% 1.17/1.42 => ! [V1y: $i] :
% 1.17/1.42 ( ( mem @ V1y @ A_27a )
% 1.17/1.42 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V0x ) @ V1y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__empty__eqn,axiom,
% 1.17/1.42 ! [A_27a: del] :
% 1.17/1.42 ( ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) )
% 1.17/1.42 = ( c_2Epred__set_2EEMPTY @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__domain__range,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Errestrict__tc,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ! [V2e: $i] :
% 1.17/1.42 ( ( mem @ V2e @ A_27a )
% 1.17/1.42 => ! [V3e_27: $i] :
% 1.17/1.42 ( ( mem @ V3e_27 @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2e ) @ V3e_27 ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1x ) ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2e ) @ V3e_27 ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__SWAP,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( c_2Epair_2ESWAP @ A_27a @ A_27a ) ) @ V0r ) )
% 1.17/1.42 = ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( c_2Epair_2ESWAP @ A_27a @ A_27a ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Eacyclic__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V0r ) )
% 1.17/1.42 <=> ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V1x ) ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eacyclic__subset,axiom,
% 1.17/1.42 ! [A_27a: del,V0r1: $i] :
% 1.17/1.42 ( ( mem @ V0r1 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1r2: $i] :
% 1.17/1.42 ( ( mem @ V1r2 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V0r1 ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V1r2 ) @ V0r1 ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V1r2 ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eacyclic__rrestrict,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V0r ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eacyclic__irreflexive,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V0r ) )
% 1.17/1.42 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V1x ) ) @ V0r ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eacyclic__SWAP,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( c_2Epair_2ESWAP @ A_27a @ A_27a ) ) @ V0r ) ) )
% 1.17/1.42 <=> ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V0r ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eacyclic__bigunion,axiom,
% 1.17/1.42 ! [A_27a: del,V0rs: $i] :
% 1.17/1.42 ( ( mem @ V0rs @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ bool ) )
% 1.17/1.42 => ( ( ! [V1r: $i] :
% 1.17/1.42 ( ( mem @ V1r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V2r_27: $i] :
% 1.17/1.42 ( ( mem @ V2r_27 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) @ V1r ) @ V0rs ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) @ V2r_27 ) @ V0rs ) )
% 1.17/1.42 & ( V1r != V2r_27 ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V1r ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V1r ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V2r_27 ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V2r_27 ) ) ) ) ) ) )
% 1.17/1.42 & ! [V3r: $i] :
% 1.17/1.42 ( ( mem @ V3r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) ) @ V3r ) @ V0rs ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V3r ) ) ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ ( ap @ ( c_2Epred__set_2EBIGUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0rs ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eacyclic__union,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1r_27: $i] :
% 1.17/1.42 ( ( mem @ V1r_27 @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2EDISJOINT @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0r ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0r ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V1r_27 ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V1r_27 ) ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ V1r_27 ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0r ) @ V1r_27 ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Ereflexive__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Ereflexive @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 <=> ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V2x ) ) @ V0r ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Eirreflexive__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Eirreflexive @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 <=> ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.42 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V2x ) ) @ V0r ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Etransitive__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ V0r ) )
% 1.17/1.42 <=> ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ! [V3z: $i] :
% 1.17/1.42 ( ( mem @ V3z @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2y ) @ V3z ) ) @ V0r ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V3z ) ) @ V0r ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etransitive__tc,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ V0r ) )
% 1.17/1.42 => ( ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r )
% 1.17/1.42 = V0r ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Etc__transitive,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Etc @ A_27a ) @ V0r ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Eantisym__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ V0r ) )
% 1.17/1.42 <=> ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V1x ) @ V2y ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2y ) @ V1x ) ) @ V0r ) ) )
% 1.17/1.42 => ( V1x = V2y ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Epartial__order__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0r ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0r ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Ereflexive @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ V0r ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Eantisym__subset,axiom,
% 1.17/1.42 ! [A_27a: del,V0t: $i] :
% 1.17/1.42 ( ( mem @ V0t @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ V0t ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V1s ) @ V0t ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ V1s ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Epartial__order__dom__rng,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ V0r ) @ V1s ) ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Epartial__order__subset,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ! [V2s_27: $i] :
% 1.17/1.42 ( ( mem @ V2s_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2s_27 ) @ V1s ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V2s_27 ) ) @ V2s_27 ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Estrict__partial__order,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r ) ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r ) ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r ) ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Estrict__partial__order__acyclic,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 => ( p @ ( ap @ ( c_2Eset__relation_2Eacyclic @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Estrict @ A_27a ) @ V0r ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Elinear__order__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0r ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0r ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Eantisym @ A_27a ) @ V0r ) )
% 1.17/1.42 & ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3y ) @ V2x ) ) @ V0r ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Elinear__order__subset,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ! [V2s_27: $i] :
% 1.17/1.42 ( ( mem @ V2s_27 @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ V2s_27 ) @ V1s ) ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0r ) @ V2s_27 ) ) @ V2s_27 ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Epartial__order__linear__order,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Epartial__order @ A_27a ) @ V0r ) @ V1s ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Estrict__linear__order__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Estrict__linear__order @ A_27a ) @ V0r ) @ V1s ) )
% 1.17/1.42 <=> ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0r ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0r ) ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( c_2Eset__relation_2Etransitive @ A_27a ) @ V0r ) )
% 1.17/1.42 & ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V2x ) ) @ V0r ) ) )
% 1.17/1.42 & ! [V3x: $i] :
% 1.17/1.42 ( ( mem @ V3x @ A_27a )
% 1.17/1.42 => ! [V4y: $i] :
% 1.17/1.42 ( ( mem @ V4y @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V4y ) @ V1s ) )
% 1.17/1.42 & ( V3x != V4y ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V3x ) @ V4y ) ) @ V0r ) )
% 1.17/1.42 | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V4y ) @ V3x ) ) @ V0r ) ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Estrict__linear__order__dom__rng,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Estrict__linear__order @ A_27a ) @ V0r ) @ V1s ) ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Elinear__order__dom__rng,axiom,
% 1.17/1.42 ! [A_27a: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ! [V2x: $i] :
% 1.17/1.42 ( ( mem @ V2x @ A_27a )
% 1.17/1.42 => ! [V3y: $i] :
% 1.17/1.42 ( ( mem @ V3y @ A_27a )
% 1.17/1.42 => ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V2x ) @ V3y ) ) @ V0r ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ V0r ) @ V1s ) ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) )
% 1.17/1.42 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3y ) @ V1s ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Ereln__to__rel__def,axiom,
% 1.17/1.42 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.42 => ( ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ A_27a @ A_27b ) @ V0r )
% 1.17/1.42 = ( lam @ A_27a
% 1.17/1.42 @ ^ [V1x: $i] :
% 1.17/1.42 ( lam @ A_27b
% 1.17/1.42 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) @ V0r ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2Erel__to__reln__def,axiom,
% 1.17/1.42 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.17/1.42 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.42 => ( ( ap @ ( c_2Eset__relation_2Erel__to__reln @ A_27a @ A_27b ) @ V0R )
% 1.17/1.42 = ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.42 @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V1x: $i] :
% 1.17/1.42 ( lam @ A_27b
% 1.17/1.42 @ ^ [V2y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2ERRUNIV__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0s: $i] :
% 1.17/1.42 ( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( ap @ ( c_2Eset__relation_2ERRUNIV @ A_27a ) @ V0s )
% 1.17/1.42 = ( lam @ A_27a
% 1.17/1.42 @ ^ [V1x: $i] :
% 1.17/1.42 ( lam @ A_27a
% 1.17/1.42 @ ^ [V2y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ V0s ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(ax_thm_2Eset__relation_2ERREFL__EXP__def,axiom,
% 1.17/1.42 ! [A_27a: del,V0R: $i] :
% 1.17/1.42 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( ( ap @ ( ap @ ( c_2Eset__relation_2ERREFL__EXP @ A_27a ) @ V0R ) @ V1s )
% 1.17/1.42 = ( ap @ ( ap @ ( c_2Erelation_2ERUNION @ A_27a @ A_27a ) @ V0R )
% 1.17/1.42 @ ( lam @ A_27a
% 1.17/1.42 @ ^ [V2x: $i] :
% 1.17/1.42 ( lam @ A_27a
% 1.17/1.42 @ ^ [V3y: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2x ) @ V3y ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V1s ) ) ) ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2ERREFL__EXP__RSUBSET,axiom,
% 1.17/1.42 ! [A_27a: del,V0R: $i] :
% 1.17/1.42 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ! [V1s: $i] :
% 1.17/1.42 ( ( mem @ V1s @ ( arr @ A_27a @ bool ) )
% 1.17/1.42 => ( p @ ( ap @ ( ap @ ( c_2Erelation_2ERSUBSET @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( ap @ ( c_2Eset__relation_2ERREFL__EXP @ A_27a ) @ V0R ) @ V1s ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2ERREFL__EXP__UNIV,axiom,
% 1.17/1.42 ! [A_27a: del,V0R: $i] :
% 1.17/1.42 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ap @ ( ap @ ( c_2Eset__relation_2ERREFL__EXP @ A_27a ) @ V0R ) @ ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.42 = V0R ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2EREL__RESTRICT__UNIV,axiom,
% 1.17/1.42 ! [A_27a: del,V0R: $i] :
% 1.17/1.42 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
% 1.17/1.42 => ( ( ap @ ( ap @ ( c_2Epred__set_2EREL__RESTRICT @ A_27a ) @ V0R ) @ ( c_2Epred__set_2EUNIV @ A_27a ) )
% 1.17/1.42 = V0R ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Ein__rel__to__reln,axiom,
% 1.17/1.42 ! [A_27a: del,A_27b: del,V0xy: $i] :
% 1.17/1.42 ( ( mem @ V0xy @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
% 1.17/1.42 => ! [V1R: $i] :
% 1.17/1.42 ( ( mem @ V1R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0xy ) @ ( ap @ ( c_2Eset__relation_2Erel__to__reln @ A_27a @ A_27b ) @ V1R ) ) )
% 1.17/1.42 <=> ( p @ ( ap @ ( ap @ V1R @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V0xy ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V0xy ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Ereln__to__rel__app,axiom,
% 1.17/1.42 ! [A_27a: del,A_27b: del,V0r: $i] :
% 1.17/1.42 ( ( mem @ V0r @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
% 1.17/1.42 => ! [V1x: $i] :
% 1.17/1.42 ( ( mem @ V1x @ A_27a )
% 1.17/1.42 => ! [V2y: $i] :
% 1.17/1.42 ( ( mem @ V2y @ A_27b )
% 1.17/1.42 => ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ A_27a @ A_27b ) @ V0r ) @ V1x ) @ V2y ) )
% 1.17/1.42 <=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V1x ) @ V2y ) ) @ V0r ) ) ) ) ) ) ).
% 1.17/1.42
% 1.17/1.42 thf(conj_thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY,axiom,
% 1.89/2.21 ! [A_27a: del,A_27b: del] :
% 1.89/2.21 ( ( c_2Eset__relation_2Erel__to__reln @ A_27a @ A_27b )
% 1.89/2.21 = ( c_2Epair_2EUNCURRY @ A_27a @ A_27b @ bool ) ) ).
% 1.89/2.21
% 1.89/2.21 thf(conj_thm_2Eset__relation_2Ereln__to__rel__IS__CURRY,axiom,
% 1.89/2.21 ! [A_27a: del,A_27b: del] :
% 1.89/2.21 ( ( c_2Eset__relation_2Ereln__to__rel @ A_27a @ A_27b )
% 1.89/2.21 = ( c_2Epair_2ECURRY @ A_27a @ A_27b @ bool ) ) ).
% 1.89/2.21
% 1.89/2.21 thf(conj_thm_2Eset__relation_2Erel__to__reln__inv,conjecture,
% 1.89/2.21 ! [A_27a: del,A_27b: del,V0R: $i] :
% 1.89/2.21 ( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
% 1.89/2.21 => ( ( ap @ ( c_2Eset__relation_2Ereln__to__rel @ A_27a @ A_27b ) @ ( ap @ ( c_2Eset__relation_2Erel__to__reln @ A_27a @ A_27b ) @ V0R ) )
% 1.89/2.21 = V0R ) ) ).
% 1.89/2.21
% 1.89/2.21 %------------------------------------------------------------------------------
% 1.89/2.21 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xf5BZ6Gadg/cvc5---1.0.5_13187.p...
% 1.89/2.21 (declare-sort $$unsorted 0)
% 1.89/2.21 (declare-sort tptp.del 0)
% 1.89/2.21 (declare-fun tptp.bool () tptp.del)
% 1.89/2.21 (declare-fun tptp.ind () tptp.del)
% 1.89/2.21 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 1.89/2.21 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 1.89/2.21 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 1.89/2.21 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 1.89/2.21 (declare-fun tptp.p ($$unsorted) Bool)
% 1.89/2.21 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 1.89/2.21 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 1.89/2.21 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 1.89/2.21 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 1.89/2.21 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 1.89/2.21 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((G $$unsorted)) (=> (@ (@ tptp.mem G) (@ (@ tptp.arr A) B)) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 1.89/2.21 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 1.89/2.21 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (assert (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))))
% 1.89/2.21 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) Q)) R)) (=> (@ tptp.p Q) (@ tptp.p R))))))))
% 1.89/2.21 (declare-fun tptp.c_2Emin_2E_40 (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a))))
% 1.89/2.21 (declare-fun tptp.ty_2Ebool_2Eitself (tptp.del) tptp.del)
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 1.89/2.21 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2E_3F (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 1.89/2.21 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A)) Q)) (exists ((X $$unsorted)) (and (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2E_3F_21 (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EARB (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EARB A_27a)) A_27a)))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EBOUNDED () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EBOUNDED) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ECOND (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 A_27a)))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EDATATYPE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EDATATYPE A_27a)) (@ (@ tptp.arr A_27a) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 1.89/2.21 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EIN (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EIN A_27a)) (@ _let_1 (@ (@ tptp.arr (@ _let_1 tptp.bool)) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ELET (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EONE__ONE (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2EONTO (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ERES__ABSTRACT (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ERES__EXISTS (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ERES__EXISTS__UNIQUE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ERES__FORALL (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ERES__SELECT (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__SELECT A_27a)) (@ _let_1 (@ _let_1 A_27a))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 1.89/2.21 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2ETYPE__DEFINITION (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27a)) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2Eitself__case (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eitself__case A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) (@ (@ tptp.arr A_27b) A_27b)))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2Eliteral__case (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2Ethe__value (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2Ethe__value A_27a)) (@ tptp.ty_2Ebool_2Eitself A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 1.89/2.21 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.lam tptp.bool))) (= true (= (@ _let_1 (lambda ((V0x $$unsorted)) V0x)) (@ _let_1 (lambda ((V1x $$unsorted)) V1x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2ET))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P)))))))
% 1.89/2.21 (assert (= tptp.c_2Ebool_2E_2F_5C (@ (@ tptp.lam tptp.bool) (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V0t1)) (@ (@ tptp.ap (@ _let_1 V1t2)) V2t)))) V2t)))))))))))
% 1.89/2.21 (assert (= tptp.c_2Ebool_2E_5C_2F (@ (@ tptp.lam tptp.bool) (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V0t1)) V2t))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V1t2)) V2t))) V2t))))))))))))
% 1.89/2.21 (assert (= false (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (@ tptp.p V0t)))))
% 1.89/2.21 (assert (= tptp.c_2Ebool_2E_7E (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V0t)) tptp.c_2Ebool_2EF)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) V0P))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V1x))) (@ _let_1 V2y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V2y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ECOND A_27a) (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1t1 $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) V0t)))) (let ((_let_3 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ _let_3 (@ _let_2 tptp.c_2Ebool_2ET))) (@ _let_1 V1t1)))) (@ (@ tptp.ap (@ _let_3 (@ _let_2 tptp.c_2Ebool_2EF))) (@ _let_1 V2t2))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x1 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x2 $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) (@ _let_1 V1x1))) (@ _let_1 V2x2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x1)) V2x2))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V1y)) (@ (@ tptp.ap V0f) V2x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27b) A_27a)) (lambda ((V1rep $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V2x_27 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V3x_27_27 $$unsorted)) (let ((_let_1 (@ tptp.ap V1rep))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 V2x_27))) (@ _let_1 V3x_27_27)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27))))))))))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) (@ (@ tptp.ap V0P) V4x))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V5x_27 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4x)) (@ (@ tptp.ap V1rep) V5x_27)))))))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or (= _let_1 true) (= _let_1 false))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0t) V1x))) V0t))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V1x) A_27a) (=> (@ tptp.p (@ _let_1 V1x)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P))))))))))
% 1.89/2.21 (declare-sort tptp.tp__i 0)
% 1.89/2.21 (declare-fun tptp.inj__i (tptp.tp__i) $$unsorted)
% 1.89/2.21 (declare-fun tptp.surj__i ($$unsorted) tptp.tp__i)
% 1.89/2.21 (assert (forall ((X tptp.tp__i)) (= (@ tptp.surj__i (@ tptp.inj__i X)) X)))
% 1.89/2.21 (assert (forall ((X tptp.tp__i)) (@ (@ tptp.mem (@ tptp.inj__i X)) tptp.ind)))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ind) (= X (@ tptp.inj__i (@ tptp.surj__i X))))))
% 1.89/2.21 (assert (exists ((V0f $$unsorted)) (and (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ind) tptp.ind)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ind) tptp.ind)) V0f)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONTO tptp.ind) tptp.ind)) V0f))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EIN A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1f $$unsorted)) (@ (@ tptp.ap V1f) V0x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__FORALL A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0p)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1m) V2x)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1m))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V3x))) (@ _let_1 V4y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__SELECT A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 1.89/2.21 (assert (= tptp.c_2Ebool_2EBOUNDED (@ (@ tptp.lam tptp.bool) (lambda ((V0v $$unsorted)) tptp.c_2Ebool_2ET))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EDATATYPE A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET)))))
% 1.89/2.21 (assert true)
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0M $$unsorted)) (=> (@ (@ tptp.mem V0M) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0M) V1x))) V0M))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or _let_1 (not _let_1))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V0f) V2x)))) V1y) (@ (@ tptp.ap V0f) V1y)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b)) V0f)) V1x) (@ (@ tptp.ap V0f) V1x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) V0f)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0f) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) V0f)) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0f) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.lam A_27b) (lambda ((V2x $$unsorted)) V0t1))) V1t2) V0t1))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> _let_2 (=> _let_1 (and _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (and _let_1 (@ tptp.p V1t2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (and (@ tptp.p V0t1) _let_1) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0t1))) (let ((_let_2 (@ tptp.p V1t2))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (= (and _let_1 _let_2) (and _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0t1))) (let ((_let_2 (@ tptp.p V1t2))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (= (and _let_1 _let_2) (and _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) tptp.bool) (forall ((V2t3 $$unsorted)) (let ((_let_1 (and (@ tptp.p V0t1) (@ tptp.p V1t2) (@ tptp.p V2t3)))) (=> (@ (@ tptp.mem V2t3) tptp.bool) (= _let_1 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> _let_1 (or _let_1 (@ tptp.p V1t2)))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> _let_1 (or (@ tptp.p V0t1) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (forall ((V1t1 $$unsorted)) (=> (@ (@ tptp.mem V1t1) tptp.bool) (forall ((V2t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (@ tptp.p V2t2))) (let ((_let_3 (@ tptp.p V1t1))) (=> (@ (@ tptp.mem V2t2) tptp.bool) (=> (or _let_3 _let_2) (=> (=> _let_3 _let_1) (=> (=> _let_2 _let_1) _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (=> _let_1 false) (not _let_1))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (not _let_1) (=> _let_1 false))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (not _let_1) (= _let_1 false))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (not (and _let_1 (not _let_1)))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (and true _let_1) _let_1) (= (and _let_1 true) _let_1) (= (and false _let_1) false) (= (and _let_1 false) false) (= (and _let_1 _let_1) _let_1))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (or true _let_1) true) (= (or _let_1 true) true) (= (or false _let_1) _let_1) (= (or _let_1 false) _let_1) (= (or _let_1 _let_1) _let_1))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (=> true _let_1) _let_1) (= (=> _let_1 true) true) (= (=> false _let_1) true) (= (=> _let_1 _let_1) true) (= (=> _let_1 false) (not _let_1)))))))
% 1.89/2.21 (assert (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= V0x V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (=> (= V0x V1y) (= V1y V0x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= V0x V1y) (= V1y V0x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap V0f) V2x) (@ (@ tptp.ap V1g) V2x)))) (= V0f V1g)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (= (= V0f V1g) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap V0f) V2x) (@ (@ tptp.ap V1g) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (=> (and (= V0x V1y) (= V1y V2z)) (= V0x V2z)))))))))
% 1.89/2.21 (assert (and (not (= true false)) (not (= false true))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (=> (@ (@ tptp.mem V1t2) A_27a) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2EF)) V0t1)) V1t2) V1t2))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) V0b)) V1t)) V1t) V1t))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0P) V1x)))))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1y)) V0x)))) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V0x)) V1y)))) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (=> (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap V0P) V2y)) (= V2y V1x)))) (= (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P) V1x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V3x)) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))) (@ tptp.p (@ (@ tptp.ap V1Q) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V1x))))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (not (@ tptp.p (@ (@ tptp.ap V0P) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V1x))))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (not (@ tptp.p (@ (@ tptp.ap V0P) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (and (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) (@ tptp.p V1Q)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (and (@ tptp.p (@ (@ tptp.ap V0P) V3x)) (@ tptp.p V1Q))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (and (@ tptp.p V0P) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (and (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (or (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (or (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (or (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) (@ tptp.p V1Q)) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (or (@ tptp.p (@ (@ tptp.ap V0P) V3x)) (@ tptp.p V1Q))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (or (@ tptp.p V0P) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (or (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p V0P) (@ tptp.p V1Q))) (and (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p V0P))) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p V1Q))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p V1Q))) (and (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (@ tptp.p V1Q))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V2x)))) (and (@ tptp.p V0P) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (or (@ tptp.p V0P) (@ tptp.p V1Q)))) (or (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p V0P))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p V1Q))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0Q $$unsorted)) (=> (@ (@ tptp.mem V0Q) tptp.bool) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (or (@ tptp.p (@ (@ tptp.ap V1P) V2x)) (@ tptp.p V0Q)))) (or (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V1P) V3x)))) (@ tptp.p V0Q))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (or (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (or (@ tptp.p V0P) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p V0P) (@ tptp.p V1Q)))) (=> (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p V0P))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p V1Q))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p V1Q)))) (=> (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (@ tptp.p V1Q))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (=> (@ tptp.p V0P) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p V0P) (@ tptp.p V1Q)))) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p V0P))) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p V1Q))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p V1Q)))) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (@ tptp.p V1Q))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (=> (@ tptp.p V0P) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (= _let_1 (or _let_2 _let_1)) (=> _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (not (=> _let_2 _let_1)) (and _let_2 (not _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (or (@ tptp.p V0A) (@ tptp.p V1B) (@ tptp.p V2C)))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= _let_1 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_1 _let_2) (or _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_1 _let_2) (or _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V0A))) (let ((_let_4 (not _let_3))) (=> (@ (@ tptp.mem V1B) tptp.bool) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2))))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (@ tptp.p V2C))) (let ((_let_2 (@ tptp.p V0A))) (let ((_let_3 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= (and _let_2 (or _let_3 _let_1)) (or (and _let_2 _let_3) (and _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V2C))) (let ((_let_3 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= (and (or _let_3 _let_2) _let_1) (or (and _let_3 _let_1) (and _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (@ tptp.p V2C))) (let ((_let_2 (@ tptp.p V0A))) (let ((_let_3 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= (or _let_2 (and _let_3 _let_1)) (and (or _let_2 _let_3) (or _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (let ((_let_2 (@ tptp.p V2C))) (let ((_let_3 (@ tptp.p V1B))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= (or (and _let_3 _let_2) _let_1) (and (or _let_3 _let_1) (or _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> _let_2 _let_1) (or (not _let_2) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (forall ((V2R $$unsorted)) (let ((_let_1 (@ tptp.p V2R))) (let ((_let_2 (@ tptp.p V1Q))) (let ((_let_3 (@ tptp.p V0P))) (=> (@ (@ tptp.mem V2R) tptp.bool) (= (=> (or _let_3 _let_2) _let_1) (and (=> _let_3 _let_1) (=> _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (forall ((V2R $$unsorted)) (let ((_let_1 (@ tptp.p V2R))) (let ((_let_2 (@ tptp.p V0P))) (let ((_let_3 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V2R) tptp.bool) (= (=> _let_2 (and _let_3 _let_1)) (and (=> _let_2 _let_3) (=> _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (=> _let_1 false) (= _let_1 false))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) tptp.bool) (forall ((V2t3 $$unsorted)) (let ((_let_1 (@ tptp.p V2t3))) (let ((_let_2 (@ tptp.p V1t2))) (let ((_let_3 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V2t3) tptp.bool) (= (=> _let_3 (=> _let_2 _let_1)) (=> (and _let_3 _let_2) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0t1))) (let ((_let_2 (@ tptp.p V1t2))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (= (= _let_1 _let_2) (and (=> _let_1 _let_2) (=> _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (= (= _let_2 _let_1) (or (and _let_2 _let_1) (and (not _let_2) (not _let_1)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2g $$unsorted)) (=> (@ (@ tptp.mem V2g) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.arr A_27a) A_27b))) V0b)) V1f)) V2g)) V3x) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) V0b)) (@ (@ tptp.ap V1f) V3x))) (@ (@ tptp.ap V2g) V3x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) tptp.bool) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V3y) A_27a) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) V1b)) V2x)) V3y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) V1b)) (@ _let_1 V2x))) (@ _let_1 V3y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2g $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V2g) _let_1) (= (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) V0b)) (@ (@ tptp.ap V1f) V3x))) (@ (@ tptp.ap V2g) V3x)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_1)) V0b)) V1f)) V2g))))))))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1t1 $$unsorted)) (=> (@ (@ tptp.mem V1t1) tptp.bool) (forall ((V2t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0b))) (=> (@ (@ tptp.mem V2t2) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0b)) V1t1)) V2t2)) (and (or (not _let_1) (@ tptp.p V1t1)) (or _let_1 (@ tptp.p V2t2))))))))))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1t1 $$unsorted)) (=> (@ (@ tptp.mem V1t1) tptp.bool) (forall ((V2t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0b))) (=> (@ (@ tptp.mem V2t2) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0b)) V1t1)) V2t2)) (and (=> _let_1 (@ tptp.p V1t1)) (=> (not _let_1) (@ tptp.p V2t2))))))))))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1t1 $$unsorted)) (=> (@ (@ tptp.mem V1t1) tptp.bool) (forall ((V2t2 $$unsorted)) (let ((_let_1 (@ tptp.p V0b))) (=> (@ (@ tptp.mem V2t2) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0b)) V1t1)) V2t2)) (or (and _let_1 (@ tptp.p V1t1)) (and (not _let_1) (@ tptp.p V2t2))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1rep $$unsorted)) (=> (@ (@ tptp.mem V1rep) (@ (@ tptp.arr A_27b) A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) V0P)) V1rep)) (and (forall ((V2x_27 $$unsorted)) (=> (@ (@ tptp.mem V2x_27) A_27b) (forall ((V3x_27_27 $$unsorted)) (let ((_let_1 (@ tptp.ap V1rep))) (=> (@ (@ tptp.mem V3x_27_27) A_27b) (=> (= (@ _let_1 V2x_27) (@ _let_1 V3x_27_27)) (= V2x_27 V3x_27_27))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (= (@ tptp.p (@ (@ tptp.ap V0P) V4x)) (exists ((V5x_27 $$unsorted)) (and (@ (@ tptp.mem V5x_27) A_27b) (= V4x (@ (@ tptp.ap V1rep) V5x_27))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b)) V0f)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (= V1y (@ (@ tptp.ap V0f) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b)) V0f)) (forall ((V1x1 $$unsorted)) (=> (@ (@ tptp.mem V1x1) A_27a) (forall ((V2x2 $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2x2) A_27a) (=> (= (@ _let_1 V1x1) (@ _let_1 V2x2)) (= V1x1 V2x2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (exists ((V1rep $$unsorted)) (and (@ (@ tptp.mem V1rep) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) V0P)) V1rep)))) (exists ((V2rep $$unsorted)) (and (@ (@ tptp.mem V2rep) (@ (@ tptp.arr A_27b) A_27a)) (exists ((V3abs $$unsorted)) (and (@ (@ tptp.mem V3abs) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V4a $$unsorted)) (=> (@ (@ tptp.mem V4a) A_27b) (= (@ (@ tptp.ap V3abs) (@ (@ tptp.ap V2rep) V4a)) V4a))) (forall ((V5r $$unsorted)) (=> (@ (@ tptp.mem V5r) A_27a) (= (@ tptp.p (@ (@ tptp.ap V0P) V5r)) (= (@ (@ tptp.ap V2rep) (@ (@ tptp.ap V3abs) V5r)) V5r))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V1N $$unsorted)) (=> (@ (@ tptp.mem V1N) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2M $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.c_2Ebool_2ELET A_27a))) (=> (@ (@ tptp.mem V2M) A_27a) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27b)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V1N) V3x))))) V2M))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 tptp.bool)) (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap V1N) V4x)))))) V2M))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0N $$unsorted)) (=> (@ (@ tptp.mem V0N) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1M $$unsorted)) (=> (@ (@ tptp.mem V1M) A_27a) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.c_2Ebool_2ELET A_27a))) (=> (@ (@ tptp.mem V2b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.arr A_27b) A_27c))) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V0N) V3x))))) V1M)) V2b) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27c)) (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0N) V4x)) V2b))))) V1M)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1x)) V2y)))))) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V4x)) V3y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1x)) V2y)))))) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27b) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V4x)) V3y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0P) V1x))))) (and (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ _let_1 V3x)) (@ tptp.p (@ _let_1 V4y))) (= V3x V4y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2M $$unsorted)) (=> (@ (@ tptp.mem V2M) A_27a) (forall ((V3N $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b)))) (=> (@ (@ tptp.mem V3N) A_27a) (=> (and (= V2M V3N) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (= V4x V3N) (= (@ (@ tptp.ap V0f) V4x) (@ (@ tptp.ap V1g) V4x)))))) (= (@ (@ tptp.ap (@ _let_1 V0f)) V2M) (@ (@ tptp.ap (@ _let_1 V1g)) V3N)))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (= _let_4 _let_2) (=> _let_2 (= _let_3 _let_1))) (= (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) tptp.bool) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) tptp.bool) (forall ((V3Q_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3Q_27))) (let ((_let_2 (@ tptp.p V1P_27))) (let ((_let_3 (@ tptp.p V2Q))) (let ((_let_4 (@ tptp.p V0P))) (=> (@ (@ tptp.mem V3Q_27) tptp.bool) (=> (and (=> _let_3 (= _let_4 _let_2)) (=> _let_2 (= _let_3 _let_1))) (= (and _let_4 _let_3) (and _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) tptp.bool) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) tptp.bool) (forall ((V3Q_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3Q_27))) (let ((_let_2 (@ tptp.p V1P_27))) (let ((_let_3 (@ tptp.p V2Q))) (let ((_let_4 (@ tptp.p V0P))) (=> (@ (@ tptp.mem V3Q_27) tptp.bool) (=> (and (= _let_4 _let_2) (=> _let_2 (= _let_3 _let_1))) (= (and _let_4 _let_3) (and _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) tptp.bool) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) tptp.bool) (forall ((V3Q_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3Q_27))) (let ((_let_2 (@ tptp.p V1P_27))) (let ((_let_3 (@ tptp.p V2Q))) (let ((_let_4 (@ tptp.p V0P))) (=> (@ (@ tptp.mem V3Q_27) tptp.bool) (=> (and (=> (not _let_3) (= _let_4 _let_2)) (=> (not _let_2) (= _let_3 _let_1))) (= (or _let_4 _let_3) (or _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) tptp.bool) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) tptp.bool) (forall ((V3Q_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3Q_27))) (let ((_let_2 (@ tptp.p V1P_27))) (let ((_let_3 (@ tptp.p V2Q))) (let ((_let_4 (@ tptp.p V0P))) (=> (@ (@ tptp.mem V3Q_27) tptp.bool) (=> (and (= _let_4 _let_2) (=> (not _let_2) (= _let_3 _let_1))) (= (or _let_4 _let_3) (or _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3x_27 $$unsorted)) (=> (@ (@ tptp.mem V3x_27) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5y_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (let ((_let_2 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V5y_27) A_27a) (=> (and (= (@ tptp.p V0P) _let_2) (=> _let_2 (= V2x V3x_27)) (=> (not _let_2) (= V4y V5y_27))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2x)) V4y) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V3x_27)) V5y_27))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3g $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)))) (=> (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (= V0P V1Q) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V1Q)) (= (@ tptp.p (@ (@ tptp.ap V2f) V4x)) (@ tptp.p (@ (@ tptp.ap V3g) V4x)))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0P)) V2f)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1Q)) V3g)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3g $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)))) (=> (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (= V0P V1Q) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V1Q)) (= (@ tptp.p (@ (@ tptp.ap V2f) V4x)) (@ tptp.p (@ (@ tptp.ap V3g) V4x)))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0P)) V2f)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1Q)) V3g)))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) tptp.bool) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) tptp.bool) (forall ((V3w $$unsorted)) (let ((_let_1 (@ tptp.p V3w))) (let ((_let_2 (@ tptp.p V1y))) (let ((_let_3 (@ tptp.p V2z))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3w) tptp.bool) (=> (and (=> _let_4 _let_2) (=> _let_3 _let_1)) (=> (and _let_4 _let_3) (and _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) tptp.bool) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) tptp.bool) (forall ((V3w $$unsorted)) (let ((_let_1 (@ tptp.p V3w))) (let ((_let_2 (@ tptp.p V1y))) (let ((_let_3 (@ tptp.p V2z))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3w) tptp.bool) (=> (and (=> _let_4 _let_2) (=> _let_3 _let_1)) (=> (or _let_4 _let_3) (or _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) tptp.bool) (forall ((V3w $$unsorted)) (let ((_let_1 (@ tptp.p V3w))) (let ((_let_2 (@ tptp.p V0y))) (let ((_let_3 (@ tptp.p V2z))) (let ((_let_4 (@ tptp.p V1x))) (=> (@ (@ tptp.mem V3w) tptp.bool) (=> (and (=> _let_2 _let_4) (=> _let_3 _let_1)) (=> (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) tptp.bool) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.p V0y))) (let ((_let_2 (@ tptp.p V1x))) (=> (@ (@ tptp.mem V1x) tptp.bool) (=> (=> _let_1 _let_2) (=> (not _let_2) (not _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) tptp.bool) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.p V0y))) (let ((_let_2 (@ tptp.p V1x))) (=> (@ (@ tptp.mem V1x) tptp.bool) (= (=> _let_1 _let_2) (=> (not _let_2) (not _let_1))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) V2x))))) (=> (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4x)))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) tptp.bool) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) tptp.bool) (forall ((V3w $$unsorted)) (=> (@ (@ tptp.mem V3w) tptp.bool) (forall ((V4b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V4b)))) (=> (@ (@ tptp.mem V4b) tptp.bool) (=> (=> (@ tptp.p V0x) (@ tptp.p V1y)) (=> (=> (@ tptp.p V2z) (@ tptp.p V3w)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0x)) V2z)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1y)) V3w)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (= V1x V0a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V0a))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (= V1a V2x) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) (@ tptp.p (@ (@ tptp.ap V0P) V1a))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (= V2x V1a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) (@ tptp.p (@ (@ tptp.ap V0P) V1a))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27a) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (= V1v V2x) (@ tptp.p (@ (@ tptp.ap V0f) V2x))))) (@ tptp.p (@ (@ tptp.ap V0f) V1v))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27a) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (= V2x V1v) (@ tptp.p (@ (@ tptp.ap V0f) V2x))))) (@ tptp.p (@ (@ tptp.ap V0f) V1v))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1x)) V2y)))))) (exists ((V3f $$unsorted)) (and (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V4x)) (@ (@ tptp.ap V3f) V4x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1))))) (forall ((V2t1 $$unsorted)) (=> (@ (@ tptp.mem V2t1) A_27a) (forall ((V3t2 $$unsorted)) (=> (@ (@ tptp.mem V3t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2EF)) V2t1)) V3t2) V3t2))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) V0b)) V1t)) V1t) V1t))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27a) (exists ((V2fn $$unsorted)) (let ((_let_1 (@ tptp.ap V2fn))) (and (@ (@ tptp.mem V2fn) (@ (@ tptp.arr tptp.bool) A_27a)) (= (@ _let_1 tptp.c_2Ebool_2ET) V0t1) (= (@ _let_1 tptp.c_2Ebool_2EF) V1t2)))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.bool) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 tptp.c_2Ebool_2ET)) (@ tptp.p (@ _let_1 tptp.c_2Ebool_2EF))) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) tptp.bool) (@ tptp.p (@ (@ tptp.ap V0P) V1b)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3x_27 $$unsorted)) (=> (@ (@ tptp.mem V3x_27) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5y_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (let ((_let_2 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V5y_27) A_27a) (=> (and (= (@ tptp.p V0P) _let_2) (=> _let_2 (= V2x V3x_27)) (=> (not _let_2) (= V4y V5y_27))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2x)) V4y) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V3x_27)) V5y_27))))))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.bool) tptp.bool)) (= (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) tptp.bool) (@ tptp.p (@ (@ tptp.ap V0P) V1b)))) (and (@ tptp.p (@ _let_1 tptp.c_2Ebool_2ET)) (@ tptp.p (@ _let_1 tptp.c_2Ebool_2EF))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 A_27a)))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap V0P) V2x))) (@ (@ tptp.ap V1Q) V2x)))))) (or (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V0P) V3x))))) (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap V1Q) V4x))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) V0t)))) (and (@ tptp.p V0t) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (= V2x V3y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1m $$unsorted)) (=> (@ (@ tptp.mem V1m) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) V0p)) V1m)) V2x) (@ (@ tptp.ap V1m) V2x))))))))) (forall ((V3p $$unsorted)) (=> (@ (@ tptp.mem V3p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4m1 $$unsorted)) (=> (@ (@ tptp.mem V4m1) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V5m2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) V3p)))) (=> (@ (@ tptp.mem V5m2) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V6x)) V3p)) (= (@ (@ tptp.ap V4m1) V6x) (@ (@ tptp.ap V5m2) V6x))))) (= (@ _let_1 V4m1) (@ _let_1 V5m2)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0P)) V1f)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0P)) (@ tptp.p (@ (@ tptp.ap V1f) V2x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0P)) V1f)) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0P)) (@ tptp.p (@ (@ tptp.ap V1f) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) V0P)) V1f)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0P)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1f) V2x))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0P)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V3x))) (@ _let_1 V4y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__SELECT A_27a)) V0P)) V1f) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0P))) (@ (@ tptp.ap V1f) V2x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2ET)))) true))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2EF)))) false))))
% 1.89/2.21 (assert (forall ((V0f $$unsorted)) (let ((_let_1 (@ tptp.lam tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.bool) tptp.bool)) (or (= V0f (@ _let_1 (lambda ((V1b $$unsorted)) tptp.c_2Ebool_2ET))) (= V0f (@ _let_1 (lambda ((V2b $$unsorted)) tptp.c_2Ebool_2EF))) (= V0f (@ _let_1 (lambda ((V3b $$unsorted)) V3b))) (= V0f (@ _let_1 (lambda ((V4b $$unsorted)) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) V4b)))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.lam tptp.bool))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.arr tptp.bool) tptp.bool)) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V1b $$unsorted)) tptp.c_2Ebool_2ET)))) (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V2b $$unsorted)) tptp.c_2Ebool_2EF)))) (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V3b $$unsorted)) V3b)))) (@ tptp.p (@ _let_2 (@ _let_1 (lambda ((V4b $$unsorted)) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) V4b)))))) (forall ((V5f $$unsorted)) (=> (@ (@ tptp.mem V5f) (@ (@ tptp.arr tptp.bool) tptp.bool)) (@ tptp.p (@ (@ tptp.ap V0P) V5f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)) V0f)) V1x) (@ (@ tptp.ap V0f) V1x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V1N $$unsorted)) (=> (@ (@ tptp.mem V1N) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2M $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.c_2Ebool_2Eliteral__case A_27a))) (=> (@ (@ tptp.mem V2M) A_27a) (= (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27b)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V1N) V3x))))) V2M)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27c)) (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap V1N) V4x)))))) V2M)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0N $$unsorted)) (=> (@ (@ tptp.mem V0N) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1M $$unsorted)) (=> (@ (@ tptp.mem V1M) A_27a) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.c_2Ebool_2Eliteral__case A_27a))) (=> (@ (@ tptp.mem V2b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.arr A_27b) A_27c))) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V0N) V3x))))) V1M)) V2b) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27c)) (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0N) V4x)) V2b))))) V1M)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2M $$unsorted)) (=> (@ (@ tptp.mem V2M) A_27a) (forall ((V3N $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)))) (=> (@ (@ tptp.mem V3N) A_27a) (=> (and (= V2M V3N) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (= V4x V3N) (= (@ (@ tptp.ap V0f) V4x) (@ (@ tptp.ap V1g) V4x)))))) (= (@ (@ tptp.ap (@ _let_1 V0f)) V2M) (@ (@ tptp.ap (@ _let_1 V1g)) V3N)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) A_27b) (forall ((V2u $$unsorted)) (=> (@ (@ tptp.mem V2u) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V0a))) V1t)) V2u))))) V0a) V1t))))))))
% 1.89/2.21 (assert (forall ((V0v $$unsorted)) (=> (@ (@ tptp.mem V0v) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2EBOUNDED) V0v)) true))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27a))) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ _let_1 V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2y)) V3z)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V2y))) V3z)))))))))) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V5y) A_27a) (= (@ (@ tptp.ap (@ _let_1 V4x)) V5y) (@ (@ tptp.ap (@ _let_1 V5y)) V4x))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (forall ((V8z $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ _let_1 V6x)))) (let ((_let_3 (@ tptp.ap (@ _let_1 V7y)))) (=> (@ (@ tptp.mem V8z) A_27a) (= (@ _let_2 (@ _let_3 V8z)) (@ _let_3 (@ _let_2 V8z))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2EDATATYPE A_27a)) V0x)) true))))
% 1.89/2.21 (assert (forall ((V0bool $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V0bool) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2EDATATYPE tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap V0bool) tptp.c_2Ebool_2ET)) tptp.c_2Ebool_2EF))) true)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (exists ((V0rep $$unsorted)) (let ((_let_1 (@ tptp.ty_2Ebool_2Eitself A_27a))) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr _let_1) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) _let_1)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ tptp.c_2Ebool_2EARB A_27a)))) V0rep)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0i $$unsorted)) (=> (@ (@ tptp.mem V0i) (@ tptp.ty_2Ebool_2Eitself A_27a)) (= V0i (@ tptp.c_2Ebool_2Ethe__value A_27a)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27b) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) A_27b)) (= (@ (@ tptp.ap V1f) (@ tptp.c_2Ebool_2Ethe__value A_27a)) V0e))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Ebool_2Ethe__value A_27a))) (forall ((V1i $$unsorted)) (=> (@ (@ tptp.mem V1i) (@ tptp.ty_2Ebool_2Eitself A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V1i))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2Eitself__case A_27a) A_27b)) (@ tptp.c_2Ebool_2Ethe__value A_27a))) V0b) V0b))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) tptp.bool)) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Ebool_2Eitself A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V1x)))) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Ebool_2Ethe__value A_27a)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) tptp.bool)) (= (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) (@ tptp.ty_2Ebool_2Eitself A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V1x)))) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Ebool_2Ethe__value A_27a)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V1Q) tptp.bool) (and (= (=> (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x)))) _let_1) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V3x)) (@ tptp.p V1Q))))) (= (and (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V4x)))) _let_1) (exists ((V5x $$unsorted)) (and (@ (@ tptp.mem V5x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V5x)) (@ tptp.p V1Q)))) (= (and _let_1 (exists ((V6x $$unsorted)) (and (@ (@ tptp.mem V6x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V6x))))) (exists ((V7x $$unsorted)) (and (@ (@ tptp.mem V7x) A_27a) (@ tptp.p V1Q) (@ tptp.p (@ (@ tptp.ap V0P) V7x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V1Q) tptp.bool) (and (= (=> _let_1 (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p V1Q) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))))) (= (and (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V4x)))) _let_1) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (and (@ tptp.p (@ (@ tptp.ap V0P) V5x)) (@ tptp.p V1Q))))) (= (and _let_1 (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V6x))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (and (@ tptp.p V1Q) (@ tptp.p (@ (@ tptp.ap V0P) V7x)))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.p V0P))) (=> (@ (@ tptp.mem V1Q) tptp.bool) (=> (=> (=> _let_1 (@ tptp.p V1Q)) _let_1) _let_1)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) A_27a) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (= V2x V1t) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) V0P))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (or _let_2 _let_1) (=> (not _let_2) _let_1)))))))))
% 1.89/2.21 (declare-fun tptp.c_2EConseqConv_2EASM__MARKER () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2EConseqConv_2EASM__MARKER) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) A_27a) (= (@ tptp.p (@ (@ tptp.ap V0P) V2s)) (@ tptp.p (@ (@ tptp.ap V1Q) V2s))))) (= (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3s)))) (forall ((V4s $$unsorted)) (=> (@ (@ tptp.mem V4s) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4s)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) A_27a) (= (@ tptp.p (@ (@ tptp.ap V0P) V2s)) (@ tptp.p (@ (@ tptp.ap V1Q) V2s))))) (= (exists ((V3s $$unsorted)) (and (@ (@ tptp.mem V3s) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V3s)))) (exists ((V4s $$unsorted)) (and (@ (@ tptp.mem V4s) A_27a) (@ tptp.p (@ (@ tptp.ap V1Q) V4s)))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> (@ tptp.p V0t) true))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))))
% 1.89/2.21 (assert (= (not true) false))
% 1.89/2.21 (assert (= (not false) true))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V2y))) (let ((_let_2 (@ tptp.p V0x))) (let ((_let_3 (@ tptp.p V3y_27))) (let ((_let_4 (@ tptp.p V1x_27))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> _let_1 (=> _let_4 _let_2)) (=> _let_4 (=> _let_3 _let_1))) (=> (and _let_4 _let_3) (and _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> _let_3 (=> _let_4 _let_2)) (=> _let_2 (=> _let_3 _let_1))) (=> (and _let_4 _let_3) (and _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (and true _let_1) _let_1)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (and _let_1 true) _let_1)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (and false (@ tptp.p V0t)) false))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (and (@ tptp.p V0t) false) false))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (and _let_1 _let_1) _let_1)))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V2y))) (let ((_let_2 (@ tptp.p V0x))) (let ((_let_3 (@ tptp.p V3y_27))) (let ((_let_4 (@ tptp.p V1x_27))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> (not _let_1) (=> _let_4 _let_2)) (=> (not _let_4) (=> _let_3 _let_1))) (=> (or _let_4 _let_3) (or _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> (not _let_3) (=> _let_4 _let_2)) (=> (not _let_2) (=> _let_3 _let_1))) (=> (or _let_4 _let_3) (or _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (or true (@ tptp.p V0t)) true))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (or (@ tptp.p V0t) true) true))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (or false _let_1) _let_1)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (or _let_1 false) _let_1)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (or _let_1 _let_1) _let_1)))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V2y))) (let ((_let_2 (@ tptp.p V0x))) (let ((_let_3 (@ tptp.p V3y_27))) (let ((_let_4 (@ tptp.p V1x_27))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> _let_2 (=> _let_3 _let_1)) (=> (not _let_3) (=> _let_2 _let_4))) (=> (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> _let_4 (=> _let_3 _let_1)) (=> (not _let_1) (=> _let_2 _let_4))) (=> (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V2y))) (let ((_let_2 (@ tptp.p V0x))) (let ((_let_3 (@ tptp.p V3y_27))) (let ((_let_4 (@ tptp.p V1x_27))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> _let_2 _let_4) (=> _let_4 (=> _let_3 _let_1))) (=> (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1x_27 $$unsorted)) (=> (@ (@ tptp.mem V1x_27) tptp.bool) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) tptp.bool) (forall ((V3y_27 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (=> _let_2 _let_4) (=> _let_2 (=> _let_3 _let_1))) (=> (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (=> true _let_1) _let_1)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (=> (@ tptp.p V0t) true) true))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (=> false (@ tptp.p V0t)) true))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (=> _let_1 _let_1) true)))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (=> _let_1 false) (not _let_1))))))
% 1.89/2.21 (assert (forall ((V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (forall ((V2x_27 $$unsorted)) (=> (@ (@ tptp.mem V2x_27) tptp.bool) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) tptp.bool) (forall ((V4y_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0c)))) (=> (@ (@ tptp.mem V4y_27) tptp.bool) (=> (and (=> (@ tptp.p V2x_27) (@ tptp.p V1x)) (=> (@ tptp.p V4y_27) (@ tptp.p V3y))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x_27)) V4y_27)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (forall ((V2x_27 $$unsorted)) (=> (@ (@ tptp.mem V2x_27) tptp.bool) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) tptp.bool) (forall ((V4y_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0c)))) (let ((_let_2 (@ tptp.p V0c))) (=> (@ (@ tptp.mem V4y_27) tptp.bool) (=> (and (=> _let_2 (=> (@ tptp.p V2x_27) (@ tptp.p V1x))) (=> (not _let_2) (=> (@ tptp.p V4y_27) (@ tptp.p V3y)))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x_27)) V4y_27)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V3y)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2EF)) V0t1)) V1t2) V1t2))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) V0b)) V1t)) V1t) V1t))))))
% 1.89/2.21 (assert (forall ((V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0c)) tptp.c_2Ebool_2ET)) V1x)) (=> (not (@ tptp.p V0c)) (@ tptp.p V1x))))))))
% 1.89/2.21 (assert (forall ((V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0c)) V1x)) tptp.c_2Ebool_2ET)) (=> (@ tptp.p V0c) (@ tptp.p V1x))))))))
% 1.89/2.21 (assert (forall ((V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0c)) tptp.c_2Ebool_2EF)) V1x)) (and (not (@ tptp.p V0c)) (@ tptp.p V1x))))))))
% 1.89/2.21 (assert (forall ((V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V0c)) V1x)) tptp.c_2Ebool_2EF)) (and (@ tptp.p V0c) (@ tptp.p V1x))))))))
% 1.89/2.21 (assert (= tptp.c_2EConseqConv_2EASM__MARKER (@ (@ tptp.lam tptp.bool) (lambda ((V0y $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1x $$unsorted)) V1x))))))
% 1.89/2.21 (assert (forall ((V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2EConseqConv_2EASM__MARKER) V0y)) V1x)) (@ tptp.p V1x)))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) tptp.bool) (forall ((V2C $$unsorted)) (let ((_let_1 (@ tptp.p V2C))) (let ((_let_2 (@ tptp.p V1B))) (let ((_let_3 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V2C) tptp.bool) (= (=> (and _let_3 _let_2) _let_1) (=> _let_3 (=> _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (= (and (not _let_1) _let_1) false)))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> _let_1 (=> (not _let_1) false))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or _let_2 _let_1)) false) (=> (not _let_2) (=> (not _let_1) false))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or _let_2 _let_1)) false) (=> (=> _let_2 false) (=> (not _let_1) false))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) tptp.bool) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.p V1B))) (let ((_let_2 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V1B) tptp.bool) (= (=> (not (or (not _let_2) _let_1)) false) (=> _let_2 (=> (not _let_1) false))))))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false))))))
% 1.89/2.21 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (= (=> (not _let_1) false) _let_1)))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (let ((_let_1 (@ tptp.p V0b))) (=> (@ (@ tptp.mem V0b) tptp.bool) (=> _let_1 (= _let_1 true))))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (let ((_let_1 (@ tptp.p V0b))) (=> (@ (@ tptp.mem V0b) tptp.bool) (=> (not _let_1) (= _let_1 false))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V1q))) (let ((_let_4 (not _let_3))) (let ((_let_5 (@ tptp.p V2r))) (let ((_let_6 (not _let_5))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (= _let_3 _let_5)) (and (or _let_1 _let_3 _let_5) (or _let_1 _let_6 _let_4) (or _let_3 _let_6 _let_2) (or _let_5 _let_4 _let_2))))))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V2r))) (let ((_let_4 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2))))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (or _let_3 _let_2)) (and (or _let_1 (not _let_3)) (or _let_1 (not _let_2)) (or _let_3 _let_2 (not _let_1))))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1))))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (not _let_2))) (=> (@ (@ tptp.mem V1q) tptp.bool) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (=> (@ (@ tptp.mem V2r) tptp.bool) (forall ((V3s $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V3s))) (let ((_let_4 (@ tptp.p V1q))) (let ((_let_5 (@ tptp.p V2r))) (let ((_let_6 (not _let_4))) (let ((_let_7 (not _let_3))) (let ((_let_8 (not _let_5))) (=> (@ (@ tptp.mem V3s) tptp.bool) (= (= _let_1 (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) V1q)) V2r)) V3s))) (and (or _let_1 _let_4 _let_7) (or _let_1 _let_8 _let_6) (or _let_1 _let_8 _let_7) (or _let_6 _let_5 _let_2) (or _let_4 _let_3 _let_2))))))))))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (not (=> _let_1 (@ tptp.p V1q))) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (not (=> (@ tptp.p V0p) _let_1)) (not _let_1))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (not (or _let_1 (@ tptp.p V1q))) (not _let_1))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (not (or (@ tptp.p V0p) _let_1)) (not _let_1))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (and _let_1 (@ tptp.p V1q)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (and (@ tptp.p V0p) _let_1) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (=> (@ (@ tptp.mem V0p) tptp.bool) (=> (not (not _let_1)) _let_1)))))
% 1.89/2.21 (declare-fun tptp.c_2EnormalForms_2EEXT__POINT (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)))) (@ (@ tptp.mem (@ (@ tptp.c_2EnormalForms_2EEXT__POINT A_27a) A_27b)) (@ _let_1 (@ _let_1 A_27a))))))
% 1.89/2.21 (declare-fun tptp.c_2EnormalForms_2EUNIV__POINT (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2EnormalForms_2EUNIV__POINT A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EnormalForms_2EEXT__POINT A_27a) A_27b)) V0f)) V1g))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (=> (= (@ (@ tptp.ap V0f) _let_1) (@ (@ tptp.ap V1g) _let_1)) (= V0f V1g))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EnormalForms_2EEXT__POINT A_27a) A_27b)) V0f)) V1g))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (= (= (@ (@ tptp.ap V0f) _let_1) (@ (@ tptp.ap V1g) _let_1)) (= V0f V1g))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap V0p) (@ (@ tptp.ap (@ tptp.c_2EnormalForms_2EUNIV__POINT A_27a)) V0p))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0p) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap V0p) (@ (@ tptp.ap (@ tptp.c_2EnormalForms_2EUNIV__POINT A_27a)) V0p))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0p) V1x))))))))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2E_3A_2D () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Emarker_2E_3A_2D) (@ (@ tptp.arr tptp.ind) (@ (@ tptp.arr tptp.bool) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2EAC () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emarker_2EAC) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2EAbbrev () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Emarker_2EAbbrev) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2ECong () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Emarker_2ECong) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2EIfCases () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Emarker_2EIfCases) tptp.bool))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2Estmarker (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emarker_2Estmarker A_27a)) (@ (@ tptp.arr A_27a) A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Emarker_2Eunint (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emarker_2Eunint A_27a)) (@ (@ tptp.arr A_27a) A_27a))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Emarker_2Estmarker A_27a)) V0x) V0x))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2m $$unsorted)) (let ((_let_1 (@ tptp.p V1q))) (let ((_let_2 (@ tptp.p V0p))) (let ((_let_3 (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Emarker_2Estmarker tptp.bool)) V2m)))) (let ((_let_4 (and _let_3 _let_2 _let_1))) (=> (@ (@ tptp.mem V2m) tptp.bool) (and (= (and _let_2 _let_3) (and _let_3 _let_2)) (= _let_4 _let_4) (= (and _let_2 _let_3 _let_1) _let_4)))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2m $$unsorted)) (let ((_let_1 (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Emarker_2Estmarker tptp.bool)) V2m)))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (@ tptp.p V0p))) (let ((_let_4 (and _let_3 _let_2 _let_1))) (=> (@ (@ tptp.mem V2m) tptp.bool) (and (= (and _let_1 _let_3) (and _let_3 _let_1)) (= _let_4 _let_4) (= (and _let_3 _let_1 _let_2) _let_4)))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2m $$unsorted)) (let ((_let_1 (@ tptp.p V1q))) (let ((_let_2 (@ tptp.p V0p))) (let ((_let_3 (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Emarker_2Estmarker tptp.bool)) V2m)))) (let ((_let_4 (or _let_3 _let_2 _let_1))) (=> (@ (@ tptp.mem V2m) tptp.bool) (and (= (or _let_2 _let_3) (or _let_3 _let_2)) (= _let_4 _let_4) (= (or _let_2 _let_3 _let_1) _let_4)))))))))))))
% 1.89/2.21 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2m $$unsorted)) (let ((_let_1 (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Emarker_2Estmarker tptp.bool)) V2m)))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (@ tptp.p V0p))) (let ((_let_4 (or _let_3 _let_2 _let_1))) (=> (@ (@ tptp.mem V2m) tptp.bool) (and (= (or _let_1 _let_3) (or _let_3 _let_1)) (= _let_4 _let_4) (= (or _let_3 _let_1 _let_2) _let_4)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Emarker_2Eunint A_27a)) V0x) V0x))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Emarker_2EAbbrev) V0x)) (@ tptp.p V0x)))))
% 1.89/2.21 (assert (= (@ tptp.p tptp.c_2Emarker_2EIfCases) true))
% 1.89/2.21 (assert (forall ((V0b1 $$unsorted)) (=> (@ (@ tptp.mem V0b1) tptp.bool) (forall ((V1b2 $$unsorted)) (=> (@ (@ tptp.mem V1b2) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emarker_2EAC) V0b1)) V1b2)) (and (@ tptp.p V0b1) (@ tptp.p V1b2))))))))
% 1.89/2.21 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Emarker_2ECong) V0x)) (@ tptp.p V0x)))))
% 1.89/2.21 (assert (forall ((V0lab tptp.tp__i) (V1argument $$unsorted)) (=> (@ (@ tptp.mem V1argument) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emarker_2E_3A_2D) (@ tptp.inj__i V0lab))) V1argument)) (@ tptp.p V1argument)))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2E_3A_3E (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2E_3A_3E A_27a) A_27b)) (@ _let_1 (@ (@ tptp.arr (@ _let_1 A_27a)) A_27a))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EASSOC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ecombin_2EASSOC A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 A_27a))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EC (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ tptp.arr A_27b))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ _let_1 (@ _let_2 A_27c))) (@ _let_2 (@ _let_1 A_27c))))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2ECOMM (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2ECOMM A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 A_27b))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EFAIL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2EFAIL A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27a)))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EFCOMM (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Ecombin_2EFCOMM A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) A_27a))) (@ (@ tptp.arr (@ (@ tptp.arr A_27c) (@ _let_1 A_27a))) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EI (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ecombin_2EI A_27a)) (@ (@ tptp.arr A_27a) A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EK (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2EK A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27a)))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2ELEFT__ID (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2ELEFT__ID A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) A_27b))) (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EMONOID (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ecombin_2EMONOID A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 A_27a))) (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2ERIGHT__ID (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2ERIGHT__ID A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ _let_1 A_27a))) (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2ES (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) A_27c))) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ _let_1 A_27c)))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EUPDATE (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) (@ _let_1 (@ (@ tptp.arr A_27b) (@ (@ tptp.arr _let_2) _let_2))))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2EW (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ecombin_2EW A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 _let_2)) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Ecombin_2Eo (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27c) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27c)) (@ _let_1 A_27b)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ecombin_2EK A_27a) A_27b) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V1y $$unsorted)) V0x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (= (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) A_27b) A_27c) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V1g $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2x)) (@ (@ tptp.ap V1g) V2x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.c_2Ecombin_2EK A_27a))) (let ((_let_2 (@ (@ tptp.arr A_27a) A_27a))) (= (@ tptp.c_2Ecombin_2EI A_27a) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) _let_2) A_27a)) (@ _let_1 _let_2))) (@ _let_1 A_27a)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (= (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27b) A_27c) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V1x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2y)) V1x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (= (@ (@ tptp.c_2Ecombin_2EW A_27a) A_27b) (@ (@ tptp.lam (@ _let_1 (@ _let_1 A_27b))) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V1x)) V1x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27c) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27b) A_27c)) V0f)) V1g) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V0f) (@ (@ tptp.ap V1g) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27b) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2E_3A_3E A_27a) A_27b)) V0x)) V1f) (@ (@ tptp.ap V1f) V0x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V0a)) V1b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V2f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V3c $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V0a)) V3c))) V1b)) (@ (@ tptp.ap V2f) V3c))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27c) A_27a)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27c) A_27b) A_27a)) V0f)) V1g)) V2x) (@ (@ tptp.ap V0f) (@ (@ tptp.ap V1g) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27c) A_27a)) (forall ((V2h $$unsorted)) (let ((_let_1 (@ tptp.c_2Ecombin_2Eo A_27d))) (let ((_let_2 (@ _let_1 A_27b))) (=> (@ (@ tptp.mem V2h) (@ (@ tptp.arr A_27d) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27a)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 A_27a) A_27c)) V1g)) V2h)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27c) A_27b) A_27a)) V0f)) V1g))) V2h)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) A_27c) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V0f) V2x))))) V1g) (@ (@ tptp.lam A_27b) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V0f) (@ (@ tptp.ap V1g) V3x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27c) A_27b)) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27b) A_27c)) V0f)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1g) V2x)))) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap V0f) (@ (@ tptp.ap V1g) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK A_27a) A_27b)) V0x)) V1y) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) A_27b) A_27c)) V0f)) V1g)) V2x) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2x)) (@ (@ tptp.ap V1g) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27c) A_27b))) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) A_27c) A_27b)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V0f) V2x))))) V1g) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V3x)) (@ (@ tptp.ap V1g) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27c) A_27b))) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) A_27c) A_27b)) V0f)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1g) V2x)))) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V3x)) (@ (@ tptp.ap V1g) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27b) A_27c)) V0f)) V1x)) V2y) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2y)) V1x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27c) A_27b))) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V1y) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27c) A_27b)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V0f) V2x))))) V1y) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V3x)) V1y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27b))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EW A_27a) A_27b)) V0f)) V1x) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V1x)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EI A_27a)) V0x) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27b))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) (@ tptp.c_2Ecombin_2EI A_27b))) V0f) V0f) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) V0f)) (@ tptp.c_2Ecombin_2EI A_27a)) V0f))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (A_27e tptp.del) (A_27f tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1v $$unsorted)) (let ((_let_1 (@ tptp.c_2Ecombin_2EK A_27c))) (=> (@ (@ tptp.mem V1v) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)) (@ (@ tptp.ap (@ _let_1 A_27b)) V1v))) V0f) (@ (@ tptp.ap (@ _let_1 A_27a)) V1v))))))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27d) A_27e)) (forall ((V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27d) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27f) A_27e) A_27d)) V2f)) (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK A_27d) A_27f)) V3v)) (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK A_27e) A_27f)) (@ (@ tptp.ap V2f) V3v))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del)) (and (forall ((V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V0a)) V1x)) V2f)) V0a) V1x))))))) (forall ((V3a $$unsorted)) (=> (@ (@ tptp.mem V3a) A_27c) (forall ((V4b $$unsorted)) (=> (@ (@ tptp.mem V4b) A_27c) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27d) (forall ((V6f $$unsorted)) (=> (@ (@ tptp.mem V6f) (@ (@ tptp.arr A_27c) A_27d)) (=> (not (= V3a V4b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27c) A_27d)) V3a)) V5x)) V6f)) V4b) (@ (@ tptp.ap V6f) V4b))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27b) (forall ((V3c $$unsorted)) (=> (@ (@ tptp.mem V3c) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V1a)) V2b)) V0f)) V3c) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1a)) V3c))) V2b)) (@ (@ tptp.ap V0f) V3c))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (forall ((V3c $$unsorted)) (=> (@ (@ tptp.mem V3c) A_27b) (forall ((V4d $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1a)) V3c)))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2b)) V4d)))) (=> (@ (@ tptp.mem V4d) A_27b) (=> (not (= V1a V2b)) (= (@ _let_2 (@ _let_3 V0f)) (@ _let_3 (@ _let_2 V0f))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27b) (forall ((V3c $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V1a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V3c)))) (=> (@ (@ tptp.mem V3c) A_27b) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2b)) V0f)) (@ _let_2 V0f)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27b) (= (= (@ (@ tptp.ap V0f) V1a) V2b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V1a)) V2b)) V0f) V0f)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) A_27b) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (=> (= (@ (@ tptp.ap V0f) V2a) V1b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V2a)) V1b)) V0f) V0f)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V1a)) (@ (@ tptp.ap V0f) V1a))) V0f) V0f))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (forall ((V3c $$unsorted)) (=> (@ (@ tptp.mem V3c) A_27b) (forall ((V4d $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2b)) V4d)) V0f))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1a)) V3c)) V0f))) (let ((_let_4 (= V1a V2b))) (=> (@ (@ tptp.mem V4d) A_27b) (= (= _let_3 _let_2) (or (and _let_4 (= V3c V4d)) (and (not _let_4) (= _let_3 V0f) (= _let_2 V0f)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27c) A_27d)) (forall ((V1f1 $$unsorted)) (=> (@ (@ tptp.mem V1f1) A_27a) (forall ((V2f2 $$unsorted)) (=> (@ (@ tptp.mem V2f2) A_27b) (forall ((V3a $$unsorted)) (=> (@ (@ tptp.mem V3a) A_27c) (forall ((V4b $$unsorted)) (=> (@ (@ tptp.mem V4b) A_27d) (forall ((V5c $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27c) A_27d)) V3a)))) (=> (@ (@ tptp.mem V5c) A_27d) (=> (not (= V4b V5c)) (not (= (@ (@ tptp.ap (@ _let_1 V4b)) V0f) (@ (@ tptp.ap (@ _let_1 V5c)) V0f))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27b) (forall ((V3c $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V1a)))) (=> (@ (@ tptp.mem V3c) A_27b) (= (= (@ (@ tptp.ap (@ _let_1 V2b)) V0f) (@ (@ tptp.ap (@ _let_1 V3c)) V0f)) (= V2b V3c))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f1 $$unsorted)) (=> (@ (@ tptp.mem V0f1) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1f2 $$unsorted)) (=> (@ (@ tptp.mem V1f2) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (forall ((V3b $$unsorted)) (=> (@ (@ tptp.mem V3b) A_27b) (forall ((V4c $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V2a)))) (=> (@ (@ tptp.mem V4c) A_27b) (=> (= (@ (@ tptp.ap (@ _let_1 V3b)) V0f1) (@ (@ tptp.ap (@ _let_1 V4c)) V1f2)) (and (= V3b V4c) (forall ((V5v $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V2a)) V5v)))) (=> (@ (@ tptp.mem V5v) A_27b) (= (@ _let_1 V0f1) (@ _let_1 V1f2)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27c) A_27b)) (forall ((V2v $$unsorted)) (let ((_let_1 (@ tptp.c_2Ebool_2ELET A_27c))) (=> (@ (@ tptp.mem V2v) A_27c) (= (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V1f)) V2v)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27c) A_27a) A_27b)) V0P)) V1f))) V2v))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27b) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.c_2Ebool_2ELET A_27b))) (=> (@ (@ tptp.mem V2x) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.arr A_27c) A_27a))) V0f)) V1v)) V2x) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27b) A_27c) A_27a)) V0f)) V2x))) V1v))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1v $$unsorted)) (let ((_let_1 (@ tptp.c_2Ecombin_2Eo A_27a))) (=> (@ (@ tptp.mem V1v) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET A_27a) tptp.bool)) V0f)) V1v)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) tptp.bool) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 (@ (@ tptp.arr tptp.bool) tptp.bool)) tptp.bool)) tptp.c_2Emin_2E_3D_3D_3E)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 tptp.bool) tptp.bool)) tptp.c_2Emarker_2EAbbrev)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27a) tptp.bool)) (@ tptp.c_2Emin_2E_3D A_27a))) V1v))))) V0f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27c) A_27b)) (forall ((V2v $$unsorted)) (let ((_let_1 (@ tptp.c_2Ebool_2Eliteral__case A_27c))) (=> (@ (@ tptp.mem V2v) A_27c) (= (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V1f)) V2v)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27c) A_27a) A_27b)) V0P)) V1f))) V2v))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27b) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.c_2Ebool_2Eliteral__case A_27b))) (=> (@ (@ tptp.mem V2x) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.arr A_27c) A_27a))) V0f)) V1v)) V2x) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27b) A_27c) A_27a)) V0f)) V2x))) V1v))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1v $$unsorted)) (let ((_let_1 (@ tptp.c_2Ecombin_2Eo A_27a))) (=> (@ (@ tptp.mem V1v) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) tptp.bool)) V0f)) V1v)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) tptp.bool) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 (@ (@ tptp.arr tptp.bool) tptp.bool)) tptp.bool)) tptp.c_2Emin_2E_3D_3D_3E)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 tptp.bool) tptp.bool)) tptp.c_2Emarker_2EAbbrev)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27a) tptp.bool)) (@ tptp.c_2Emin_2E_3D A_27a))) V1v))))) V0f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27a))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EASSOC A_27a)) V0f)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ _let_1 V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2y)) V3z)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V2y))) V3z)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27b))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2ECOMM A_27a) A_27b)) V0f)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ (@ tptp.ap (@ _let_1 V1x)) V2y) (@ (@ tptp.ap (@ _let_1 V2y)) V1x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27a))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27c) (@ (@ tptp.arr A_27a) A_27a))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EFCOMM A_27a) A_27b) A_27c)) V0f)) V1g)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27c) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (forall ((V4z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V1g) V2x)))) (let ((_let_2 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V4z) A_27b) (= (@ _let_1 (@ (@ tptp.ap (@ _let_2 V3y)) V4z)) (@ (@ tptp.ap (@ _let_2 (@ _let_1 V3y))) V4z))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27a))) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2ERIGHT__ID A_27a) A_27b)) V0f)) V1e)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2x)) V1e) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2ELEFT__ID A_27a) A_27b)) V0f)) V1e)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap V0f) V1e)) V2x) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27a))) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EMONOID A_27a)) V0f)) V1e)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EASSOC A_27a)) V0f)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2ERIGHT__ID A_27a) A_27a)) V0f)) V1e)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2ELEFT__ID A_27a) A_27a)) V0f)) V1e))))))))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EASSOC tptp.bool)) tptp.c_2Ebool_2E_2F_5C)))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27a))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EASSOC A_27a)) V0f)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ _let_1 V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (= (@ (@ tptp.ap (@ _let_1 (@ _let_2 V2y))) V3z) (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2y)) V3z))))))))))))))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EASSOC tptp.bool)) tptp.c_2Ebool_2E_5C_2F)))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27a))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EFCOMM A_27a) A_27a) A_27a)) V0f)) V0f)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EASSOC A_27a)) V0f)))))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EMONOID tptp.bool)) tptp.c_2Ebool_2E_2F_5C)) tptp.c_2Ebool_2ET)))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EMONOID tptp.bool)) tptp.c_2Ebool_2E_5C_2F)) tptp.c_2Ebool_2EF)))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ecombin_2EFAIL A_27a) A_27b) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V1y $$unsorted)) V0x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EFAIL A_27a) A_27b)) V0x)) V1y) V0x))))))
% 1.89/2.21 (declare-fun tptp.ty_2Enum_2Enum () tptp.del)
% 1.89/2.21 (declare-sort tptp.tp__ty_2Enum_2Enum 0)
% 1.89/2.21 (declare-fun tptp.inj__ty_2Enum_2Enum (tptp.tp__ty_2Enum_2Enum) $$unsorted)
% 1.89/2.21 (declare-fun tptp.surj__ty_2Enum_2Enum ($$unsorted) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ tptp.inj__ty_2Enum_2Enum X)) X)))
% 1.89/2.21 (assert (forall ((X tptp.tp__ty_2Enum_2Enum)) (@ (@ tptp.mem (@ tptp.inj__ty_2Enum_2Enum X)) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Enum_2Enum) (= X (@ tptp.inj__ty_2Enum_2Enum (@ tptp.surj__ty_2Enum_2Enum X))))))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2E0 () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2E0) tptp.ty_2Enum_2Enum))
% 1.89/2.21 (declare-fun tptp.fo__c_2Enum_2E0 () tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (= (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0) tptp.c_2Enum_2E0))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2EABS__num () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2EABS__num) (@ (@ tptp.arr tptp.ind) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Enum_2EABS__num (tptp.tp__i) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__i)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enum_2EABS__num X0)) (@ (@ tptp.ap tptp.c_2Enum_2EABS__num) (@ tptp.inj__i X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2EIS__NUM__REP () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2EIS__NUM__REP) (@ (@ tptp.arr tptp.ind) tptp.bool)))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2EREP__num () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2EREP__num) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ind)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Enum_2EREP__num (tptp.tp__ty_2Enum_2Enum) tptp.tp__i)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__i (@ tptp.fo__c_2Enum_2EREP__num X0)) (@ (@ tptp.ap tptp.c_2Enum_2EREP__num) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2ESUC () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2ESUC) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Enum_2ESUC (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enum_2ESUC X0)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2ESUC__REP () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2ESUC__REP) (@ (@ tptp.arr tptp.ind) tptp.ind)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Enum_2ESUC__REP (tptp.tp__i) tptp.tp__i)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__i)) (= (@ tptp.inj__i (@ tptp.fo__c_2Enum_2ESUC__REP X0)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC__REP) (@ tptp.inj__i X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Enum_2EZERO__REP () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Enum_2EZERO__REP) tptp.ind))
% 1.89/2.21 (declare-fun tptp.fo__c_2Enum_2EZERO__REP () tptp.tp__i)
% 1.89/2.21 (assert (= (@ tptp.inj__i tptp.fo__c_2Enum_2EZERO__REP) tptp.c_2Enum_2EZERO__REP))
% 1.89/2.21 (assert (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ind) tptp.ind)) tptp.c_2Enum_2ESUC__REP)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONTO tptp.ind) tptp.ind)) tptp.c_2Enum_2ESUC__REP)))))
% 1.89/2.21 (assert (forall ((V0y tptp.tp__i)) (not (= tptp.fo__c_2Enum_2EZERO__REP (@ tptp.surj__i (@ (@ tptp.ap tptp.c_2Enum_2ESUC__REP) (@ tptp.inj__i V0y)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__i)) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Enum_2EIS__NUM__REP) (@ tptp.inj__i V0m))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr tptp.ind) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 (@ tptp.inj__i tptp.fo__c_2Enum_2EZERO__REP))) (forall ((V2n tptp.tp__i)) (let ((_let_1 (@ tptp.inj__i V2n))) (let ((_let_2 (@ tptp.ap V1P))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC__REP) _let_1)))))))) (@ tptp.p (@ _let_1 (@ tptp.inj__i V0m))))))))))
% 1.89/2.21 (assert (exists ((V0rep $$unsorted)) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ind)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION tptp.ind) tptp.ty_2Enum_2Enum)) tptp.c_2Enum_2EIS__NUM__REP)) V0rep)))))
% 1.89/2.21 (assert (and (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2EABS__num) (@ (@ tptp.ap tptp.c_2Enum_2EREP__num) (@ tptp.inj__ty_2Enum_2Enum V0a)))) V0a)) (forall ((V1r tptp.tp__i)) (let ((_let_1 (@ tptp.inj__i V1r))) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Enum_2EIS__NUM__REP) _let_1)) (= (@ tptp.surj__i (@ (@ tptp.ap tptp.c_2Enum_2EREP__num) (@ (@ tptp.ap tptp.c_2Enum_2EABS__num) _let_1))) V1r))))))
% 1.89/2.21 (assert (= tptp.fo__c_2Enum_2E0 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2EABS__num) (@ tptp.inj__i tptp.fo__c_2Enum_2EZERO__REP)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2EABS__num) (@ (@ tptp.ap tptp.c_2Enum_2ESUC__REP) (@ (@ tptp.ap tptp.c_2Enum_2EREP__num) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (not (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0n))) tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enum_2ESUC))) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (= V0m V1n)))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V2n))))))))
% 1.89/2.21 (declare-fun tptp.ty_2Eone_2Eone () tptp.del)
% 1.89/2.21 (declare-sort tptp.tp__ty_2Eone_2Eone 0)
% 1.89/2.21 (declare-fun tptp.inj__ty_2Eone_2Eone (tptp.tp__ty_2Eone_2Eone) $$unsorted)
% 1.89/2.21 (declare-fun tptp.surj__ty_2Eone_2Eone ($$unsorted) tptp.tp__ty_2Eone_2Eone)
% 1.89/2.21 (assert (forall ((X tptp.tp__ty_2Eone_2Eone)) (= (@ tptp.surj__ty_2Eone_2Eone (@ tptp.inj__ty_2Eone_2Eone X)) X)))
% 1.89/2.21 (assert (forall ((X tptp.tp__ty_2Eone_2Eone)) (@ (@ tptp.mem (@ tptp.inj__ty_2Eone_2Eone X)) tptp.ty_2Eone_2Eone)))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Eone_2Eone) (= X (@ tptp.inj__ty_2Eone_2Eone (@ tptp.surj__ty_2Eone_2Eone X))))))
% 1.89/2.21 (declare-fun tptp.c_2Eone_2Eone () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Eone_2Eone) tptp.ty_2Eone_2Eone))
% 1.89/2.21 (declare-fun tptp.fo__c_2Eone_2Eone () tptp.tp__ty_2Eone_2Eone)
% 1.89/2.21 (assert (= (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone) tptp.c_2Eone_2Eone))
% 1.89/2.21 (declare-fun tptp.c_2Eone_2Eone__CASE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eone_2Eone__CASE A_27a)) (@ (@ tptp.arr tptp.ty_2Eone_2Eone) (@ (@ tptp.arr A_27a) A_27a)))))
% 1.89/2.21 (assert (exists ((V0rep $$unsorted)) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr tptp.ty_2Eone_2Eone) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION tptp.bool) tptp.ty_2Eone_2Eone)) (@ (@ tptp.lam tptp.bool) (lambda ((V1b $$unsorted)) V1b)))) V0rep)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Eone_2Eone)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) tptp.ty_2Eone_2Eone)) (= V0f V1g))))))
% 1.89/2.21 (assert (= tptp.fo__c_2Eone_2Eone (@ tptp.surj__ty_2Eone_2Eone (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 tptp.ty_2Eone_2Eone)) (@ (@ tptp.lam tptp.ty_2Eone_2Eone) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET))))))
% 1.89/2.21 (assert (forall ((V0v tptp.tp__ty_2Eone_2Eone)) (= V0v tptp.fo__c_2Eone_2Eone)))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0e $$unsorted)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Eone_2Eone) A_27a))) (=> (@ (@ tptp.mem V0e) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V1fn $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ (@ tptp.ap V1fn) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone)))) V0e)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (exists ((V1fn $$unsorted)) (and (@ (@ tptp.mem V1fn) (@ (@ tptp.arr tptp.ty_2Eone_2Eone) A_27a)) (= (@ (@ tptp.ap V1fn) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone)) V0e))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Eone_2Eone) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone))) (forall ((V1x tptp.tp__ty_2Eone_2Eone)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Eone_2Eone V1x))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Eone_2Eone) tptp.bool)) (= (forall ((V1x tptp.tp__ty_2Eone_2Eone)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Eone_2Eone V1x)))) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0u tptp.tp__ty_2Eone_2Eone) (V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eone_2Eone__CASE A_27a)) (@ tptp.inj__ty_2Eone_2Eone V0u))) V1x) V1x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eone_2Eone__CASE A_27a)) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone))) V0x) V0x))))
% 1.89/2.21 (declare-fun tptp.ty_2Esum_2Esum (tptp.del tptp.del) tptp.del)
% 1.89/2.21 (declare-fun tptp.c_2Esum_2E_2B_2B (tptp.del tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del)) (@ (@ tptp.mem (@ (@ (@ (@ tptp.c_2Esum_2E_2B_2B A_27a) A_27b) A_27c) A_27d)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27d)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (@ (@ tptp.ty_2Esum_2Esum A_27c) A_27d)))))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EABS__sum (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EABS__sum A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EINL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EINR (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EISL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EISR (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EIS__SUM__REP (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EIS__SUM__REP A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EOUTL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EOUTL A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EOUTR (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EOUTR A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) A_27b))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2EREP__sum (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2EREP__sum A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2ESUM__ALL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Esum_2ESUM__ALL A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Esum_2Esum__CASE (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Esum_2Esum__CASE A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27c)) A_27c))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EIS__SUM__REP A_27a) A_27b)) V0f)) (exists ((V1v1 $$unsorted)) (and (@ (@ tptp.mem V1v1) A_27a) (exists ((V2v2 $$unsorted)) (let ((_let_1 (@ tptp.lam tptp.bool))) (and (@ (@ tptp.mem V2v2) A_27b) (or (= V0f (@ _let_1 (lambda ((V3b $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V5y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4x)) V1v1))) V3b)))))))) (= V0f (@ _let_1 (lambda ((V6b $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V7x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V8y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V8y)) V2v2))) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) V6b)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (exists ((V0rep $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (let ((_let_2 (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))))) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr _let_1) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION _let_2) _let_1)) (@ (@ tptp.c_2Esum_2EIS__SUM__REP A_27a) A_27b))) V0rep))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EABS__sum A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EREP__sum A_27a) A_27b)) V0a)) V0a))) (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EIS__SUM__REP A_27a) A_27b)) V1r)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EREP__sum A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EABS__sum A_27a) A_27b)) V1r)) V1r)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0e) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EABS__sum A_27a) A_27b)) (@ (@ tptp.lam tptp.bool) (lambda ((V1b $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V2x)) V0e))) V1b))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V0e) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EABS__sum A_27a) A_27b)) (@ (@ tptp.lam tptp.bool) (lambda ((V1b $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V3y)) V0e))) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) V1b)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)))) (=> (@ (@ tptp.mem V1y) A_27a) (= (= (@ _let_1 V0x) (@ _let_1 V1y)) (= V0x V1y))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27b) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)))) (=> (@ (@ tptp.mem V1y) A_27b) (= (= (@ _let_1 V0x) (@ _let_1 V1y)) (= V0x V1y))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27a) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)))) (=> (@ (@ tptp.mem V1x) A_27a) (= (= (@ _let_1 V1x) (@ _let_1 V0y)) (= V1x V0y))))))) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)))) (=> (@ (@ tptp.mem V3x) A_27b) (= (= (@ _let_1 V3x) (@ _let_1 V2y)) (= V3x V2y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0v1 $$unsorted)) (=> (@ (@ tptp.mem V0v1) A_27a) (forall ((V1v2 $$unsorted)) (=> (@ (@ tptp.mem V1v2) A_27b) (not (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V1v2) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0v1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) A_27c))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27c)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2h $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) A_27c))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) _let_1)) V2h)) (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)))) V0f))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27b) A_27c))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) A_27c) _let_1)) V2h)) (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)))) V1g)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.bool)) (=> (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V1x))))) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V2y)))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap V0P) V3s))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.bool)) (= (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap V0P) V1s)))) (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V2x))))) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V3y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.bool)) (= (exists ((V1s $$unsorted)) (and (@ (@ tptp.mem V1s) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap V0P) V1s)))) (or (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V2x))))) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27b) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V3y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27c)) (exists ((V2h $$unsorted)) (and (@ (@ tptp.mem V2h) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) A_27c)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ (@ tptp.ap V2h) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V3x)) (@ (@ tptp.ap V0f) V3x)))) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27b) (= (@ (@ tptp.ap V2h) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V4y)) (@ (@ tptp.ap V1g) V4y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0ss $$unsorted)) (=> (@ (@ tptp.mem V0ss) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (or (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (= V0ss (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V1x)))) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (= V0ss (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V2y))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (not (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0x) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V1y))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (not (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V1y) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0x))))) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V1y)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V0x))))) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V1y)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EOUTL A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0x)) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EOUTR A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V0x)) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) V0x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) V0x)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EOUTL A_27a) A_27b)) V0x)) V0x)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) V0x)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EOUTR A_27a) A_27b)) V0x)) V0x)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (and (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V2f1 $$unsorted)) (=> (@ (@ tptp.mem V2f1) (@ (@ tptp.arr A_27b) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Esum_2Esum__CASE A_27a) A_27b) A_27c)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V0x))) V1f)) V2f1) (@ (@ tptp.ap V1f) V0x)))))))) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (forall ((V4f $$unsorted)) (=> (@ (@ tptp.mem V4f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V5f1 $$unsorted)) (=> (@ (@ tptp.mem V5f1) (@ (@ tptp.arr A_27b) A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Esum_2Esum__CASE A_27a) A_27b) A_27c)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V3y))) V4f)) V5f1) (@ (@ tptp.ap V5f1) V3y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f_27 $$unsorted)) (=> (@ (@ tptp.mem V0f_27) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1f1_27 $$unsorted)) (=> (@ (@ tptp.mem V1f1_27) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V2M $$unsorted)) (=> (@ (@ tptp.mem V2M) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (forall ((V3M_27 $$unsorted)) (=> (@ (@ tptp.mem V3M_27) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (forall ((V4f $$unsorted)) (=> (@ (@ tptp.mem V4f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V5f1 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Esum_2Esum__CASE A_27a) A_27b) A_27c)))) (=> (@ (@ tptp.mem V5f1) (@ (@ tptp.arr A_27b) A_27c)) (=> (and (= V2M V3M_27) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (=> (= V3M_27 (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V6x)) (= (@ (@ tptp.ap V4f) V6x) (@ (@ tptp.ap V0f_27) V6x))))) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27b) (=> (= V3M_27 (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V7y)) (= (@ (@ tptp.ap V5f1) V7y) (@ (@ tptp.ap V1f1_27) V7y)))))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2M)) V4f)) V5f1) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V3M_27)) V0f_27)) V1f1_27)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27d)) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Esum_2E_2B_2B A_27a) A_27b) A_27c) A_27d)) V0f)) V1g)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V2a)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27c) A_27d)) (@ (@ tptp.ap V0f) V2a))))))))) (forall ((V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V4g $$unsorted)) (=> (@ (@ tptp.mem V4g) (@ (@ tptp.arr A_27b) A_27d)) (forall ((V5b $$unsorted)) (=> (@ (@ tptp.mem V5b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Esum_2E_2B_2B A_27a) A_27b) A_27c) A_27d)) V3f)) V4g)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V5b)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27c) A_27d)) (@ (@ tptp.ap V4g) V5b))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27d)) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Esum_2E_2B_2B A_27a) A_27b) A_27c) A_27d)) V0f)) V1g)) V2z) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Esum_2Esum A_27c) A_27d))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) V2z))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27c) A_27d)) (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EOUTL A_27a) A_27b)) V2z))))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27c) A_27d)) (@ (@ tptp.ap V1g) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EOUTR A_27a) A_27b)) V2z))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27d)) (forall ((V2z $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27c) A_27d))) (=> (@ (@ tptp.mem V2z) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Esum_2E_2B_2B A_27a) A_27b) A_27c) A_27d)) V0f)) V1g)) V2z) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Esum_2Esum__CASE A_27a) A_27b) _let_1)) V2z)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) _let_1) A_27c)) (@ (@ tptp.c_2Esum_2EINL A_27c) A_27d))) V0f))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) _let_1) A_27d)) (@ (@ tptp.c_2Esum_2EINR A_27c) A_27d))) V1g)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Esum_2E_2B_2B A_27a) A_27b) A_27a) A_27b)) (@ tptp.c_2Ecombin_2EI A_27a))) (@ tptp.c_2Ecombin_2EI A_27b)) (@ tptp.c_2Ecombin_2EI (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (A_27e tptp.del) (A_27f tptp.del) (A_27g tptp.del) (A_27h tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27b) A_27a)))) (=> (@ (@ tptp.mem V3z) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Esum_2Esum A_27b) A_27a))) V0P)) (@ _let_1 V1x))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27b) A_27a)) V2y)) (@ _let_1 V3z)) (and (@ tptp.p V0P) (= V3z V1x)))))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27c) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27d) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27d) A_27c)))) (=> (@ (@ tptp.mem V6z) A_27d) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Esum_2Esum A_27d) A_27c))) V0P)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27d) A_27c)) V4x))) (@ _let_1 V5y)) (@ _let_1 V6z)) (and (not (@ tptp.p V0P)) (= V6z V5y)))))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27e) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27f) (forall ((V9z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27e) A_27f)))) (=> (@ (@ tptp.mem V9z) A_27e) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Esum_2Esum A_27e) A_27f))) V0P)) (@ _let_1 V7x))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27e) A_27f)) V8y)) (@ _let_1 V9z)) (and (@ tptp.p V0P) (= V9z V7x)))))))))) (forall ((V10x $$unsorted)) (=> (@ (@ tptp.mem V10x) A_27g) (forall ((V11y $$unsorted)) (=> (@ (@ tptp.mem V11y) A_27h) (forall ((V12z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27g) A_27h)))) (=> (@ (@ tptp.mem V12z) A_27h) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Esum_2Esum A_27g) A_27h))) V0P)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27g) A_27h)) V10x))) (@ _let_1 V11y)) (@ _let_1 V12z)) (and (not (@ tptp.p V0P)) (= V12z V11y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) V0x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISR A_27a) A_27b)) V0x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EISL A_27a) A_27b)) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2ESUM__ALL A_27a) A_27b)) V0P)) V1Q)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V2x))) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))))))) (forall ((V3P $$unsorted)) (=> (@ (@ tptp.mem V3P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4Q $$unsorted)) (=> (@ (@ tptp.mem V4Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2ESUM__ALL A_27a) A_27b)) V3P)) V4Q)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V5y))) (@ tptp.p (@ (@ tptp.ap V4Q) V5y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V3Q_27 $$unsorted)) (=> (@ (@ tptp.mem V3Q_27) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V4s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2ESUM__ALL A_27a) A_27b)))) (=> (@ (@ tptp.mem V4s) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (=> (and (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V5x)) (@ tptp.p (@ (@ tptp.ap V1P_27) V5x))))) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap V2Q) V6y)) (@ tptp.p (@ (@ tptp.ap V3Q_27) V6y)))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2Q)) V4s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1P_27)) V3Q_27)) V4s))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (forall ((V1s_27 $$unsorted)) (=> (@ (@ tptp.mem V1s_27) (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3P_27 $$unsorted)) (=> (@ (@ tptp.mem V3P_27) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4Q $$unsorted)) (=> (@ (@ tptp.mem V4Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V5Q_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Esum_2ESUM__ALL A_27a) A_27b)))) (=> (@ (@ tptp.mem V5Q_27) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (= V0s V1s_27) (forall ((V6a $$unsorted)) (=> (@ (@ tptp.mem V6a) A_27a) (=> (= V1s_27 (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V6a)) (= (@ tptp.p (@ (@ tptp.ap V2P) V6a)) (@ tptp.p (@ (@ tptp.ap V3P_27) V6a)))))) (forall ((V7b $$unsorted)) (=> (@ (@ tptp.mem V7b) A_27b) (=> (= V1s_27 (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V7b)) (= (@ tptp.p (@ (@ tptp.ap V4Q) V7b)) (@ tptp.p (@ (@ tptp.ap V5Q_27) V7b))))))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2P)) V4Q)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V3P_27)) V5Q_27)) V1s_27))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0sum $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (=> (@ (@ tptp.mem V0sum) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) _let_1)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) _let_1)) A_27c))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2EDATATYPE A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap V0sum) (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b))) (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ECR (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ECR A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EEMPTY__REL (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EEMPTY__REL A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EEQC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EEQC A_27a)) (@ (@ tptp.arr _let_2) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EIDEM (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27z tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EIDEM A_27z)) (@ (@ tptp.arr (@ (@ tptp.arr A_27z) A_27z)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EINDUCTIVE__INVARIANT (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.arr (@ (@ tptp.arr _let_2) _let_2)) tptp.bool))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EINDUCTIVE__INVARIANT__ON (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (let ((_let_3 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT__ON A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 _let_3)) (@ (@ tptp.arr _let_3) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.arr (@ (@ tptp.arr _let_2) _let_2)) tptp.bool))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EINVOL (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27z tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EINVOL A_27z)) (@ (@ tptp.arr (@ (@ tptp.arr A_27z) A_27z)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ELinearOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ELinearOrder A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EO (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27g tptp.del) (A_27h tptp.del) (A_27k tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27k) tptp.bool))) (let ((_let_2 (@ tptp.arr A_27g))) (let ((_let_3 (@ tptp.arr A_27h))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Erelation_2EO A_27g) A_27h) A_27k)) (@ (@ tptp.arr (@ _let_3 _let_1)) (@ (@ tptp.arr (@ _let_2 (@ _let_3 tptp.bool))) (@ _let_2 _let_1)))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27g tptp.del)) (let ((_let_1 (@ tptp.arr A_27g))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EOrder A_27g)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EPreOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EPreOrder A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ERC A_27a)) (@ (@ tptp.arr _let_2) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERCOMPL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERCOMPL A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERDOM (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERDOM A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERDOM__DELETE (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool)))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERDOM__DELETE A_27a) A_27b)) (@ (@ tptp.arr _let_2) (@ _let_1 _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERESTRICT (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) (@ (@ tptp.arr _let_2) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) (@ _let_1 _let_2))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERINTER (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27b)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERRANGE (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERRANGE A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) _let_1)) _let_1)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERRESTRICT (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool)))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERRESTRICT A_27a) A_27b)) (@ (@ tptp.arr _let_2) (@ (@ tptp.arr (@ _let_1 tptp.bool)) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERSUBSET (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERTC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ERTC A_27a)) (@ (@ tptp.arr _let_2) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERUNION (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27b)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ERUNIV (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2ERUNIV A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ESC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ESC A_27a)) (@ (@ tptp.arr _let_2) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ESN (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ESN A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ESTRORD (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ESTRORD A_27a)) (@ (@ tptp.arr _let_2) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EStrongLinearOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EStrongLinearOrder A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EStrongOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27g tptp.del)) (let ((_let_1 (@ tptp.arr A_27g))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EStrongOrder A_27g)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2ETC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2ETC A_27a)) (@ (@ tptp.arr _let_2) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EWCR (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EWCR A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EWF (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EWF A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EWFP (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EWFP A_27a)) (@ (@ tptp.arr (@ _let_1 _let_2)) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EWFREC (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) (@ (@ tptp.arr (@ (@ tptp.arr _let_2) _let_2)) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EWeakLinearOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EWeakLinearOrder A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2EWeakOrder (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27g tptp.del)) (let ((_let_1 (@ tptp.arr A_27g))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2EWeakOrder A_27g)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Eantisymmetric (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Eantisymmetric A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Eapprox (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (let ((_let_3 (@ tptp.arr _let_2))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2Eapprox A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) (@ (@ tptp.arr (@ _let_3 _let_2)) (@ _let_1 (@ _let_3 tptp.bool))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Ediag (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Ediag A_27a)) (@ (@ tptp.arr _let_2) (@ _let_1 _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Ediamond (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Ediamond A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Eequivalence (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Eequivalence A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Einv (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ tptp.arr A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ _let_2 tptp.bool))) (@ _let_2 (@ _let_1 tptp.bool))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Einv__image (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ tptp.arr A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2Einv__image A_27a) A_27b)) (@ (@ tptp.arr (@ _let_2 (@ _let_2 tptp.bool))) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ _let_1 (@ _let_1 tptp.bool)))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Eirreflexive (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Eirreflexive A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Enf (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2Enf A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Ercdiamond (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Ercdiamond A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Ereflexive (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Ereflexive A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Esymmetric (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Esymmetric A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Ethe__fun (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Erelation_2Ethe__fun A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) (@ (@ tptp.arr (@ (@ tptp.arr _let_2) _let_2)) (@ _let_1 _let_2))))))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Etotal (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Etotal A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Etransitive (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Etransitive A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Erelation_2Etrichotomous (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Erelation_2Etrichotomous A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (let ((_let_2 (@ tptp.ap (@ _let_1 V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ _let_2 V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V3z))) (@ tptp.p (@ _let_2 V3z))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V1x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V1x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V1x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V1x))) (= V1x V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eequivalence A_27a)) V0R)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etotal A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2y) A_27a) (or (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V1x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etrichotomous A_27a)) V0R)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2b) A_27a) (or (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1a)) V2b)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2b)) V1a)) (= V1a V2b))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1a)) V2b)) (forall ((V3P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V3P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3P) V4x)) V5y))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (forall ((V8z $$unsorted)) (let ((_let_1 (@ tptp.ap V3P))) (let ((_let_2 (@ tptp.ap (@ _let_1 V6x)))) (=> (@ (@ tptp.mem V8z) A_27a) (=> (and (@ tptp.p (@ _let_2 V7y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V7y)) V8z))) (@ tptp.p (@ _let_2 V8z)))))))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3P) V1a)) V2b)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1a)) V2b)) (forall ((V3P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V3P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3P) V4x)) V4x)))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27a) (forall ((V7z $$unsorted)) (let ((_let_1 (@ tptp.ap V3P))) (=> (@ (@ tptp.mem V7z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V5x)) V6y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V6y)) V7z))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5x)) V7z))))))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3P) V1a)) V2b)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) V1x)) V2y)) (or (= V1x V2y) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R)) V1x)) V2y)) (or (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V1x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V5z))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V5z))))))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V6x)) V7y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V6x)) V7y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y))))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V3x)))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ _let_2 V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V5z))) (@ tptp.p (@ _let_2 V5z))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V1x)))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (forall ((V4z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))) (=> (@ (@ tptp.mem V4z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V4z))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x)) V4z)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V4y)) V5z)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V5z))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V5z))))))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V6x)) V7y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V6x)) V7y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V3z)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V3z)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V2x))) (@ _let_1 V3y)))))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V4x))) (@ _let_1 V5y)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) V4x)) V5y))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V2x)) V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ _let_1 V2x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V2x)) V3y))) (@ tptp.p (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ _let_1 V4x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V1R)) V4x)) V5y))) (@ tptp.p (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (= (@ _let_1 V2x) (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) V4x)) V5y)) (= (@ _let_1 V4x) (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V2x))) (@ _let_1 V3y)))))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R)))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V4x))) (@ _let_1 V5y)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (= (@ _let_1 V2x) (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R)) V4x)) V5y)) (= (@ _let_1 V4x) (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) V4x)) V5y))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V2x)) V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ _let_1 V0R)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (let ((_let_2 (@ tptp.ap (@ _let_1 V4x)))) (=> (@ (@ tptp.mem V6z) A_27a) (=> (and (@ tptp.p (@ _let_2 V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5y)) V6z))) (@ tptp.p (@ _let_2 V6z)))))))))))) (forall ((V7u $$unsorted)) (=> (@ (@ tptp.mem V7u) A_27a) (forall ((V8v $$unsorted)) (=> (@ (@ tptp.mem V8v) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V7u)) V8v)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V7u)) V8v)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V6z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5y)) V6z))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4x)) V6z))))))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V7x)) V8y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V7x)) V8y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V1P) V4x)))) (=> (@ (@ tptp.mem V6z) A_27a) (=> (and (@ tptp.p (@ _let_1 V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V5y)) V6z))) (@ tptp.p (@ _let_1 V6z))))))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V7x)) V8y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V7x)) V8y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (let ((_let_2 (@ tptp.ap (@ _let_1 V4x)))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))) (=> (@ (@ tptp.mem V6z) A_27a) (=> (and (@ tptp.p (@ _let_2 V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5y)) V6z)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V5y)) V6z))) (@ tptp.p (@ _let_2 V6z))))))))))))) (forall ((V7u $$unsorted)) (=> (@ (@ tptp.mem V7u) A_27a) (forall ((V8v $$unsorted)) (=> (@ (@ tptp.mem V8v) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V7u)) V8v)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V7u)) V8v)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V6z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5y)) V6z)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V5y)) V6z))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4x)) V6z))))))))))) (forall ((V7u $$unsorted)) (=> (@ (@ tptp.mem V7u) A_27a) (forall ((V8v $$unsorted)) (=> (@ (@ tptp.mem V8v) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V7u)) V8v)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V7u)) V8v)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V1P) V4x)))) (=> (@ (@ tptp.mem V6z) A_27a) (=> (and (@ tptp.p (@ _let_1 V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V5y)) V6z))) (@ tptp.p (@ _let_1 V6z))))))))))) (forall ((V7u $$unsorted)) (=> (@ (@ tptp.mem V7u) A_27a) (forall ((V8v $$unsorted)) (=> (@ (@ tptp.mem V8v) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V7u)) V8v)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V7u)) V8v)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) A_27a) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V3x)) V0b)) (@ tptp.p (@ (@ tptp.ap V2Q) V3x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V2Q))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V4x)) V5y)) (@ tptp.p (@ _let_1 V5y))) (@ tptp.p (@ _let_1 V4x))))))))) (forall ((V6a $$unsorted)) (=> (@ (@ tptp.mem V6a) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V1R)) V6a)) V0b)) (@ tptp.p (@ (@ tptp.ap V2Q) V6a))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V0a)) V3y)) (@ tptp.p (@ (@ tptp.ap V2Q) V3y))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V2Q))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ _let_1 V4x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V4x)) V5y))) (@ tptp.p (@ _let_1 V5y))))))))) (forall ((V6b $$unsorted)) (=> (@ (@ tptp.mem V6b) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V1R)) V0a)) V6b)) (@ tptp.p (@ (@ tptp.ap V2Q) V6b))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V2x))) (@ _let_1 V3y)))))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V4x))) (@ _let_1 V5y)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ _let_1 V2x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V2x)) V3y))) (@ tptp.p (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ _let_1 V4x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V1R)) V4x)) V5y))) (@ tptp.p (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (= (@ _let_1 V2x) (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V4x)) V5y)) (= (@ _let_1 V4x) (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (=> (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V2f))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) (@ _let_1 V3x))) (@ _let_1 V4y))))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27b)) V1Q))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (let ((_let_1 (@ tptp.ap V2f))) (=> (@ (@ tptp.mem V6y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V5x)) V6y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) (@ _let_1 V5x))) (@ _let_1 V6y)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y)) (not (= V1x V2y))) (exists ((V3z $$unsorted)) (and (@ (@ tptp.mem V3z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V3z)) (not (= V1x V3z)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)))) (let ((_let_4 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_4 (@ _let_4 tptp.bool))) (and (= (@ _let_2 (@ _let_3 V0R)) _let_1) (= (@ _let_3 (@ _let_2 V0R)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1a)) V2b)) (forall ((V3Q $$unsorted)) (let ((_let_1 (@ tptp.ap V3Q))) (=> (@ (@ tptp.mem V3Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V2b)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V3Q))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ _let_1 V5y))) (@ tptp.p (@ _let_1 V4x))))))))) (@ tptp.p (@ _let_1 V1a)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V1Q) V2b)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1Q))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)) (@ tptp.p (@ _let_1 V4y))) (@ tptp.p (@ _let_1 V3x))))))))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V5x)) V2b)) (@ tptp.p (@ (@ tptp.ap V1Q) V5x))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1a)) V2b)) (forall ((V3Q $$unsorted)) (let ((_let_1 (@ tptp.ap V3Q))) (=> (@ (@ tptp.mem V3Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V1a)) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.ap V3Q))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ _let_1 V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4y)) V5z))) (@ tptp.p (@ _let_1 V5z))))))))) (@ tptp.p (@ _let_1 V2b)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V1Q) V2a)) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (forall ((V4z $$unsorted)) (let ((_let_1 (@ tptp.ap V1Q))) (=> (@ (@ tptp.mem V4z) A_27a) (=> (and (@ tptp.p (@ _let_1 V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V4z))) (@ tptp.p (@ _let_1 V4z))))))))) (forall ((V5z $$unsorted)) (=> (@ (@ tptp.mem V5z) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V2a)) V5z)) (@ tptp.p (@ (@ tptp.ap V1Q) V5z))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V1P) V3x)))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ _let_1 V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4y)) V5z))) (@ tptp.p (@ _let_1 V5z))))))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V6x)) V7y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V6x)) V7y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V1x)))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (forall ((V4z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V2x)))) (=> (@ (@ tptp.mem V4z) A_27a) (=> (and (@ tptp.p (@ _let_1 V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V4z))) (@ tptp.p (@ _let_1 V4z)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V1P) V3x)))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ _let_1 V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4y)) V5z))) (@ tptp.p (@ _let_1 V5z))))))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V6x)) V7y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V6x)) V7y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V2y)) V3z))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V3z)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2z)) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V3y)) V2z)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R)) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R) V0R))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R)) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R) V0R))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R)) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R) V0R))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 _let_2) _let_2)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 _let_2) _let_2)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 _let_2) _let_2)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)))) (let ((_let_3 (@ _let_2 V0R))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)))) (let ((_let_5 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_5 (@ _let_5 tptp.bool))) (and (= (@ _let_4 _let_3) (@ _let_2 (@ _let_4 V0R))) (= (@ _let_2 _let_3) _let_3) (= (@ _let_1 _let_3) (@ _let_2 (@ _let_1 V0R))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ _let_1 V0R)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ _let_1 V0R)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eequivalence A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 _let_2) _let_2)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 _let_2) _let_2)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (or (= V1x V2y) (exists ((V3u $$unsorted)) (and (@ (@ tptp.mem V3u) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V3u)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V3u)) V2y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (or (= V1x V2y) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (or (= V1x V2y) (exists ((V3u $$unsorted)) (and (@ (@ tptp.mem V3u) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V3u)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3u)) V2y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (exists ((V3u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))) (and (@ (@ tptp.mem V3u) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V3u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3u)) V2y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2z)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2z)) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V3y)) V2z))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2z)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2z)) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V3y)) V2z))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2z)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2z)) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V2z))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2z)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2z)) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V2z))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) V4x)) V5y))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V2x)) V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) V4x)) V5y))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V2x)) V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V4x)) V4x)))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V6y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5x)) V6y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V6y)) V5x)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (forall ((V9z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (let ((_let_2 (@ tptp.ap (@ _let_1 V7x)))) (=> (@ (@ tptp.mem V9z) A_27a) (=> (and (@ tptp.p (@ _let_2 V8y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V8y)) V9z))) (@ tptp.p (@ _let_2 V9z)))))))))))) (forall ((V10x $$unsorted)) (=> (@ (@ tptp.mem V10x) A_27a) (forall ((V11y $$unsorted)) (=> (@ (@ tptp.mem V11y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)) V10x)) V11y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V10x)) V11y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)) V1x)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V1x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ _let_2 V2y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V3z))) (@ tptp.p (@ _let_2 V3z)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (and (= (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) _let_2) (= (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)) V0R)) _let_2) (= (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) _let_2))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V4x)) V4x)))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V6y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)) V5x)) V6y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5x)) V6y))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V6y)) V5x)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (forall ((V9z $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (let ((_let_2 (@ tptp.ap (@ _let_1 V7x)))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)))) (=> (@ (@ tptp.mem V9z) A_27a) (=> (and (@ tptp.p (@ _let_2 V8y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V8y)) V9z)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V7x)) V8y)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V8y)) V9z))) (@ tptp.p (@ _let_2 V9z))))))))))))) (forall ((V10x $$unsorted)) (=> (@ (@ tptp.mem V10x) A_27a) (forall ((V11y $$unsorted)) (=> (@ (@ tptp.mem V11y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)) V10x)) V11y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V10x)) V11y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eequivalence A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (let ((_let_2 (@ _let_1 V1x))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap _let_2) V2y)) (= _let_2 (@ _let_1 V2y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R_27) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R_27) V4x)) V5y))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1R_27)) V2x)) V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)) V0R)) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V2x))) (@ _let_1 V3y)))))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V4x))) (@ _let_1 V5y)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (=> (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V2f))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) (@ _let_1 V3x))) (@ _let_1 V4y))))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27b)) V1Q)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27b)) V1Q))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (let ((_let_1 (@ tptp.ap V2f))) (=> (@ (@ tptp.mem V6y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V5x)) V6y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) (@ _let_1 V5x))) (@ _let_1 V6y)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (= (@ _let_1 V2x) (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V4x)) V5y)) (= (@ _let_1 V4x) (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ _let_1 V2x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V2x)) V3y))) (@ tptp.p (@ _let_1 V3y)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ _let_1 V4x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V1R)) V4x)) V5y))) (@ tptp.p (@ _let_1 V5y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (exists ((V2w $$unsorted)) (and (@ (@ tptp.mem V2w) A_27a) (@ tptp.p (@ (@ tptp.ap V1B) V2w)))) (exists ((V3min $$unsorted)) (and (@ (@ tptp.mem V3min) A_27a) (@ tptp.p (@ (@ tptp.ap V1B) V3min)) (forall ((V4b $$unsorted)) (=> (@ (@ tptp.mem V4b) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4b)) V3min)) (not (@ tptp.p (@ (@ tptp.ap V1B) V4b))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V2x)) (@ tptp.p (@ (@ tptp.ap V1P) V3y))))) (@ tptp.p (@ (@ tptp.ap V1P) V2x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1P) V4x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V2x)) (@ tptp.p (@ (@ tptp.ap V1P) V3y))))) (@ tptp.p (@ (@ tptp.ap V1P) V2x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1P) V4x))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V2x)) (@ tptp.p (@ (@ tptp.ap V1P) V3y))))) (@ tptp.p (@ (@ tptp.ap V1P) V2x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap V1P) V4x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)) (not (= V1x V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EEMPTY__REL A_27a)) V0x)) V1y)) false))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) (@ tptp.c_2Erelation_2EEMPTY__REL A_27a)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1P) (@ _let_2 (@ _let_2 tptp.bool))) (=> (and (@ tptp.p (@ _let_1 V0R)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)))))))) (@ tptp.p (@ _let_1 V1P)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ _let_1 V0R)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y)) (not (= V1x V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27a) A_27b)) V0R)) V1f) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (@ (@ tptp.ap (@ (@ tptp.ap V0R) (@ _let_1 V2x))) (@ _let_1 V3y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V3y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27a) A_27b)) V0R)) V1f)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) (@ _let_1 V2x))) (@ _let_1 V3y)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27b)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27a) A_27b)) V0R)) V1f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etotal A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etotal A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27b) A_27a)) V0R)) V1f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27b) A_27a)) V0R)) V1f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27b) A_27a)) V0R)) V1f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27b) A_27a)) V0R)) V1f))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) V0f)) V1R)) V2x) (@ (@ tptp.lam A_27a) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap V1R) V3y)) V2x))) (@ (@ tptp.ap V0f) V3y))) (@ tptp.c_2Ebool_2EARB A_27b)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (=> (@ (@ tptp.mem V3z) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V2y)) V3z)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) V0f)) V1R)) V3z)) V2y) (@ (@ tptp.ap V0f) V2y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Eapprox A_27a) A_27b)) V0R)) V1M)) V2x)) V3f)) (= V3f (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V1M) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) V3f)) V0R)) V4y))) V4y))))) V0R)) V2x))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Ethe__fun A_27a) A_27b)) V0R)) V1M)) V2x) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V3f $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Eapprox A_27a) A_27b)) V0R)) V1M)) V2x)) V3f)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr _let_1) _let_1)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V0R)) V1M) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V1M) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Ethe__fun A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R))) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V3f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V4v $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V1M) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) V3f)) V0R)) V4v))) V4v))))))) V2x))) V0R)) V2x))) V2x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V0R)) V1M))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap _let_1) V2x) (@ (@ tptp.ap (@ (@ tptp.ap V1M) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) _let_1)) V0R)) V2x))) V2x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V0M) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (=> (= V2f (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V1R)) V0M)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V1R)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ (@ tptp.ap V2f) V3x) (@ (@ tptp.ap (@ (@ tptp.ap V0M) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) V2f)) V1R)) V3x))) V3x)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (forall ((V1M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr _let_1) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) (@ (@ tptp.ap V2f) V3x))) (@ (@ tptp.ap (@ (@ tptp.ap V1M) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERESTRICT A_27a) A_27b)) V2f)) V0R)) V3x))) V3x)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V1a)) (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4y)) V3x)) (@ tptp.p (@ (@ tptp.ap V2P) V4y))))) (@ tptp.p (@ (@ tptp.ap V2P) V3x))))) (@ tptp.p (@ (@ tptp.ap V2P) V1a))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (=> (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2y)) V1x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V2y))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V1x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3y)) V2x)) (@ tptp.p (@ (@ tptp.ap V1P) V3y))))) (@ tptp.p (@ (@ tptp.ap V1P) V2x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V4x)) (@ tptp.p (@ (@ tptp.ap V1P) V4x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V1x)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2y)) V1x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V2y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V1R)) V2x)) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V3y)) V2x)) (@ tptp.p (@ (@ tptp.ap V0P) V3y)))))) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V1R)) V4x)) (@ tptp.p (@ (@ tptp.ap V0P) V4x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWFP A_27a)) V0R)) V1x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V2M) (@ (@ tptp.arr _let_1) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT A_27a) A_27b)) V0R)) V1P)) V2M)) (forall ((V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V5y)) V4x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V5y)) (@ (@ tptp.ap V3f) V5y)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V4x)) (@ (@ tptp.ap (@ (@ tptp.ap V2M) V3f)) V4x))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1D $$unsorted)) (=> (@ (@ tptp.mem V1D) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V3M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V3M) (@ (@ tptp.arr _let_1) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT__ON A_27a) A_27b)) V0R)) V1D)) V2P)) V3M)) (forall ((V4f $$unsorted)) (=> (@ (@ tptp.mem V4f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V1D) V5x)) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V1D) V6y)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V6y)) V5x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2P) V6y)) (@ (@ tptp.ap V4f) V6y)))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2P) V5x)) (@ (@ tptp.ap (@ (@ tptp.ap V3M) V4f)) V5x))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V2M) (@ (@ tptp.arr _let_1) _let_1)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT A_27a) A_27b)) V0R)) V1P)) V2M))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V3x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V0R)) V2M)) V3x)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V3M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V3M) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (and (= V0f (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V1R)) V3M)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V1R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT A_27a) A_27b)) V1R)) V2P)) V3M))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2P) V4x)) (@ (@ tptp.ap V0f) V4x)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V2M) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V3D $$unsorted)) (=> (@ (@ tptp.mem V3D) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT__ON A_27a) A_27b)) V0R)) V3D)) V1P)) V2M)) (@ tptp.p (@ (@ tptp.ap V3D) V4x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V4x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V0R)) V2M)) V4x)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2D $$unsorted)) (=> (@ (@ tptp.mem V2D) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3P $$unsorted)) (=> (@ (@ tptp.mem V3P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V4M $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V4M) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (=> (and (= V0f (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC A_27a) A_27b)) V1R)) V4M)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V1R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EINDUCTIVE__INVARIANT__ON A_27a) A_27b)) V1R)) V2D)) V3P)) V4M)) (@ tptp.p (@ (@ tptp.ap V2D) V5x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3P) V5x)) (@ (@ tptp.ap V0f) V5x)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27b)) V0R)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2y)) V1x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27b) A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27b)) V0R)) V0R))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 (@ _let_2 V0R)) (@ _let_2 (@ _let_1 V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)))) (let ((_let_4 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_4 (@ _let_4 tptp.bool))) (and (= (@ _let_3 _let_2) _let_2) (= (@ _let_1 (@ _let_3 V0R)) _let_2)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (= (@ _let_1 (@ _let_2 V0R)) (@ _let_2 (@ _let_1 V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)))) (let ((_let_2 (@ _let_1 V0R))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)))) (let ((_let_4 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_4 (@ _let_4 tptp.bool))) (and (= (@ _let_3 _let_2) _let_2) (= (@ _let_1 (@ _let_3 V0R)) _let_2)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2EEQC A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)))) (let ((_let_3 (@ _let_2 V0R))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)))) (let ((_let_5 (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)))) (let ((_let_6 (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)))) (let ((_let_7 (@ tptp.ap (@ tptp.c_2Erelation_2ESC A_27a)))) (let ((_let_8 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_8 (@ _let_8 tptp.bool))) (and (= (@ _let_2 _let_3) V0R) (= (@ _let_7 _let_3) (@ _let_7 V0R)) (= (@ _let_6 _let_3) (@ _let_2 (@ _let_6 V0R))) (= (@ _let_5 _let_3) (@ _let_2 (@ _let_5 V0R))) (= (@ _let_4 _let_3) (@ _let_2 (@ _let_4 V0R))) (= (@ _let_1 _let_3) (@ _let_1 V0R))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R) V0R))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eequivalence A_27a)) V0R)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R) V0R))))))
% 1.89/2.21 (assert (forall ((A_27z tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27z) A_27z)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EINVOL A_27z)) V0f)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27z) A_27z) A_27z)) V0f)) V0f) (@ tptp.c_2Ecombin_2EI A_27z))))))
% 1.89/2.21 (assert (forall ((A_27z tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27z) A_27z)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EINVOL A_27z)) V0f)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V1x) A_27z) (= (@ _let_1 (@ _let_1 V1x)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27z tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27z) A_27z)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EINVOL A_27z)) V0f)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27z) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2b) A_27z) (= (= (@ _let_1 V1a) (@ _let_1 V2b)) (= V1a V2b)))))))))))
% 1.89/2.21 (assert (forall ((A_27z tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27z) A_27z)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EINVOL A_27z)) V0f)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27z) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2b) A_27z) (= (= (@ _let_1 V1a) V2b) (= V1a (@ _let_1 V2b))))))))))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EINVOL tptp.bool)) tptp.c_2Ebool_2E_7E)))
% 1.89/2.21 (assert (forall ((A_27z tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27z) A_27z)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM A_27z)) V0f)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27z) A_27z) A_27z)) V0f)) V0f) V0f)))))
% 1.89/2.21 (assert (forall ((A_27z tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27z) A_27z)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM A_27z)) V0f)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ _let_1 V1x))) (=> (@ (@ tptp.mem V1x) A_27z) (= (@ _let_1 _let_2) _let_2)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EINVOL (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a))))))
% 1.89/2.21 (assert (forall ((A_27g tptp.del) (A_27h tptp.del) (A_27k tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27h) (@ (@ tptp.arr A_27k) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27g) (@ (@ tptp.arr A_27h) tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27g) (forall ((V3z $$unsorted)) (=> (@ (@ tptp.mem V3z) A_27k) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27g) A_27h) A_27k)) V0R1)) V1R2)) V2x)) V3z)) (exists ((V4y $$unsorted)) (and (@ (@ tptp.mem V4y) A_27h) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V2x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V4y)) V3z))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R_27 $$unsorted)) (let ((_let_1 (@ tptp.c_2Erelation_2Einv A_27c))) (=> (@ (@ tptp.mem V1R_27) (@ (@ tptp.arr A_27c) (@ (@ tptp.arr A_27a) tptp.bool))) (= (@ (@ tptp.ap (@ _let_1 A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27c) A_27a) A_27b)) V0R)) V1R_27)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27b) A_27a) A_27c)) (@ (@ tptp.ap (@ _let_1 A_27a)) V1R_27))) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27b)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)) V0R1)) V1R2)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V2x)) V3y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R2) (@ _let_2 (@ _let_2 tptp.bool))) (=> (and (@ tptp.p (@ _let_1 V1R2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)) V0R1)) V1R2))) (@ tptp.p (@ _let_1 V0R1)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27b)) V0R1)) V1R2)) V2x)) V3y)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V2x)) V3y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27b)))) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ _let_1 V0R1)) V1R2) (@ (@ tptp.ap (@ _let_1 V1R2)) V0R1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2R3 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0R1)))) (=> (@ (@ tptp.mem V2R3) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1R2)) V2R3)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1R2))) V2R3)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27b)) V0R1)) V1R2)) V2x)) V3y)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V2x)) V3y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27b)))) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ _let_1 V0R1)) V1R2) (@ (@ tptp.ap (@ _let_1 V1R2)) V0R1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2R3 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0R1)))) (=> (@ (@ tptp.mem V2R3) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1R2)) V2R3)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1R2))) V2R3)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27a)))) (let ((_let_2 (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27a)) V0R1)) V1R2))))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R2) (@ _let_3 (@ _let_3 tptp.bool))) (and (=> (@ tptp.p (@ _let_1 V0R1)) _let_2) (=> (@ tptp.p (@ _let_1 V1R2)) _let_2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R2) (@ _let_2 (@ _let_2 tptp.bool))) (=> (and (@ tptp.p (@ _let_1 V0R1)) (@ tptp.p (@ _let_1 V1R2))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27a)) V0R1)) V1R2))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERCOMPL A_27a) A_27b)) V0R)) V1x)) V2y)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)) (@ tptp.c_2Emin_2E_3D A_27a))) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27a) A_27a) A_27a)) V0R)) V0R))) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EPreOrder A_27a)) V0R)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27g tptp.del) (V0Z $$unsorted)) (let ((_let_1 (@ tptp.arr A_27g))) (=> (@ (@ tptp.mem V0Z) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EOrder A_27g)) V0Z)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27g)) V0Z)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27g)) V0Z))))))))
% 1.89/2.21 (assert (forall ((A_27g tptp.del) (V0Z $$unsorted)) (let ((_let_1 (@ tptp.arr A_27g))) (=> (@ (@ tptp.mem V0Z) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27g)) V0Z)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27g)) V0Z)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27g)) V0Z)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27g)) V0Z))))))))
% 1.89/2.21 (assert (forall ((A_27g tptp.del) (V0Z $$unsorted)) (let ((_let_1 (@ tptp.arr A_27g))) (=> (@ (@ tptp.mem V0Z) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongOrder A_27g)) V0Z)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27g)) V0Z)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27g)) V0Z))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EOrder A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EOrder A_27a)) V0R)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27a)) V0R)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2z $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2z) A_27a) (= (= V1y V2z) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1y)) V2z)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2z)) V1y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)))) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0R1)) V1R2)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1R2)) V0R1))) (= V0R1 V1R2))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eantisymmetric (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)))) (=> (@ (@ tptp.mem V1z) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (= V0y V1z) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0y)) V1z)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1z)) V0y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESTRORD A_27a)) V0R)) V1a)) V2b)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1a)) V2b)) (not (= V1a V2b))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESTRORD A_27a)) V0R) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERINTER A_27a) A_27a)) V0R)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERCOMPL A_27a) A_27a)) (@ tptp.c_2Emin_2E_3D A_27a))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27a)) V0R)) (@ tptp.c_2Emin_2E_3D A_27a)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongOrder A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESTRORD A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongOrder A_27a)) V0R)) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESTRORD A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)) V0R))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27a)) V0R)) (= (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESTRORD A_27a)) V0R)) V0R))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM (@ _let_1 (@ _let_1 tptp.bool)))) (@ tptp.c_2Erelation_2ESTRORD A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM (@ _let_1 (@ _let_1 tptp.bool)))) (@ tptp.c_2Erelation_2ERC A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM (@ _let_1 (@ _let_1 tptp.bool)))) (@ tptp.c_2Erelation_2ESC A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM (@ _let_1 (@ _let_1 tptp.bool)))) (@ tptp.c_2Erelation_2ETC A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EIDEM (@ _let_1 (@ _let_1 tptp.bool)))) (@ tptp.c_2Erelation_2ERTC A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Etrichotomous A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESTRORD A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Etrichotomous A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R))) (@ tptp.p (@ _let_1 V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2ELinearOrder A_27a)) V0R)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etrichotomous A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongLinearOrder A_27a)) V0R)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etrichotomous A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakLinearOrder A_27a)) V0R)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etrichotomous A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakLinearOrder A_27a)) V0R)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWeakOrder A_27a)) V0R)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (=> (@ (@ tptp.mem V2b) A_27a) (or (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1a)) V2b)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2b)) V1a))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ediag A_27a)) V0A)) V1x)) V2y)) (and (= V1x V2y) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0A)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27c) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27d) (@ (@ tptp.arr A_27c) tptp.bool))) (forall ((V2R3 $$unsorted)) (let ((_let_1 (@ tptp.c_2Erelation_2EO A_27a))) (let ((_let_2 (@ _let_1 A_27d))) (=> (@ (@ tptp.mem V2R3) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27d) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 A_27c) A_27b)) V0R1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27c)) V1R2)) V2R3)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27d) A_27c) A_27b)) V0R1)) V1R2))) V2R3)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27a) A_27b) A_27b)) (@ tptp.c_2Emin_2E_3D A_27b))) V0R) V0R))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27a) A_27a) A_27b)) V0R)) (@ tptp.c_2Emin_2E_3D A_27a)) V0R))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0R1 $$unsorted)) (=> (@ (@ tptp.mem V0R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1R2 $$unsorted)) (=> (@ (@ tptp.mem V1R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2S1 $$unsorted)) (=> (@ (@ tptp.mem V2S1) (@ (@ tptp.arr A_27c) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V3S2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Erelation_2EO A_27c) A_27a) A_27b)))) (let ((_let_2 (@ tptp.c_2Erelation_2ERSUBSET A_27c))) (=> (@ (@ tptp.mem V3S2) (@ (@ tptp.arr A_27c) (@ (@ tptp.arr A_27a) tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)) V0R1)) V1R2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27a)) V2S1)) V3S2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27b)) (@ (@ tptp.ap (@ _let_1 V0R1)) V2S1))) (@ (@ tptp.ap (@ _let_1 V1R2)) V3S2)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.c_2Emin_2E_3D A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) _let_1) _let_1))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0A $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ediag A_27a)) V0A))) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) _let_1) _let_1)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM A_27a) A_27b)) V0R)) V1x)) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1R $$unsorted)) (=> (@ (@ tptp.mem V1R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM A_27a) A_27b)) V1R))) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V0x)) V2y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERRANGE A_27a) A_27b)) V0R)) V1y)) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V1y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27a) (forall ((V1R $$unsorted)) (=> (@ (@ tptp.mem V1R) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27a) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0y)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERRANGE A_27b) A_27a)) V1R))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V2x)) V0y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1R1 $$unsorted)) (=> (@ (@ tptp.mem V1R1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2R2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (=> (@ (@ tptp.mem V2R2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ _let_2 (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27b)) V1R1)) V2R2)))) (or (@ tptp.p (@ _let_2 (@ _let_1 V1R1))) (@ tptp.p (@ _let_2 (@ _let_1 V2R2))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNIV A_27a) A_27b)) V0x)) V1y)) true))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ (@ tptp.c_2Erelation_2ERUNIV A_27a) A_27b))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27b)))) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (and (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) V0R)) (= V0R _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V0R)) _let_1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.c_2Erelation_2EEMPTY__REL A_27a))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)))) (let ((_let_3 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_3 (@ _let_3 tptp.bool))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) V0R)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 V0R)) _let_1)) (= V0R _let_1)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERRESTRICT A_27a) A_27b)) V0R)) V1s)) V2x)) V3y)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1R $$unsorted)) (=> (@ (@ tptp.mem V1R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM A_27a) A_27b)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERRESTRICT A_27a) A_27b)) V1R)) V2s)))) (and (@ tptp.p (@ _let_1 (@ _let_2 V1R))) (@ tptp.p (@ _let_1 V2s)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2u $$unsorted)) (=> (@ (@ tptp.mem V2u) A_27a) (forall ((V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM__DELETE A_27a) A_27b)) V0R)) V1x)) V2u)) V3v)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2u)) V3v)) (not (= V2u V1x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1R $$unsorted)) (=> (@ (@ tptp.mem V1R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2k $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (=> (@ (@ tptp.mem V2k) A_27a) (= (@ tptp.p (@ _let_2 (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERDOM__DELETE A_27a) A_27b)) V1R)) V2k)))) (and (@ tptp.p (@ _let_2 (@ _let_1 V1R))) (not (= V0x V2k)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ediamond A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V0R) V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ _let_1 V2y)) (@ tptp.p (@ _let_1 V3z))) (exists ((V4u $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (and (@ (@ tptp.mem V4u) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V4u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3z)) V4u))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ercdiamond A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V0R) V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ _let_1 V2y)) (@ tptp.p (@ _let_1 V3z))) (exists ((V4u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)))) (and (@ (@ tptp.mem V4u) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V4u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3z)) V4u))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2ECR A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ediamond A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWCR A_27a)) V0R)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V0R) V1x)))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ _let_1 V2y)) (@ tptp.p (@ _let_1 V3z))) (exists ((V4u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)))) (and (@ (@ tptp.mem V4u) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) V4u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3z)) V4u))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESN A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Enf A_27a) A_27b)) V0R)) V1x)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ercdiamond A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ediamond A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Ediamond A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ _let_1 V0R)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERC A_27a)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Erelation_2Ediamond A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ _let_1 V0R)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2ECR A_27a)) V0R)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_2 (@ _let_2 tptp.bool))) (and (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ercdiamond A_27a)) V0R)) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ediamond A_27a)) V0R)) _let_1)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWCR A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2ESN A_27a)) V0R))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2ECR A_27a)) V0R)))))))
% 1.89/2.21 (declare-fun tptp.ty_2Eoption_2Eoption (tptp.del) tptp.del)
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EIS__NONE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EIS__NONE A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EIS__SOME (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EIS__SOME A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2ENONE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2ENONE A_27a)) (@ tptp.ty_2Eoption_2Eoption A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__ALL (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EOPTION__ALL A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__APPLY (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTION__APPLY A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption (@ (@ tptp.arr A_27b) A_27a))) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27b)) (@ tptp.ty_2Eoption_2Eoption A_27a))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__BIND (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) _let_1)) _let_1))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__CHOICE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EOPTION__CHOICE A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.21 (declare-sort tptp.tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone 0)
% 1.89/2.21 (declare-fun tptp.inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (tptp.tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone) $$unsorted)
% 1.89/2.21 (declare-fun tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone ($$unsorted) tptp.tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone)
% 1.89/2.21 (assert (forall ((X tptp.tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone)) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ tptp.inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone X)) X)))
% 1.89/2.21 (assert (forall ((X tptp.tp__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone)) (@ (@ tptp.mem (@ tptp.inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone X)) (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Eone_2Eone))))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Eone_2Eone)) (= X (@ tptp.inj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone X))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__GUARD () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Eoption_2EOPTION__GUARD) (@ (@ tptp.arr tptp.bool) (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Eone_2Eone))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__IGNORE__BIND (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTION__IGNORE__BIND A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27b)) (@ (@ tptp.arr _let_1) _let_1))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__JOIN (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption _let_1)) _let_1)))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__MAP (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.ty_2Eoption_2Eoption A_27b))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__MAP2 (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27c)) (@ tptp.ty_2Eoption_2Eoption A_27a)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTION__MCOMP (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.arr A_27c))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Eoption_2EOPTION__MCOMP A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) _let_1)) (@ (@ tptp.arr (@ _let_2 (@ tptp.ty_2Eoption_2Eoption A_27b))) (@ _let_2 _let_1))))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2EOPTREL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27b)) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2ESOME (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27a)))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2ETHE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2Eoption__ABS (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2Eoption__ABS A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) tptp.ty_2Eone_2Eone)) (@ tptp.ty_2Eoption_2Eoption A_27a)))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2Eoption__CASE (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) A_27b))))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2Eoption__REP (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2Eoption__REP A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ (@ tptp.ty_2Esum_2Esum A_27a) tptp.ty_2Eone_2Eone)))))
% 1.89/2.21 (declare-fun tptp.c_2Eoption_2Esome (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eoption_2Esome A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.ty_2Eoption_2Eoption A_27a)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (exists ((V0rep $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) tptp.ty_2Eone_2Eone))) (let ((_let_2 (@ tptp.ty_2Eoption_2Eoption A_27a))) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr _let_2) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION _let_1) _let_2)) (@ (@ tptp.lam _let_1) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2ET)))) V0rep))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2Eoption__ABS A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2Eoption__REP A_27a)) V0a)) V0a))) (forall ((V1r $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) tptp.ty_2Eone_2Eone))) (=> (@ (@ tptp.mem V1r) _let_1) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.lam _let_1) (lambda ((V2x $$unsorted)) tptp.c_2Ebool_2ET))) V1r)) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2Eoption__REP A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2Eoption__ABS A_27a)) V1r)) V1r))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0x) (@ (@ tptp.ap (@ tptp.c_2Eoption_2Eoption__ABS A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) tptp.ty_2Eone_2Eone)) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Eoption_2ENONE A_27a) (@ (@ tptp.ap (@ tptp.c_2Eoption_2Eoption__ABS A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) tptp.ty_2Eone_2Eone)) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27b) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (exists ((V2fn $$unsorted)) (and (@ (@ tptp.mem V2fn) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) A_27b)) (= (@ (@ tptp.ap V2fn) (@ tptp.c_2Eoption_2ENONE A_27a)) V0e) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ (@ tptp.ap V2fn) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x)) (@ (@ tptp.ap V1f) V3x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Eoption_2ENONE A_27a))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1a)))))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0opt $$unsorted)) (=> (@ (@ tptp.mem V0opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (or (= V0opt (@ tptp.c_2Eoption_2ENONE A_27a)) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (= V0opt (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0v $$unsorted)) (=> (@ (@ tptp.mem V0v) A_27b) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ tptp.c_2Eoption_2ENONE A_27a))) V0v)) V1f) V0v))))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27b) (forall ((V4f $$unsorted)) (=> (@ (@ tptp.mem V4f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))) V3v)) V4f) (@ (@ tptp.ap V4f) V2x)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)) (= (forall ((V1opt $$unsorted)) (=> (@ (@ tptp.mem V1opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V1opt)))) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Eoption_2ENONE A_27a))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)) (= (exists ((V1opt $$unsorted)) (and (@ (@ tptp.mem V1opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V1opt)))) (or (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Eoption_2ENONE A_27a))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)))) (=> (@ (@ tptp.mem V1y) A_27a) (= (= (@ _let_1 V0x) (@ _let_1 V1y)) (= V0x V1y))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (not (= (@ tptp.c_2Eoption_2ENONE A_27a) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (not (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0x) (@ tptp.c_2Eoption_2ENONE A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V0f)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1x)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) (@ (@ tptp.ap V0f) V1x))))))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V2f)) (@ tptp.c_2Eoption_2ENONE A_27a)) (@ tptp.c_2Eoption_2ENONE A_27b)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0x))) true))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) (@ tptp.c_2Eoption_2ENONE A_27a))) false))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0x))) false))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) (@ tptp.c_2Eoption_2ENONE A_27a))) true))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0x)) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27b)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) (@ tptp.ty_2Eoption_2Eoption A_27c)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)) V1x)) V2y) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27b)) V1x))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27c)) V2y)))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27b)) V1x))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27c)) V2y))))) (@ tptp.c_2Eoption_2ENONE A_27a))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ tptp.c_2Eoption_2ENONE (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ tptp.c_2Eoption_2ENONE A_27a)) (forall ((V0x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V0x) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME _let_1)) V0x)) V0x)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2ENONE A_27a))) (let ((_let_2 (@ tptp.c_2Eoption_2ENONE A_27c))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27a) A_27b) A_27c)) V0f)))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.c_2Eoption_2ENONE A_27b))))) (let ((_let_5 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27c)) V2y))) (let ((_let_6 (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V1x))))) (=> (@ (@ tptp.mem V2y) A_27c) (and (= (@ _let_6 _let_5) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V1x)) V2y))) (= (@ _let_6 _let_2) _let_1) (= (@ _let_4 _let_5) _let_1) (= (@ _let_4 _let_2) _let_1)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0opt $$unsorted)) (=> (@ (@ tptp.mem V0opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V0opt)) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (= V0opt (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) V0x)) (= V0x (@ tptp.c_2Eoption_2ENONE A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V0x))) (= V0x (@ tptp.c_2Eoption_2ENONE A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V0x) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V0x)) (@ tptp.c_2Eoption_2ENONE A_27a))) (@ tptp.c_2Eoption_2ESOME A_27a)) V0x)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V0x) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V0x)) V0x)) (@ tptp.c_2Eoption_2ESOME A_27a)) V0x)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27b) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2e $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2ENONE A_27a))) (let ((_let_2 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V2e) _let_2) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)))) (=> (@ (@ tptp.mem V4y) A_27a) (= (= (@ _let_1 V3x) (@ _let_1 V4y)) (= V3x V4y))))))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V5x)) V5x))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (not (= (@ tptp.c_2Eoption_2ENONE A_27a) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V6x))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (not (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V7x) (@ tptp.c_2Eoption_2ENONE A_27a))))) (forall ((V8x $$unsorted)) (=> (@ (@ tptp.mem V8x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V8x))) true))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) _let_1)) false) (forall ((V9x $$unsorted)) (=> (@ (@ tptp.mem V9x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) V9x)) (= V9x (@ tptp.c_2Eoption_2ENONE A_27a))))) (forall ((V10x $$unsorted)) (=> (@ (@ tptp.mem V10x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V10x))) (= V10x (@ tptp.c_2Eoption_2ENONE A_27a))))) (forall ((V11x $$unsorted)) (=> (@ (@ tptp.mem V11x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V11x)) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) V11x)) V11x)))) (forall ((V12x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V12x) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V12x)) (@ tptp.c_2Eoption_2ENONE A_27a))) (@ tptp.c_2Eoption_2ESOME A_27a)) V12x)))) (forall ((V13x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V13x) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V13x)) V13x)) (@ tptp.c_2Eoption_2ESOME A_27a)) V13x)))) (forall ((V14x $$unsorted)) (=> (@ (@ tptp.mem V14x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) V14x)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) V14x)) V0e)) V1f) V0e)))) (forall ((V15x $$unsorted)) (=> (@ (@ tptp.mem V15x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V15x)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) V15x)) V0e)) V1f) (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) V15x)))))) (forall ((V16x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V16x) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V16x)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V16x)) V2e)) (@ tptp.c_2Eoption_2ESOME A_27a)) V16x))))) (forall ((V17v $$unsorted)) (=> (@ (@ tptp.mem V17v) A_27b) (forall ((V18f $$unsorted)) (=> (@ (@ tptp.mem V18f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ tptp.c_2Eoption_2ENONE A_27a))) V17v)) V18f) V17v))))) (forall ((V19x $$unsorted)) (=> (@ (@ tptp.mem V19x) A_27a) (forall ((V20v $$unsorted)) (=> (@ (@ tptp.mem V20v) A_27b) (forall ((V21f $$unsorted)) (=> (@ (@ tptp.mem V21f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V19x))) V20v)) V21f) (@ (@ tptp.ap V21f) V19x)))))))) (forall ((V22f $$unsorted)) (=> (@ (@ tptp.mem V22f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V23x $$unsorted)) (=> (@ (@ tptp.mem V23x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V22f)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V23x)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) (@ (@ tptp.ap V22f) V23x))))))) (forall ((V24f $$unsorted)) (=> (@ (@ tptp.mem V24f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V24f)) (@ tptp.c_2Eoption_2ENONE A_27a)) (@ tptp.c_2Eoption_2ENONE A_27b)))) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ tptp.c_2Eoption_2ENONE _let_2)) _let_1) (forall ((V25x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V25x) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME _let_1)) V25x)) V25x))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27b) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) V0x)) V1e)) V2f) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V0x))) (@ (@ tptp.ap V2f) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) V0x)))) V1e)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (= V1x V2y))) (let ((_let_2 (@ tptp.p V0P))) (let ((_let_3 (not _let_2))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)))) (let ((_let_5 (@ _let_4 V2y))) (let ((_let_6 (@ _let_4 V1x))) (let ((_let_7 (@ tptp.c_2Eoption_2ENONE A_27a))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) V0P)))) (let ((_let_9 (@ (@ tptp.ap (@ _let_8 _let_7)) _let_6))) (let ((_let_10 (@ (@ tptp.ap (@ _let_8 _let_6)) _let_7))) (=> (@ (@ tptp.mem V2y) A_27a) (and (= (= _let_10 _let_7) _let_3) (= (= _let_9 _let_7) _let_2) (= (= _let_10 _let_5) (and _let_2 _let_1)) (= (= _let_9 _let_5) (and _let_3 _let_1))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))) (let ((_let_2 (= V1X _let_1))) (let ((_let_3 (@ tptp.p V0P))) (let ((_let_4 (@ tptp.c_2Eoption_2ENONE A_27a))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) V0P)))) (let ((_let_6 (@ (@ tptp.ap (@ _let_5 _let_4)) V1X))) (let ((_let_7 (@ (@ tptp.ap (@ _let_5 V1X)) _let_4))) (=> (@ (@ tptp.mem V2x) A_27a) (and (= (= _let_7 _let_4) (=> _let_3 (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__NONE A_27a)) V1X)))) (= (= _let_6 _let_4) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V1X)) _let_3)) (= (= _let_7 _let_1) (and _let_3 _let_2)) (= (= _let_6 _let_1) (and (not _let_3) _let_2)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V0f)) V1x) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V2y)) (exists ((V3z $$unsorted)) (and (@ (@ tptp.mem V3z) A_27a) (= V1x (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3z)) (= V2y (@ (@ tptp.ap V0f) V3z))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V0f)) V1x) (@ tptp.c_2Eoption_2ENONE A_27b)) (= V1x (@ tptp.c_2Eoption_2ENONE A_27a))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V1x $$unsorted)) (let ((_let_1 (= V1x (@ tptp.c_2Eoption_2ENONE A_27b)))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27b) A_27a)) V0f)) V1x))) (let ((_let_3 (@ tptp.c_2Eoption_2ENONE A_27a))) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27b)) (and (= (= _let_2 _let_3) _let_1) (= (= _let_3 _let_2) _let_1))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27c) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2EOPTION__MAP A_27a))) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27c) A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) V1g)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27b) A_27c)) V0f)) V1g))) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0opt1 $$unsorted)) (=> (@ (@ tptp.mem V0opt1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1opt2 $$unsorted)) (=> (@ (@ tptp.mem V1opt2) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2f1 $$unsorted)) (=> (@ (@ tptp.mem V2f1) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V3f2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)))) (=> (@ (@ tptp.mem V3f2) (@ (@ tptp.arr A_27a) A_27b)) (=> (and (= V0opt1 V1opt2) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (= V1opt2 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V4x)) (= (@ (@ tptp.ap V2f1) V4x) (@ (@ tptp.ap V3f2) V4x)))))) (= (@ (@ tptp.ap (@ _let_1 V2f1)) V0opt1) (@ (@ tptp.ap (@ _let_1 V3f2)) V1opt2)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V0f)) V1x))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eoption_2Eoption (@ tptp.ty_2Eoption_2Eoption A_27a))) (forall ((V1y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1y))) (=> (@ (@ tptp.mem V1y) A_27a) (= (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__JOIN A_27a)) V0x) _let_1) (= V0x (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME (@ tptp.ty_2Eoption_2Eoption A_27a))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1o1 $$unsorted)) (=> (@ (@ tptp.mem V1o1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2o2 $$unsorted)) (=> (@ (@ tptp.mem V2o2) (@ tptp.ty_2Eoption_2Eoption A_27b)) (forall ((V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27c) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27c) A_27a) A_27b)) V0f)) V1o1)) V2o2) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27c)) V3v)) (exists ((V4x1 $$unsorted)) (and (@ (@ tptp.mem V4x1) A_27a) (exists ((V5x2 $$unsorted)) (and (@ (@ tptp.mem V5x2) A_27b) (= V1o1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V4x1)) (= V2o2 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V5x2)) (= V3v (@ (@ tptp.ap (@ (@ tptp.ap V0f) V4x1)) V5x2))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1o1 $$unsorted)) (=> (@ (@ tptp.mem V1o1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2o2 $$unsorted)) (=> (@ (@ tptp.mem V2o2) (@ tptp.ty_2Eoption_2Eoption A_27b)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27c) A_27a) A_27b)) V0f)) V1o1)) V2o2) (@ tptp.c_2Eoption_2ENONE A_27c)) (or (= V1o1 (@ tptp.c_2Eoption_2ENONE A_27a)) (= V2o2 (@ tptp.c_2Eoption_2ENONE A_27b)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0x1 $$unsorted)) (=> (@ (@ tptp.mem V0x1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1x2 $$unsorted)) (=> (@ (@ tptp.mem V1x2) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2y1 $$unsorted)) (=> (@ (@ tptp.mem V2y1) (@ tptp.ty_2Eoption_2Eoption A_27b)) (forall ((V3y2 $$unsorted)) (=> (@ (@ tptp.mem V3y2) (@ tptp.ty_2Eoption_2Eoption A_27b)) (forall ((V4f1 $$unsorted)) (=> (@ (@ tptp.mem V4f1) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V5f2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27c) A_27a) A_27b)))) (=> (@ (@ tptp.mem V5f2) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (=> (and (= V0x1 V1x2) (= V2y1 V3y2) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27b) (=> (and (= V1x2 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V6x)) (= V3y2 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V7y))) (= (@ (@ tptp.ap (@ (@ tptp.ap V4f1) V6x)) V7y) (@ (@ tptp.ap (@ (@ tptp.ap V5f2) V6x)) V7y)))))))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V4f1)) V0x1)) V2y1) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V5f2)) V1x2)) V3y2)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27b))) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) A_27b)) V0f)) V1x) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) _let_1)) V1x)) (@ tptp.c_2Eoption_2ENONE A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) _let_1) A_27b)) (@ tptp.c_2Eoption_2ESOME A_27b))) V0f)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ tptp.ty_2Eoption_2Eoption A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27a) A_27b)) (@ tptp.c_2Eoption_2ENONE A_27b))) V0f) (@ tptp.c_2Eoption_2ENONE A_27a)))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27b) (@ tptp.ty_2Eoption_2Eoption A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V1x))) V2f) (@ (@ tptp.ap V2f) V1x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0o1 $$unsorted)) (=> (@ (@ tptp.mem V0o1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1o2 $$unsorted)) (=> (@ (@ tptp.mem V1o2) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2f1 $$unsorted)) (=> (@ (@ tptp.mem V2f1) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27b))) (forall ((V3f2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27b) A_27a)))) (=> (@ (@ tptp.mem V3f2) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27b))) (=> (and (= V0o1 V1o2) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (= V1o2 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V4x)) (= (@ (@ tptp.ap V2f1) V4x) (@ (@ tptp.ap V3f2) V4x)))))) (= (@ (@ tptp.ap (@ _let_1 V0o1)) V2f1) (@ (@ tptp.ap (@ _let_1 V1o2)) V3f2)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27b))) (forall ((V2y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27b) A_27a)) V0p)) V1f))) (=> (@ (@ tptp.mem V2y) A_27b) (and (= (= _let_1 (@ tptp.c_2Eoption_2ENONE A_27b)) (or (= V0p (@ tptp.c_2Eoption_2ENONE A_27a)) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (= V0p (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x)) (= (@ (@ tptp.ap V1f) V3x) (@ tptp.c_2Eoption_2ENONE A_27b)))))) (= (= _let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V2y)) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (= V0p (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V4x)) (= (@ (@ tptp.ap V1f) V4x) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V2y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27b))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27b) A_27a)) V0x)) V1g))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eoption_2EIS__SOME A_27a)) V0x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0m1 $$unsorted)) (=> (@ (@ tptp.mem V0m1) (@ tptp.ty_2Eoption_2Eoption A_27b)) (forall ((V1m2 $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V1m2) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__IGNORE__BIND A_27a) A_27b)) V0m1)) V1m2) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27a) A_27b)) V0m1)) (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK _let_1) A_27b)) V1m2)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0m $$unsorted)) (=> (@ (@ tptp.mem V0m) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1v $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2EOPTION__IGNORE__BIND A_27a))) (=> (@ (@ tptp.mem V1v) A_27c) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) (@ tptp.c_2Eoption_2ENONE A_27b))) V0m) (@ tptp.c_2Eoption_2ENONE A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27c)) V1v))) V0m) V0m))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0m1 $$unsorted)) (=> (@ (@ tptp.mem V0m1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1m2 $$unsorted)) (=> (@ (@ tptp.mem V1m2) (@ tptp.ty_2Eoption_2Eoption A_27b)) (forall ((V2y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__IGNORE__BIND A_27b) A_27a)) V0m1)) V1m2))) (let ((_let_2 (@ tptp.c_2Eoption_2ENONE A_27b))) (=> (@ (@ tptp.mem V2y) A_27b) (and (= (= _let_1 _let_2) (or (= V0m1 (@ tptp.c_2Eoption_2ENONE A_27a)) (= V1m2 _let_2))) (= (= _let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V2y)) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (= V0m1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x)) (= V1m2 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V2y)))))))))))))))
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.ap tptp.c_2Eoption_2EOPTION__GUARD))) (and (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ _let_1 tptp.c_2Ebool_2ET)) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Eone_2Eone)) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone)))) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ _let_1 tptp.c_2Ebool_2EF)) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ tptp.c_2Eoption_2ENONE tptp.ty_2Eone_2Eone))))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ (@ tptp.ap tptp.c_2Eoption_2EOPTION__GUARD) V0b)) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Eone_2Eone))) V0b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Eone_2Eone)) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone)))) (@ tptp.c_2Eoption_2ENONE tptp.ty_2Eone_2Eone)))))))
% 1.89/2.21 (assert (forall ((V0b $$unsorted)) (let ((_let_1 (@ tptp.p V0b))) (let ((_let_2 (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ (@ tptp.ap tptp.c_2Eoption_2EOPTION__GUARD) V0b)))) (=> (@ (@ tptp.mem V0b) tptp.bool) (and (= (= _let_2 (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Eone_2Eone)) (@ tptp.inj__ty_2Eone_2Eone tptp.fo__c_2Eone_2Eone)))) _let_1) (= (= _let_2 (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Eone_2Eone (@ tptp.c_2Eoption_2ENONE tptp.ty_2Eone_2Eone))) (not _let_1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0m2 $$unsorted)) (=> (@ (@ tptp.mem V0m2) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__CHOICE A_27a)) (@ tptp.c_2Eoption_2ENONE A_27a))) V0m2) V0m2))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2m2 $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1x))) (=> (@ (@ tptp.mem V2m2) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__CHOICE A_27a)) _let_1)) V2m2) _let_1)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0m1 $$unsorted)) (=> (@ (@ tptp.mem V0m1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1m2 $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2ENONE A_27a))) (=> (@ (@ tptp.mem V1m2) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__CHOICE A_27a)) V0m1)) V1m2) _let_1) (and (= V0m1 _let_1) (= V1m2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0m1 $$unsorted)) (=> (@ (@ tptp.mem V0m1) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__CHOICE A_27a)) V0m1)) (@ tptp.c_2Eoption_2ENONE A_27a)) V0m1))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0g $$unsorted)) (=> (@ (@ tptp.mem V0g) (@ (@ tptp.arr A_27b) (@ tptp.ty_2Eoption_2Eoption A_27a))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27c) (@ tptp.ty_2Eoption_2Eoption A_27b))) (forall ((V2m $$unsorted)) (=> (@ (@ tptp.mem V2m) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MCOMP A_27a) A_27b) A_27c)) V0g)) V1f)) V2m) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__BIND A_27a) A_27b)) (@ (@ tptp.ap V1f) V2m))) V0g)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27d) (@ tptp.ty_2Eoption_2Eoption A_27c))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) (@ tptp.ty_2Eoption_2Eoption A_27d))) (forall ((V2h $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2EOPTION__MCOMP A_27c))) (let ((_let_2 (@ _let_1 A_27d))) (=> (@ (@ tptp.mem V2h) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27b))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27a)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MCOMP A_27d) A_27b) A_27a)) V1g)) V2h)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_1 A_27b) A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27b)) V0f)) V1g))) V2h)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0g $$unsorted)) (=> (@ (@ tptp.mem V0g) (@ (@ tptp.arr A_27c) (@ tptp.ty_2Eoption_2Eoption A_27d))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ tptp.ty_2Eoption_2Eoption A_27b))) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MCOMP A_27d) A_27c) A_27c)) V0g)) (@ tptp.c_2Eoption_2ESOME A_27c)) V0g) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MCOMP A_27b) A_27b) A_27a)) (@ tptp.c_2Eoption_2ESOME A_27b))) V1f) V1f)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eoption_2Eoption A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY A_27a) A_27b)) (@ tptp.c_2Eoption_2ENONE (@ (@ tptp.arr A_27b) A_27a)))) V0x) (@ tptp.c_2Eoption_2ENONE A_27a)))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME (@ (@ tptp.arr A_27b) A_27a))) V1f))) V2x) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27b) A_27a)) V1f)) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) (@ tptp.ty_2Eoption_2Eoption A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY A_27c) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__MAP A_27a) (@ (@ tptp.arr A_27b) A_27c))) V0f)) V1x))) V2y) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eoption_2EOPTION__MAP2 A_27c) A_27a) A_27b)) V0f)) V1x)) V2y)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY A_27a) A_27b)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME (@ (@ tptp.arr A_27b) A_27a))) V0f))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V1x)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap V0f) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ tptp.ty_2Eoption_2Eoption (@ (@ tptp.arr A_27a) A_27b))) (forall ((V1x $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (let ((_let_2 (@ tptp.c_2Eoption_2EOPTION__APPLY A_27b))) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27a)) V0f)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 _let_1)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME (@ (@ tptp.arr _let_1) A_27b))) (@ (@ tptp.lam _let_1) (lambda ((V2f $$unsorted)) (@ (@ tptp.ap V2f) V1x)))))) V0f)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ tptp.ty_2Eoption_2Eoption (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ tptp.ty_2Eoption_2Eoption (@ (@ tptp.arr A_27a) A_27b))) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.c_2Eoption_2EOPTION__APPLY A_27c))) (let ((_let_2 (@ tptp.arr A_27a))) (let ((_let_3 (@ _let_2 A_27c))) (let ((_let_4 (@ _let_2 A_27b))) (let ((_let_5 (@ (@ tptp.arr _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.arr A_27b) A_27c))) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY _let_3) _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY _let_5) _let_6)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME (@ (@ tptp.arr _let_6) _let_5))) (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)))) V0f))) V1g))) V2x) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTION__APPLY A_27b) A_27a)) V1g)) V2x))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) (@ tptp.ty_2Eoption_2Eoption A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27b)) V0R)) V1x)) V2y)) (or (and (= V1x (@ tptp.c_2Eoption_2ENONE A_27a)) (= V2y (@ tptp.c_2Eoption_2ENONE A_27b))) (exists ((V3x0 $$unsorted)) (and (@ (@ tptp.mem V3x0) A_27a) (exists ((V4y0 $$unsorted)) (and (@ (@ tptp.mem V4y0) A_27b) (= V1x (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x0)) (= V2y (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27b)) V4y0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x0)) V4y0)))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27b)))) (=> (@ (@ tptp.mem V3y) (@ tptp.ty_2Eoption_2Eoption A_27b)) (=> (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1Q) V4x)) V5y))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V2x)) V3y))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V1x)))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2EOPTREL A_27a) A_27a)) V0R)) V2x)) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2Esome A_27a)) V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ _let_1 (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0P) V1x)))))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V0P) V2x))))))) (@ tptp.c_2Eoption_2ENONE A_27a)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.ap V1Q))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x)))))) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (not (@ tptp.p (@ (@ tptp.ap V0P) V3x))))) (@ tptp.p (@ _let_1 (@ tptp.c_2Eoption_2ENONE A_27a))))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2Esome A_27a)) V0P))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0Q $$unsorted)) (=> (@ (@ tptp.mem V0Q) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.ap V0Q))) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2Esome A_27a)) V1P))) (or (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V1P) V2x)) (@ tptp.p (@ (@ tptp.ap V0Q) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))))) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (not (@ tptp.p (@ (@ tptp.ap V1P) V3x))))) (@ tptp.p (@ _let_1 (@ tptp.c_2Eoption_2ENONE A_27a))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ tptp.c_2Eoption_2Esome A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2EF))) (@ tptp.c_2Eoption_2ENONE A_27a))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V0y))) (let ((_let_2 (@ tptp.lam A_27a))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Eoption_2Esome A_27a)))) (=> (@ (@ tptp.mem V0y) A_27a) (and (= (@ _let_3 (@ _let_2 (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V0y)))) _let_1) (= (@ _let_3 (@ _let_2 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V0y)) V2x)))) _let_1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0v_27 $$unsorted)) (=> (@ (@ tptp.mem V0v_27) A_27b) (forall ((V1f_27 $$unsorted)) (=> (@ (@ tptp.mem V1f_27) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2M $$unsorted)) (=> (@ (@ tptp.mem V2M) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V3M_27 $$unsorted)) (=> (@ (@ tptp.mem V3M_27) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V4v $$unsorted)) (=> (@ (@ tptp.mem V4v) A_27b) (forall ((V5f $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)))) (=> (@ (@ tptp.mem V5f) (@ (@ tptp.arr A_27a) A_27b)) (=> (and (= V2M V3M_27) (=> (= V3M_27 (@ tptp.c_2Eoption_2ENONE A_27a)) (= V4v V0v_27)) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (=> (= V3M_27 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V6x)) (= (@ (@ tptp.ap V5f) V6x) (@ (@ tptp.ap V1f_27) V6x)))))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2M)) V4v)) V5f) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V3M_27)) V0v_27)) V1f_27)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__ALL A_27a)) V0P)) (@ tptp.c_2Eoption_2ENONE A_27a))) true))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__ALL A_27a)) V1P)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))) (@ tptp.p (@ (@ tptp.ap V1P) V2x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2opt $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__ALL A_27a)))) (=> (@ (@ tptp.mem V2opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V3x)) (@ tptp.p (@ (@ tptp.ap V1P_27) V3x))))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0P)) V2opt)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1P_27)) V2opt))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0opt $$unsorted)) (=> (@ (@ tptp.mem V0opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1opt_27 $$unsorted)) (=> (@ (@ tptp.mem V1opt_27) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3P_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2EOPTION__ALL A_27a)))) (=> (@ (@ tptp.mem V3P_27) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (= V0opt V1opt_27) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (= V1opt_27 (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V4x)) (= (@ tptp.p (@ (@ tptp.ap V2P) V4x)) (@ tptp.p (@ (@ tptp.ap V3P_27) V4x))))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2P)) V0opt)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3P_27)) V1opt_27))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0opt $$unsorted)) (=> (@ (@ tptp.mem V0opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (forall ((V1nc $$unsorted)) (=> (@ (@ tptp.mem V1nc) A_27b) (forall ((V2sc $$unsorted)) (=> (@ (@ tptp.mem V2sc) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27b) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eoption_2Eoption__CASE A_27a) A_27b)) V0opt)) V1nc)) V2sc) V3v) (or (and (= V0opt (@ tptp.c_2Eoption_2ENONE A_27a)) (= V1nc V3v)) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (= V0opt (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V4x)) (= (@ (@ tptp.ap V2sc) V4x) V3v))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.bool)) (=> (and (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1a))))) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Eoption_2ENONE A_27a)))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) (@ tptp.ty_2Eoption_2Eoption A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0opt $$unsorted)) (=> (@ (@ tptp.mem V0opt) (@ tptp.ty_2Eoption_2Eoption A_27a)) (or (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (= V0opt (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V1x)))) (= V0opt (@ tptp.c_2Eoption_2ENONE A_27a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0option $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))) (=> (@ (@ tptp.mem V0option) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) _let_1)) A_27b))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2EDATATYPE A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap V0option) (@ tptp.c_2Eoption_2ENONE A_27a))) (@ tptp.c_2Eoption_2ESOME A_27a))))))))
% 1.89/2.21 (declare-fun tptp.ty_2Epair_2Eprod (tptp.del tptp.del) tptp.del)
% 1.89/2.21 (declare-fun tptp.c_2Epair_2E_23_23 (tptp.del tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del)) (@ (@ tptp.mem (@ (@ (@ (@ tptp.c_2Epair_2E_23_23 A_27a) A_27b) A_27c) A_27d)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27d)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ (@ tptp.ty_2Epair_2Eprod A_27c) A_27d)))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2E_2C (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2EABS__prod (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2EABS__prod A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2ECURRY (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Epair_2ECURRY A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2EFST (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27a))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2ELEX (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)))) (let ((_let_2 (@ tptp.arr A_27b))) (let ((_let_3 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) (@ (@ tptp.arr (@ _let_3 (@ _let_3 tptp.bool))) (@ (@ tptp.arr (@ _let_2 (@ _let_2 tptp.bool))) (@ _let_1 (@ _let_1 tptp.bool))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2EPROD__ALL (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2EPROD__ALL A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2EREP__prod (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2EREP__prod A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2ERPROD (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)))) (let ((_let_2 (@ tptp.arr A_27b))) (let ((_let_3 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2ERPROD A_27a) A_27b)) (@ (@ tptp.arr (@ _let_3 (@ _let_3 tptp.bool))) (@ (@ tptp.arr (@ _let_2 (@ _let_2 tptp.bool))) (@ _let_1 (@ _let_1 tptp.bool))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2ESND (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27b))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2ESWAP (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2ESWAP A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2EUNCURRY (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)))))
% 1.89/2.21 (declare-fun tptp.c_2Epair_2Epair__CASE (tptp.del tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Epair_2Epair__CASE A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) A_27a)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (exists ((V0rep $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr _let_2) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION _let_1) _let_2)) (@ (@ tptp.lam _let_1) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) V1p)) (@ (@ tptp.lam A_27a) (lambda ((V4a $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V5b $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4a)) V2x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V5b)) V3y))))))))))))))))) V0rep))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EABS__prod A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EREP__prod A_27a) A_27b)) V0a)) V0a))) (forall ((V1r $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) (=> (@ (@ tptp.mem V1r) _let_1) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.lam _let_1) (lambda ((V2p $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))) V2p)) (@ (@ tptp.lam A_27a) (lambda ((V5a $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V6b $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V5a)) V3x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V6b)) V4y)))))))))))))))) V1r)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EREP__prod A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EABS__prod A_27a) A_27b)) V1r)) V1r))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V1y) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EABS__prod A_27a) A_27b)) (@ (@ tptp.lam A_27a) (lambda ((V2a $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3b $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V2a)) V0x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V3b)) V1y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (forall ((V3b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))) (=> (@ (@ tptp.mem V3b) A_27b) (= (= (@ (@ tptp.ap (@ _let_1 V0x)) V1y) (@ (@ tptp.ap (@ _let_1 V2a)) V3b)) (and (= V0x V2a) (= V1y V3b)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (forall ((V3b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))) (=> (@ (@ tptp.mem V3b) A_27b) (= (= (@ (@ tptp.ap (@ _let_1 V0x)) V1y) (@ (@ tptp.ap (@ _let_1 V2a)) V3b)) (and (= V0x V2a) (= V1y V3b)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (exists ((V1q $$unsorted)) (and (@ (@ tptp.mem V1q) A_27a) (exists ((V2r $$unsorted)) (and (@ (@ tptp.mem V2r) A_27b) (= V0x (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1q)) V2r)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (exists ((V1q $$unsorted)) (and (@ (@ tptp.mem V1q) A_27a) (exists ((V2r $$unsorted)) (and (@ (@ tptp.mem V2r) A_27b) (= V0x (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1q)) V2r)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V0x))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V0x)) V0x))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V1y)) V0x))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V1y)) V1y))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)))) (=> (@ (@ tptp.mem V1q) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (= V0p V1q) (and (= (@ _let_2 V0p) (@ _let_2 V1q)) (= (@ _let_1 V0p) (@ _let_1 V1q)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESWAP A_27a) A_27b)) V0a) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27b) A_27a)) V0a))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27b) A_27a)) V0a))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2ECURRY A_27a) A_27b) A_27c)) V0f)) V1x)) V2y) (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) V0f)) V1v) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V1v))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V1v))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) V0f)) V1v) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V1v))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V1v))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (= (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) V0f) (@ (@ tptp.lam (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V1x))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V1x))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V1x)) V2y)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (= (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2ECURRY A_27a) A_27b) A_27c)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) V0f)) V0f))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) (= (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2ECURRY A_27a) A_27b) A_27c)) V0f)) V0f))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2ECURRY A_27a) A_27b) A_27c)))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) (= (= (@ _let_1 V0f) (@ _let_1 V1g)) (= V0f V1g))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (= (= (@ _let_1 V0f) (@ _let_1 V1g)) (= V0f V1g))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (exists ((V1fn $$unsorted)) (and (@ (@ tptp.mem V1fn) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (= (@ (@ tptp.ap V1fn) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2x)) V3y)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2x)) V3y)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f_27 $$unsorted)) (=> (@ (@ tptp.mem V0f_27) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (forall ((V2M_27 $$unsorted)) (=> (@ (@ tptp.mem V2M_27) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V3M $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)))) (=> (@ (@ tptp.mem V3M) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (=> (and (= V3M V2M_27) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27b) (=> (= V2M_27 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V4x)) V5y)) (= (@ (@ tptp.ap (@ (@ tptp.ap V1f) V4x)) V5y) (@ (@ tptp.ap (@ (@ tptp.ap V0f_27) V4x)) V5y)))))))) (= (@ (@ tptp.ap (@ _let_1 V1f)) V3M) (@ (@ tptp.ap (@ _let_1 V0f_27)) V2M_27)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr _let_1) A_27c)) (= (@ (@ tptp.lam _let_1) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap V0P) V1p))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) A_27c)) (@ (@ tptp.lam A_27a) (lambda ((V2p1 $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3p2 $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2p1)) V3p2))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (= (exists ((V1p $$unsorted)) (and (@ (@ tptp.mem V1p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap V0P) V1p)))) (exists ((V2p__1 $$unsorted)) (and (@ (@ tptp.mem V2p__1) A_27a) (exists ((V3p__2 $$unsorted)) (and (@ (@ tptp.mem V3p__2) A_27b) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2p__1)) V3p__2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (= (forall ((V1p $$unsorted)) (=> (@ (@ tptp.mem V1p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap V0P) V1p)))) (forall ((V2p__1 $$unsorted)) (=> (@ (@ tptp.mem V2p__1) A_27a) (forall ((V3p__2 $$unsorted)) (=> (@ (@ tptp.mem V3p__2) A_27b) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2p__1)) V3p__2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (=> (forall ((V1p__1 $$unsorted)) (=> (@ (@ tptp.mem V1p__1) A_27a) (forall ((V2p__2 $$unsorted)) (=> (@ (@ tptp.mem V2p__2) A_27b) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1p__1)) V2p__2))))))) (forall ((V3p $$unsorted)) (=> (@ (@ tptp.mem V3p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap V0P) V3p))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EPROD__ALL A_27a) A_27b)) V0P)) V1Q)) V2p)) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V2p))) (@ tptp.p (@ (@ tptp.ap V1Q) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V2p))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EPROD__ALL A_27a) A_27b)) V0P)) V1Q)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2x)) V3y))) (and (@ tptp.p (@ (@ tptp.ap V0P) V2x)) (@ tptp.p (@ (@ tptp.ap V1Q) V3y)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P_27 $$unsorted)) (=> (@ (@ tptp.mem V1P_27) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V3Q_27 $$unsorted)) (=> (@ (@ tptp.mem V3Q_27) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V4p $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2EPROD__ALL A_27a) A_27b)))) (=> (@ (@ tptp.mem V4p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (=> (and (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V5x)) (@ tptp.p (@ (@ tptp.ap V1P_27) V5x))))) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap V2Q) V6y)) (@ tptp.p (@ (@ tptp.ap V3Q_27) V6y)))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2Q)) V4p)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1P_27)) V3Q_27)) V4p))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V1p_27 $$unsorted)) (=> (@ (@ tptp.mem V1p_27) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3P_27 $$unsorted)) (=> (@ (@ tptp.mem V3P_27) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4Q $$unsorted)) (=> (@ (@ tptp.mem V4Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V5Q_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2EPROD__ALL A_27a) A_27b)))) (=> (@ (@ tptp.mem V5Q_27) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (= V0p V1p_27) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27b) (=> (= V1p_27 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V6x)) V7y)) (= (@ tptp.p (@ (@ tptp.ap V2P) V6x)) (@ tptp.p (@ (@ tptp.ap V3P_27) V6x)))))))) (forall ((V8x $$unsorted)) (=> (@ (@ tptp.mem V8x) A_27a) (forall ((V9y $$unsorted)) (=> (@ (@ tptp.mem V9y) A_27b) (=> (= V1p_27 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V8x)) V9y)) (= (@ tptp.p (@ (@ tptp.ap V4Q) V9y)) (@ tptp.p (@ (@ tptp.ap V5Q_27) V9y))))))))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2P)) V4Q)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V3P_27)) V5Q_27)) V1p_27))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (exists ((V1p $$unsorted)) (and (@ (@ tptp.mem V1p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V1p))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V1p))))) (exists ((V2p1 $$unsorted)) (and (@ (@ tptp.mem V2p1) A_27a) (exists ((V3p2 $$unsorted)) (and (@ (@ tptp.mem V3p2) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V2p1)) V3p2))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (forall ((V1p $$unsorted)) (=> (@ (@ tptp.mem V1p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V1p))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V1p))))) (forall ((V2p1 $$unsorted)) (=> (@ (@ tptp.mem V2p1) A_27a) (forall ((V3p2 $$unsorted)) (=> (@ (@ tptp.mem V3p2) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V2p1)) V3p2))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1x)) V2y)))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0P) V3x)) V4y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1x)) V2y)))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0P) V3x)) V4y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0P) V1x)))))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.ap V0P) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0P) V1x)))))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.ap V0P) V2x)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27d)) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Epair_2E_23_23 A_27a) A_27b) A_27c) A_27d)) V0f)) V1g)) V2p) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27c) A_27d)) (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V2p)))) (@ (@ tptp.ap V1g) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V2p)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27c) A_27d)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27c) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Epair_2E_23_23 A_27a) A_27c) A_27b) A_27d)) V0f)) V1g)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27c)) V2x)) V3y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27d)) (@ (@ tptp.ap V0f) V2x))) (@ (@ tptp.ap V1g) V3y))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V2g $$unsorted)) (=> (@ (@ tptp.mem V2g) (@ (@ tptp.arr A_27b) A_27d)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27c) A_27d)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Epair_2E_23_23 A_27a) A_27b) A_27c) A_27d)) V1f)) V2g)) V0p)) (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V0p))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V2g $$unsorted)) (=> (@ (@ tptp.mem V2g) (@ (@ tptp.arr A_27b) A_27d)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27c) A_27d)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ (@ tptp.c_2Epair_2E_23_23 A_27a) A_27b) A_27c) A_27d)) V1f)) V2g)) V0p)) (@ (@ tptp.ap V2g) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V0p))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27c) A_27d)) (forall ((V1M $$unsorted)) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V2N $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b))) (let ((_let_3 (@ tptp.c_2Ebool_2ELET (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)))) (=> (@ (@ tptp.mem V2N) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (= (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 A_27c)) (@ (@ tptp.ap (@ _let_2 A_27c)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V2N) V3x)) V4y)))))))) V1M)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 A_27d)) (@ (@ tptp.ap (@ _let_2 A_27d)) (@ _let_1 (lambda ((V5x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V6y $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap V2N) V5x)) V6y))))))))) V1M))))))))))))
% 1.89/2.21 (assert (forall ((A_27a1 tptp.del) (A_27a2 tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0M $$unsorted)) (=> (@ (@ tptp.mem V0M) (@ (@ tptp.ty_2Epair_2Eprod A_27a1) A_27a2)) (forall ((V1N $$unsorted)) (=> (@ (@ tptp.mem V1N) (@ (@ tptp.arr A_27a1) (@ (@ tptp.arr A_27a2) (@ (@ tptp.arr A_27b) A_27c)))) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a1))) (let ((_let_2 (@ (@ tptp.c_2Epair_2EUNCURRY A_27a1) A_27a2))) (let ((_let_3 (@ tptp.c_2Ebool_2ELET (@ (@ tptp.ty_2Epair_2Eprod A_27a1) A_27a2)))) (let ((_let_4 (@ (@ tptp.arr A_27b) A_27c))) (=> (@ (@ tptp.mem V2b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_4)) (@ (@ tptp.ap (@ _let_2 _let_4)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.lam A_27a2) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V1N) V3x)) V4y)))))))) V0M)) V2b) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 A_27c)) (@ (@ tptp.ap (@ _let_2 A_27c)) (@ _let_1 (lambda ((V5x $$unsorted)) (@ (@ tptp.lam A_27a2) (lambda ((V6y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap V1N) V5x)) V6y)) V2b)))))))) V0M)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27d) A_27c)) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (let ((_let_2 (@ _let_1 A_27d))) (let ((_let_3 (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) _let_2)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27c) A_27d)) V0f)) (@ (@ tptp.ap (@ _let_3 A_27d)) V1g)) (@ (@ tptp.ap (@ _let_3 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) (@ _let_1 A_27c)) _let_2)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) A_27c) A_27d)) V0f))) V1g)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27d) A_27c)))) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27d))) (let ((_let_2 (@ _let_1 A_27c))) (let ((_let_3 (@ tptp.arr A_27b))) (let ((_let_4 (@ _let_3 A_27c))) (let ((_let_5 (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b))) (=> (@ (@ tptp.mem V1x) A_27d) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) A_27d) A_27c)) (@ (@ tptp.ap (@ _let_5 _let_2)) V0f))) V1x) (@ (@ tptp.ap (@ _let_5 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27d) _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) (@ _let_1 _let_4)) (@ _let_3 _let_2))) (@ (@ (@ tptp.c_2Ecombin_2EC A_27b) A_27d) A_27c))) V0f))) V1x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ (@ tptp.arr A_27d) A_27c))) (forall ((V1g $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (let ((_let_2 (@ (@ tptp.arr A_27d) A_27c))) (let ((_let_3 (@ tptp.arr A_27b))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.c_2Ecombin_2Eo A_27a))) (let ((_let_6 (@ _let_3 A_27c))) (let ((_let_7 (@ _let_3 A_27d))) (let ((_let_8 (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) _let_7)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES _let_1) A_27d) A_27c)) V0f)) (@ (@ tptp.ap (@ _let_8 A_27d)) V1g)) (@ (@ tptp.ap (@ _let_8 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) _let_7) _let_6)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_5 (@ (@ tptp.arr _let_7) _let_6)) _let_4)) (@ (@ (@ tptp.c_2Ecombin_2ES A_27b) A_27d) A_27c))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_5 _let_4) (@ _let_3 _let_1))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) _let_2) _let_1)) V0f))) (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b))))) V1g))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) V0f))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) tptp.bool) _let_1)) (@ tptp.c_2Ebool_2E_21 A_27b))) V0f))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod (@ _let_1 A_27b)) (@ _let_1 A_27c)))) (let ((_let_3 (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr _let_3) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 _let_3)) (@ (@ tptp.lam _let_3) (lambda ((V1f $$unsorted)) (@ (@ tptp.ap V0P) V1f))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 _let_2)) (@ (@ tptp.lam _let_2) (lambda ((V2p $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.lam A_27a) (lambda ((V3a $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27c))) (let ((_let_3 (@ _let_1 A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST _let_3) _let_2)) V2p)) V3a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND _let_3) _let_2)) V2p)) V3a)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2Epair__CASE A_27a) A_27b) A_27c)) V0p)) V1f) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27b) A_27c)) V0p))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27b) A_27c)) V0p))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27b) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27c) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2Epair__CASE A_27a) A_27b) A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27c)) V0x)) V1y))) V2f) (@ (@ tptp.ap (@ (@ tptp.ap V2f) V0x)) V1y)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27b) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27c) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2Epair__CASE A_27a) A_27b) A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27c)) V0x)) V1y))) V2f) (@ (@ tptp.ap (@ (@ tptp.ap V2f) V0x)) V1y)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f_27 $$unsorted)) (=> (@ (@ tptp.mem V0f_27) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (forall ((V1M $$unsorted)) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)) (forall ((V2M_27 $$unsorted)) (=> (@ (@ tptp.mem V2M_27) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)) (forall ((V3f $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2Epair__CASE A_27a) A_27b) A_27c)))) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (=> (and (= V1M V2M_27) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27b) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27c) (=> (= V2M_27 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27c)) V4x)) V5y)) (= (@ (@ tptp.ap (@ (@ tptp.ap V3f) V4x)) V5y) (@ (@ tptp.ap (@ (@ tptp.ap V0f_27) V4x)) V5y)))))))) (= (@ (@ tptp.ap (@ _let_1 V1M)) V3f) (@ (@ tptp.ap (@ _let_1 V2M_27)) V0f_27)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27c) A_27a))) (forall ((V2v $$unsorted)) (=> (@ (@ tptp.mem V2v) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2Epair__CASE A_27a) A_27b) A_27c)) V0p)) V1f) V2v) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27b) (exists ((V4y $$unsorted)) (and (@ (@ tptp.mem V4y) A_27c) (= V0p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27c)) V3x)) V4y)) (= (@ (@ tptp.ap (@ (@ tptp.ap V1f) V3x)) V4y) V2v)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0pair $$unsorted)) (=> (@ (@ tptp.mem V0pair) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)))) A_27c)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2EDATATYPE A_27c)) (@ (@ tptp.ap V0pair) (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R1)) V1R2) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V2s $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3t $$unsorted)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) (@ (@ tptp.lam A_27a) (lambda ((V4u $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V5v $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V2s)) V4u))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V2s)) V4u))) (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V3t)) V5v)))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (forall ((V3b $$unsorted)) (=> (@ (@ tptp.mem V3b) A_27b) (forall ((V4c $$unsorted)) (=> (@ (@ tptp.mem V4c) A_27a) (forall ((V5d $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))) (=> (@ (@ tptp.mem V5d) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R1)) V1R2)) (@ (@ tptp.ap (@ _let_1 V2a)) V3b))) (@ (@ tptp.ap (@ _let_1 V4c)) V5d))) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V2a)) V4c)) (and (= V2a V4c) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V3b)) V5d)))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2R3 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V2R3) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V3R4 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V3R4) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)))) (=> (@ (@ tptp.mem V5y) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (=> (and (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V6x)) V7y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V6x)) V7y))))))) (forall ((V8x $$unsorted)) (=> (@ (@ tptp.mem V8x) A_27b) (forall ((V9y $$unsorted)) (=> (@ (@ tptp.mem V9y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2R3) V8x)) V9y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3R4) V8x)) V9y)))))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R1)) V2R3)) V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1R2)) V3R4)) V4x)) V5y))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27b)) V1Q))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R)) V1Q)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ERPROD A_27a) A_27b)) V0R1)) V1R2) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V2s $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3t $$unsorted)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool)) (@ (@ tptp.lam A_27a) (lambda ((V4u $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V5v $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V2s)) V4u))) (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V3t)) V5v))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27b)) V1Q))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ERPROD A_27a) A_27b)) V0R)) V1Q)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etotal A_27a)) V0R1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etotal A_27b)) V1R2))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etotal (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R1)) V1R2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27b)) V1R2))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R1)) V1R2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R1)) V1R2))) (or (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27a)) V0R1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Ereflexive A_27b)) V1R2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27a)) V0R1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric A_27b)) V1R2))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Esymmetric (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)) V0R1)) V1R2)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R1 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R1) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1R2 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1R2) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2v1 $$unsorted)) (=> (@ (@ tptp.mem V2v1) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V3v2 $$unsorted)) (=> (@ (@ tptp.mem V3v2) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V4R1_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V4R1_27) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V5R2_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V5R2_27) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V6v1_27 $$unsorted)) (=> (@ (@ tptp.mem V6v1_27) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V7v2_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2ELEX A_27a) A_27b)))) (=> (@ (@ tptp.mem V7v2_27) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (=> (and (= V2v1 V6v1_27) (= V3v2 V7v2_27) (forall ((V8a $$unsorted)) (=> (@ (@ tptp.mem V8a) A_27a) (forall ((V9b $$unsorted)) (=> (@ (@ tptp.mem V9b) A_27b) (forall ((V10c $$unsorted)) (=> (@ (@ tptp.mem V10c) A_27a) (forall ((V11d $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))) (=> (@ (@ tptp.mem V11d) A_27b) (=> (and (= V6v1_27 (@ (@ tptp.ap (@ _let_1 V8a)) V9b)) (= V7v2_27 (@ (@ tptp.ap (@ _let_1 V10c)) V11d))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R1) V8a)) V10c)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V4R1_27) V8a)) V10c))))))))))))) (forall ((V12a $$unsorted)) (=> (@ (@ tptp.mem V12a) A_27a) (forall ((V13b $$unsorted)) (=> (@ (@ tptp.mem V13b) A_27b) (forall ((V14c $$unsorted)) (=> (@ (@ tptp.mem V14c) A_27a) (forall ((V15d $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))) (=> (@ (@ tptp.mem V15d) A_27b) (=> (and (= V6v1_27 (@ (@ tptp.ap (@ _let_1 V12a)) V13b)) (= V7v2_27 (@ (@ tptp.ap (@ _let_1 V14c)) V15d)) (= V12a V14c)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R2) V13b)) V15d)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V5R2_27) V13b)) V15d)))))))))))))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0R1)) V1R2)) V2v1)) V3v2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V4R1_27)) V5R2_27)) V6v1_27)) V7v2_27))))))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V0p) V1x) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (= V0p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27b) A_27a)) V0p) V1y) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27b) (= V0p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27a)) V2x)) V1y))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2E_3C () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Eprim__rec_2E_3C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2EPRE () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Eprim__rec_2EPRE) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Eprim__rec_2EPRE (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Eprim__rec_2EPRE X0)) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2EPRIM__REC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (let ((_let_2 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eprim__rec_2EPRIM__REC A_27a)) (@ _let_2 (@ (@ tptp.arr (@ _let_2 _let_1)) _let_1)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2EPRIM__REC__FUN (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 A_27a))) (let ((_let_3 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eprim__rec_2EPRIM__REC__FUN A_27a)) (@ _let_3 (@ (@ tptp.arr (@ _let_3 _let_2)) (@ _let_1 _let_2)))))))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2ESIMP__REC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eprim__rec_2ESIMP__REC A_27a)) (@ _let_1 (@ (@ tptp.arr (@ _let_1 A_27a)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2ESIMP__REC__REL (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eprim__rec_2ESIMP__REC__REL A_27a)) (@ (@ tptp.arr (@ _let_1 A_27a)) (@ _let_2 (@ (@ tptp.arr (@ _let_2 A_27a)) (@ _let_1 tptp.bool)))))))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2Emeasure (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eprim__rec_2Emeasure A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Enum_2Enum)) (@ _let_1 (@ _let_1 tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eprim__rec_2Ewellfounded (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eprim__rec_2Ewellfounded A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.bool))) tptp.bool)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) (exists ((V2P $$unsorted)) (let ((_let_1 (@ tptp.ap V2P))) (and (@ (@ tptp.mem V2P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.ap V2P))) (=> (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (@ tptp.p (@ _let_2 _let_1)))))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (not (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (= V0m V1n)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_2)) _let_1))) _let_1)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V1n))))))))))))
% 1.89/2.21 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0) (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0m)))) V0m))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.lam tptp.ty_2Enum_2Enum))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC tptp.ty_2Enum_2Enum)) (@ _let_3 (lambda ((V2x $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V3y)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V2x)))))))) _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC tptp.ty_2Enum_2Enum)) (@ _let_3 (lambda ((V4x $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V5y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V5y)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V4x)))))))) _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1m $$unsorted)) (=> (@ (@ tptp.mem V1m) A_27a) (forall ((V2n $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (=> (@ (@ tptp.mem V2n) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4y)) (@ (@ tptp.ap V0f) V3x)))))))) (@ (@ tptp.ap V0f) V1m))) V2n)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) (@ _let_1 (lambda ((V5x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V6y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V6y)) (@ (@ tptp.ap V0f) V5x)))))))) V1m)) V2n)))))))))))
% 1.89/2.21 (assert (= tptp.c_2Eprim__rec_2E_3C (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V1y)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V0x)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (=> (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (or (= V0m V1n) (@ tptp.p (@ _let_2 _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (=> (or (= V0m V1n) (@ tptp.p (@ _let_2 _let_1))) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (or (= V0m V1n) (@ tptp.p (@ _let_2 _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (=> (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (=> (not (= V0m V1n)) (@ tptp.p (@ _let_2 _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) V1n) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (not (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0n))) V0n))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (= V0m V1n) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) (not (= V0m V1n)))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0fun $$unsorted)) (=> (@ (@ tptp.mem V0fun) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC__REL A_27a)) V0fun)) V1x)) V2f)) (@ tptp.inj__ty_2Enum_2Enum V3n))) (and (= (@ (@ tptp.ap V0fun) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V1x) (forall ((V4m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4m))) (let ((_let_2 (@ tptp.ap V0fun))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V3n))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap V2f) (@ _let_2 _let_1)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (exists ((V3fun $$unsorted)) (and (@ (@ tptp.mem V3fun) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC__REL A_27a)) V3fun)) V0x)) V1f)) (@ tptp.inj__ty_2Enum_2Enum V2n)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2g1 $$unsorted)) (=> (@ (@ tptp.mem V2g1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V3g2 $$unsorted)) (=> (@ (@ tptp.mem V3g2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V4m1 tptp.tp__ty_2Enum_2Enum) (V5m2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC__REL A_27a)))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V2g1)) V0x)) V1f)) (@ tptp.inj__ty_2Enum_2Enum V4m1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V3g2)) V0x)) V1f)) (@ tptp.inj__ty_2Enum_2Enum V5m2)))) (forall ((V6n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)))) (=> (and (@ tptp.p (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V4m1))) (@ tptp.p (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V5m2)))) (= (@ (@ tptp.ap V2g1) _let_1) (@ (@ tptp.ap V3g2) _let_1))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3y $$unsorted)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V4g $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC__REL A_27a)) V4g)) V0x)) V1f)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3y)) (@ (@ tptp.ap V4g) _let_1))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f_27 $$unsorted)) (=> (@ (@ tptp.mem V1f_27) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (exists ((V3g $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC__REL A_27a)) V3g)) V0x)) V1f_27)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC A_27a)) V0x)) V1f_27)) _let_1) (@ (@ tptp.ap V3g) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)))) (and (@ tptp.p (@ _let_4 _let_3)) (@ tptp.p (@ _let_4 (@ _let_2 _let_3))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC A_27a)) V0x)) V1f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V0x) (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC A_27a)) V0x)) V1f)))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap V1f) (@ _let_2 _let_1))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) _let_1)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC__FUN A_27a)) V0x)) V1f) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2ESIMP__REC _let_1)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2n $$unsorted)) V0x)))) (@ (@ tptp.lam _let_1) (lambda ((V3fun $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ (@ tptp.ap V3fun) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) V4n)))) V4n)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (and (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC__FUN A_27a)) V0x)) V1f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V2n)) V0x)) (forall ((V3m tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3m))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC__FUN A_27a)) V0x)) V1f)))) (= (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)))) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC A_27a)) V0x)) V1f)) _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC__FUN A_27a)) V0x)) V1f)) _let_1)) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC A_27a)) V0x)) V1f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V0x) (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2EPRIM__REC A_27a)) V0x)) V1f)))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ _let_2 _let_1))) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) V2a)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V3x)) (exists ((V4y $$unsorted)) (and (@ (@ tptp.mem V4y) A_27a) (@ tptp.p (@ (@ tptp.ap V0P) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) V3x)) V4y)))))))) (exists ((V5f $$unsorted)) (and (@ (@ tptp.mem V5f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap V5f) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V2a) (forall ((V6n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6n))) (let ((_let_2 (@ tptp.ap V5f))) (let ((_let_3 (@ _let_2 _let_1))) (and (@ tptp.p (@ (@ tptp.ap V0P) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (forall ((V1f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2fn1 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ (@ tptp.ap V2fn1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) V0e))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3n $$unsorted)) (let ((_let_1 (@ tptp.ap V2fn1))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V3n)))) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ _let_1 V3n))) V3n)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) A_27a))) (exists ((V2fn $$unsorted)) (and (@ (@ tptp.mem V2fn) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap V2fn) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V0e) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.ap V2fn))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap V1f) _let_1)) (@ _let_2 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Ewellfounded A_27a)) V0R)) (not (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.ap V1f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))) (@ _let_2 _let_1))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V0R)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Ewellfounded A_27a)) V0R)))))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V1y)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V0x)))))))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF tptp.ty_2Enum_2Enum)) tptp.c_2Eprim__rec_2E_3C)))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Eprim__rec_2Emeasure A_27a) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv__image A_27a) tptp.ty_2Enum_2Enum)) tptp.c_2Eprim__rec_2E_3C))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Emeasure A_27a)) V0m))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Emeasure A_27a)) V0f)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_1 V1x))) (@ _let_1 V2y))))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Ebottom (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Ebottom A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Ecarrier (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Ecarrier A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Echain (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Echain A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr _let_2) tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Ecomplete (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Ecomplete A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Econtinuous (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Econtinuous A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr (@ _let_1 A_27a)) tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Edown__continuous (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Edown__continuous A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr (@ _let_1 A_27a)) tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Efunction (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Eposet_2Efunction A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.arr (@ _let_1 A_27b)) tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Egfp (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Egfp A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr (@ _let_1 A_27a)) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Eglb (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Eglb A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Elfp (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Elfp A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr (@ _let_1 A_27a)) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Elub (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Elub A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Emonotonic (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Emonotonic A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr (@ _let_1 A_27a)) tptp.bool)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Epointwise__lift (tptp.del tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ tptp.arr (@ _let_1 A_27b)))) (let ((_let_3 (@ _let_2 tptp.bool))) (let ((_let_4 (@ tptp.arr A_27b))) (let ((_let_5 (@ _let_4 tptp.bool))) (@ (@ tptp.mem (@ (@ tptp.c_2Eposet_2Epointwise__lift A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_5) (@ _let_4 _let_5))) (@ (@ tptp.ty_2Epair_2Eprod _let_3) (@ _let_2 _let_3))))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Eposet (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Eposet A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Erelation (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Erelation A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) _let_3)) _let_3)))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Etop (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Etop A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) _let_2))))))
% 1.89/2.21 (declare-fun tptp.c_2Eposet_2Eup__continuous (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eposet_2Eup__continuous A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (@ (@ tptp.arr (@ _let_1 A_27a)) tptp.bool)))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Efunction A_27a) A_27b)) V0a)) V1b)) V2f)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0a) V3x)) (@ tptp.p (@ (@ tptp.ap V1b) (@ (@ tptp.ap V2f) V3x))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (=> (@ (@ tptp.mem V1r) _let_3) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) _let_3)) V0s)) V1r))) (and (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0s) V2x)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0s) V3x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V3x)) V3x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V1r))) (let ((_let_2 (@ tptp.ap V0s))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ _let_2 V4x)) (@ tptp.p (@ _let_2 V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V5y)) V4x))) (= V4x V5y)))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (forall ((V8z $$unsorted)) (let ((_let_1 (@ tptp.ap V1r))) (let ((_let_2 (@ tptp.ap (@ _let_1 V6x)))) (let ((_let_3 (@ tptp.ap V0s))) (=> (@ (@ tptp.mem V8z) A_27a) (=> (and (@ tptp.p (@ _let_3 V6x)) (@ tptp.p (@ _let_3 V7y)) (@ tptp.p (@ _let_3 V8z)) (@ tptp.p (@ _let_2 V7y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V7y)) V8z))) (@ tptp.p (@ _let_2 V8z))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (=> (@ (@ tptp.mem V1r) _let_3) (= (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecarrier A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) _let_3)) V0s)) V1r)) V0s)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (=> (@ (@ tptp.mem V1r) _let_3) (= (@ (@ tptp.ap (@ tptp.c_2Eposet_2Erelation A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) _let_3)) V0s)) V1r)) V1r)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Etop A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2x)) (and (@ tptp.p (@ (@ tptp.ap V0s) V2x)) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0s) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V3y)) V2x)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ebottom A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2x)) (and (@ tptp.p (@ (@ tptp.ap V0s) V2x)) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0s) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V2x)) V3y)))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2c $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2c) _let_2) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Echain A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2c)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1r))) (let ((_let_2 (@ tptp.ap V2c))) (let ((_let_3 (@ tptp.ap V0s))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ _let_3 V3x)) (@ tptp.p (@ _let_3 V4y)) (@ tptp.p (@ _let_2 V3x)) (@ tptp.p (@ _let_2 V4y))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V3x))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elub A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2p)) V3x)) (and (@ tptp.p (@ (@ tptp.ap V0s) V3x)) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V4y)) (@ tptp.p (@ (@ tptp.ap V2p) V4y))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V4y)) V3x))))) (forall ((V5z $$unsorted)) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V5z)) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V6y)) (@ tptp.p (@ (@ tptp.ap V2p) V6y))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V6y)) V5z)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V3x)) V5z)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eglb A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2p)) V3x)) (and (@ tptp.p (@ (@ tptp.ap V0s) V3x)) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V4y)) (@ tptp.p (@ (@ tptp.ap V2p) V4y))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V3x)) V4y))))) (forall ((V5z $$unsorted)) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V5z)) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V6y)) (@ tptp.p (@ (@ tptp.ap V2p) V6y))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V5z)) V6y)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V5z)) V3x)))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (forall ((V1c $$unsorted)) (=> (@ (@ tptp.mem V1c) (@ (@ tptp.arr A_27a) tptp.bool)) (and (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elub A_27a)) V0p)) V1c)) V2x)))) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eglb A_27a)) V0p)) V1c)) V3x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (=> (@ (@ tptp.mem V1r) _let_3) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) _let_3)) V0s)) V1r))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap V0s) V2x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) (@ tptp.p (@ (@ tptp.ap V0s) V2x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1r) V2x)) V2x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V1r))) (let ((_let_2 (@ tptp.ap V0s))) (let ((_let_3 (@ tptp.arr A_27a))) (let ((_let_4 (@ _let_3 tptp.bool))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_4) (@ _let_3 _let_4))) V0s)) V1r))) (@ tptp.p (@ _let_2 V2x)) (@ tptp.p (@ _let_2 V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V2x))) (= V2x V3y))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (forall ((V4z $$unsorted)) (let ((_let_1 (@ tptp.ap V1r))) (let ((_let_2 (@ tptp.ap (@ _let_1 V2x)))) (let ((_let_3 (@ tptp.ap V0s))) (let ((_let_4 (@ tptp.arr A_27a))) (let ((_let_5 (@ _let_4 tptp.bool))) (=> (@ (@ tptp.mem V4z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_5) (@ _let_4 _let_5))) V0s)) V1r))) (@ tptp.p (@ _let_3 V2x)) (@ tptp.p (@ _let_3 V3y)) (@ tptp.p (@ _let_3 V4z)) (@ tptp.p (@ _let_2 V3y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V4z))) (@ tptp.p (@ _let_2 V4z))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elub A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.lam A_27a) (lambda ((V4j $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V0s) V4j))) (@ (@ tptp.ap V2p) V4j)))))) V3x)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V2p)) V3x))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eglb A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.lam A_27a) (lambda ((V4j $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V0s) V4j))) (@ (@ tptp.ap V2p) V4j)))))) V3x)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V2p)) V3x))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1c $$unsorted)) (=> (@ (@ tptp.mem V1c) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elub A_27a)) V0p)) V1c)) V2x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1c $$unsorted)) (=> (@ (@ tptp.mem V1c) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eglb A_27a)) V0p)) V1c)) V2x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p))) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Etop A_27a)) V0p)) V1x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p))) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ebottom A_27a)) V0p)) V1x))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2r $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (let ((_let_2 (@ tptp.arr _let_1))) (let ((_let_3 (@ _let_2 tptp.bool))) (let ((_let_4 (@ tptp.arr A_27b))) (let ((_let_5 (@ _let_4 tptp.bool))) (let ((_let_6 (@ _let_4 _let_5))) (=> (@ (@ tptp.mem V2r) _let_6) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Epointwise__lift A_27a) A_27b)) V0t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_5) _let_6)) V1s)) V2r)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_3) (@ _let_2 _let_3))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Efunction A_27a) A_27b)) V0t)) V1s))) (@ (@ tptp.lam _let_1) (lambda ((V3f $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V4g $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V5x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap V0t) V5x))) (@ (@ tptp.ap (@ (@ tptp.ap V2r) (@ (@ tptp.ap V3f) V5x))) (@ (@ tptp.ap V4g) V5x)))))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.arr A_27b))) (=> (@ (@ tptp.mem V1t) (@ _let_1 tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete (@ _let_1 A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Epointwise__lift A_27b) A_27a)) V1t)) V0p))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2f) (@ _let_1 A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Emonotonic A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2f)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V2f))) (let ((_let_2 (@ tptp.ap V1r))) (let ((_let_3 (@ tptp.ap V0s))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ _let_3 V3x)) (@ tptp.p (@ _let_3 V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V3x)) V4y))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V3x))) (@ _let_1 V4y))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2f) (@ _let_1 A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eup__continuous A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2f)) (forall ((V3c $$unsorted)) (=> (@ (@ tptp.mem V3c) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elub A_27a)) _let_3)))) (=> (@ (@ tptp.mem V4x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Echain A_27a)) _let_3)) V3c)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 V3c)) V4x))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.lam A_27a) (lambda ((V5y $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Ebool_2E_2F_5C))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap V0s) V6z))) (@ (@ tptp.ap V3c) V6z)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V5y)) (@ (@ tptp.ap V2f) V6z))))))))))) (@ (@ tptp.ap V2f) V4x)))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V2f) (@ _let_1 A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Edown__continuous A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2f)) (forall ((V3c $$unsorted)) (=> (@ (@ tptp.mem V3c) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eglb A_27a)) _let_3)))) (=> (@ (@ tptp.mem V4x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Echain A_27a)) _let_3)) V3c)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 V3c)) V4x))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.lam A_27a) (lambda ((V5y $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Ebool_2E_2F_5C))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap V0s) V6z))) (@ (@ tptp.ap V3c) V6z)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V5y)) (@ (@ tptp.ap V2f) V6z))))))))))) (@ (@ tptp.ap V2f) V4x)))))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Econtinuous A_27a)) V0p)) V1f)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eup__continuous A_27a)) V0p)) V1f)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Edown__continuous A_27a)) V0p)) V1f)))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elfp A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2f)) V3x)) (and (@ tptp.p (@ (@ tptp.ap V0s) V3x)) (= (@ (@ tptp.ap V2f) V3x) V3x) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1r))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap V2f) V4y))) V4y))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V4y))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1r $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1r) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Egfp A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) (@ _let_1 _let_2))) V0s)) V1r))) V2f)) V3x)) (and (@ tptp.p (@ (@ tptp.ap V0s) V3x)) (= (@ (@ tptp.ap V2f) V3x) V3x) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap V1r) V4y)))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0s) V4y)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap V2f) V4y)))) (@ tptp.p (@ _let_1 V3x))))))))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3x_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elfp A_27a)) V0p)) V1f)))) (=> (@ (@ tptp.mem V3x_27) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ _let_1 V2x)) (@ tptp.p (@ _let_1 V3x_27))) (= V2x V3x_27))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3x_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Egfp A_27a)) V0p)) V1f)))) (=> (@ (@ tptp.mem V3x_27) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ _let_1 V2x)) (@ tptp.p (@ _let_1 V3x_27))) (= V2x V3x_27))))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1f $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecarrier A_27a)) V0p))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Efunction A_27a) A_27a)) _let_1)) _let_1)) V1f)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Emonotonic A_27a)) V0p)) V1f))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elfp A_27a)) V0p)) V1f)) V2x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1f $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecarrier A_27a)) V0p))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Efunction A_27a) A_27a)) _let_1)) _let_1)) V1f)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Emonotonic A_27a)) V0p)) V1f))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Egfp A_27a)) V0p)) V1f)) V2x)))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ _let_1 _let_2))) (forall ((V1f $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecarrier A_27a)) V0p))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Eposet A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eposet_2Ecomplete A_27a)) V0p)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eposet_2Efunction A_27a) A_27a)) _let_1)) _let_1)) V1f)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Emonotonic A_27a)) V0p)) V1f))) (and (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Elfp A_27a)) V0p)) V1f)) V2x)))) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eposet_2Egfp A_27a)) V0p)) V1f)) V3x))))))))))))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2E_2A () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2A) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2E_2A (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2A X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2E_2B () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2B) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2E_2B (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2B X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2E_2D () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2D) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2E_2D (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2D X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2E_3C_3D () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2E_3E () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2E_3E_3D () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_3E_3D) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EABS__DIFF () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EABS__DIFF) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EABS__DIFF (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2EABS__DIFF X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EBIT1 () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EBIT1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EBIT1 (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2EBIT1 X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EBIT2 () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EBIT2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EBIT2 (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2EBIT2 X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EDIV () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EDIV) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EDIV (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2EDIV X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EDIV2 () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EDIV2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EDIV2 (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2EDIV2 X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-sort tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum 0)
% 1.89/2.21 (declare-fun tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) $$unsorted)
% 1.89/2.21 (declare-fun tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ($$unsorted) tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X)) X)))
% 1.89/2.21 (assert (forall ((X tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X)) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (let ((_let_1 (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem X) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))) (= X (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X)))))))
% 1.89/2.21 (declare-sort tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum 0)
% 1.89/2.21 (declare-fun tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) $$unsorted)
% 1.89/2.21 (declare-fun tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ($$unsorted) tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X)) X)))
% 1.89/2.21 (assert (forall ((X tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)) (@ (@ tptp.mem (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X)) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.21 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (= X (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X))))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EDIVMOD () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.arr (@ _let_1 _let_2)) _let_2)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EEVEN () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EEVEN) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EEXP () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EEXP) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EEXP (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2EEXP X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EFACT () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EFACT) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EFACT (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2EFACT X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EFACT) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EFUNPOW (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27a))) (@ (@ tptp.mem (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) _let_1))))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EMAX () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EMAX) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EMAX (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2EMAX X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EMIN () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EMIN) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EMIN (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2EMIN X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EMOD () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EMOD) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EMOD (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2EMOD X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EMODEQ () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2EMODEQ) (@ _let_1 (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2ENRC (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Earithmetic_2ENRC A_27a)) (@ (@ tptp.arr _let_2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) _let_2)))))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2ENUMERAL () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2ENUMERAL (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2ENUMERAL X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EODD () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EODD) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2EZERO () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2EZERO) tptp.ty_2Enum_2Enum))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2EZERO () tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (= (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO) tptp.c_2Earithmetic_2EZERO))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2Efindq () $$unsorted)
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.arr (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))) tptp.ty_2Enum_2Enum))))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2Efindq (tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2Efindq X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2Enat__elim____magic () $$unsorted)
% 1.89/2.21 (assert (@ (@ tptp.mem tptp.c_2Earithmetic_2Enat__elim____magic) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.21 (declare-fun tptp.fo__c_2Earithmetic_2Enat__elim____magic (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.21 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Earithmetic_2Enat__elim____magic X0)) (@ (@ tptp.ap tptp.c_2Earithmetic_2Enat__elim____magic) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.21 (declare-fun tptp.c_2Earithmetic_2Enum__CASE (tptp.del) $$unsorted)
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem (@ tptp.c_2Earithmetic_2Enum__CASE A_27a)) (@ _let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr (@ _let_1 A_27a)) A_27a)))))))
% 1.89/2.21 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) V0n)) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ tptp.inj__ty_2Enum_2Enum V0x))) V0x)))
% 1.89/2.21 (assert (= tptp.fo__c_2Earithmetic_2EZERO tptp.fo__c_2Enum_2E0))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_3 (@ _let_1 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2Enat__elim____magic) (@ tptp.inj__ty_2Enum_2Enum V0n))) V0n)))
% 1.89/2.21 (assert (and (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0m))) tptp.fo__c_2Enum_2E0)) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) tptp.fo__c_2Enum_2E0)) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) _let_1)))))))))
% 1.89/2.21 (assert (and (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) (@ _let_3 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= V0m V1n)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D) _let_2)) _let_1)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) _let_2)) _let_1)) (= V0m V1n)))))))
% 1.89/2.21 (assert (and (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) true) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (not (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (and (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) false) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (not (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0v $$unsorted)) (=> (@ (@ tptp.mem V0v) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2Enum__CASE A_27a)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0v)) V1f) V0v))))) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27a) (forall ((V4f $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ (@ tptp.mem V4f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2Enum__CASE A_27a)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) V3v)) V4f) (@ (@ tptp.ap V4f) _let_1))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V0f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V1x) V1x))))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4x $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V2f)))) (=> (@ (@ tptp.mem V4x) A_27a) (= (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) V4x) (@ (@ tptp.ap (@ _let_2 _let_1)) (@ (@ tptp.ap V2f) V4x))))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del)) (and (forall ((V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V1x)) V2y)) (= V1x V2y))))))))) (forall ((V3R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V3R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V4n tptp.tp__ty_2Enum_2Enum) (V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V3R)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V4n)))) V5x)) V6y)) (exists ((V7z $$unsorted)) (and (@ (@ tptp.mem V7z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V3R) V5x)) V7z)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V3R)) (@ tptp.inj__ty_2Enum_2Enum V4n))) V7z)) V6y)))))))))))))))
% 1.89/2.21 (assert (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))
% 1.89/2.21 (assert (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))
% 1.89/2.21 (assert (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) tptp.fo__c_2Enum_2E0))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) A_27a) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2Enum__CASE A_27a)) _let_1)) V0f)) V1g) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) V0f)) (@ (@ tptp.ap V1g) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (not (= tptp.fo__c_2Enum_2E0 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0n)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0m)))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_6 (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 (@ _let_4 _let_1))))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_7)) _let_2)) V0m) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_7)) V0m) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_5 _let_2))) _let_1)) _let_6) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_5 _let_1))) _let_6)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (or (= V0m tptp.fo__c_2Enum_2E0) (exists ((V1n tptp.tp__ty_2Enum_2Enum)) (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1n))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (not (= V0n tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (= V0n tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (= tptp.c_2Earithmetic_2E_3C_3D (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V1y)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V0x)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.inj__ty_2Enum_2Enum V0m))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V2p))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0m)))))
% 1.89/2.21 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive tptp.ty_2Enum_2Enum)) tptp.c_2Eprim__rec_2E_3C)))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_1))) (@ tptp.p (@ _let_3 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (not (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (not (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))
% 1.89/2.21 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Emeasure A_27a)) V0f))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1)) (not (= (@ tptp.surj__ty_2Enum_2Enum _let_3) V1n))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1)) (not (= V1n (@ tptp.surj__ty_2Enum_2Enum _let_3)))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (or (= tptp.fo__c_2Enum_2E0 V0m) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0m))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) (not (= V0m V1n))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0m) (= V1n tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.inj__ty_2Enum_2Enum V0m))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V2p))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0m)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.inj__ty_2Enum_2Enum V0m))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2p)))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0m)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (not (= V1n tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (not (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (= V0n tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) V0m)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0m)))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V0m)))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) (@ _let_3 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0m))) V0m)))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V0m)))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ _let_4 _let_1))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_7 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_8 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_9)) _let_2)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_9)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_8)) _let_2)) V0m) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_8)) V0m) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_7 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 _let_5)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_7 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 _let_2)) _let_5)))))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2p))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1))) _let_1)) V0m))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) tptp.fo__c_2Enum_2E0) (and (= V0m tptp.fo__c_2Enum_2E0) (= V1n tptp.fo__c_2Enum_2E0)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) _let_1) (or (and (= V0m _let_1) (= V1n tptp.fo__c_2Enum_2E0)) (and (= V0m tptp.fo__c_2Enum_2E0) (= V1n _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0m) (= V1n tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0m))) V1n))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_4 _let_3)) (@ tptp.p (@ _let_4 _let_1))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1))) (= V0m V1n)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) _let_1)) V2p) (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V2p))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) _let_1))) (= V0m V1n))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_1))) (@ tptp.p (@ _let_3 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (and (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_3)) _let_1))) (@ tptp.p (@ _let_2 _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum) (V3q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_5)) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_1)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2i tptp.tp__ty_2Enum_2Enum) (V3j tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3j))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2i))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_5)) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2p))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.inj__ty_2Enum_2Enum V0m))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))
% 1.89/2.21 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1q))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V2n))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0p))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (not (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ _let_2 _let_3)) _let_3))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 _let_1)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (= V0n V1m)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1n))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V2p))) (@ tptp.inj__ty_2Enum_2Enum V1m))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (exists ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (exists ((V2n tptp.tp__ty_2Enum_2Enum)) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V2n))) (forall ((V3m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2n))) (not (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (=> (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1n))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V3n))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))
% 1.89/2.21 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0m))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1m)))) _let_1)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0m) (or (= V0m tptp.fo__c_2Enum_2E0) (= V1n tptp.fo__c_2Enum_2E0)))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2i))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1i tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1i))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2n)))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1i tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2n)))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1i)))) (= V0m V1i)))))
% 1.89/2.21 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0p)))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) _let_1))) (= V2n V1m))))))
% 1.89/2.21 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum) (V3m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1q)))) (@ tptp.inj__ty_2Enum_2Enum V0p)))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V3m))) _let_1))) (= V2n V3m))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2p)))) (= V1n V2p)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) _let_1))) (= V0m V1n))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2p)))) (or (= V0m tptp.fo__c_2Enum_2E0) (= V1n V2p))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) _let_1))) (or (= V0m tptp.fo__c_2Enum_2E0) (= V1n V2p)))))))
% 1.89/2.21 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1c))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0a))) _let_1))) _let_1)) V0a))))
% 1.89/2.21 (assert (forall ((V0c tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0c))) (@ tptp.inj__ty_2Enum_2Enum V1b))) (forall ((V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V2a))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0c))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) _let_1)) tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V1b))) (@ tptp.inj__ty_2Enum_2Enum V0a))) (forall ((V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1c tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V1c))) (@ tptp.inj__ty_2Enum_2Enum V0b))) (forall ((V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1c))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ _let_4 _let_1)) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m))) (forall ((V2p tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V1m))) (@ tptp.inj__ty_2Enum_2Enum V2p))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1p tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1p))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1p))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0p))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1m)))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))
% 1.89/2.21 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0p))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_1)) _let_2))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1))) (= V1n V2m))))))))))
% 1.89/2.21 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)))) (=> (and (@ tptp.p (@ _let_5 _let_4)) (@ tptp.p (@ _let_5 _let_2))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (= V1n V2m))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (not (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (@ tptp.inj__ty_2Enum_2Enum V0m))) tptp.fo__c_2Enum_2E0))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (@ tptp.inj__ty_2Enum_2Enum V0m))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (exists ((V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_1 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (@ tptp.inj__ty_2Enum_2Enum V1m)))) (or (= V0n (@ tptp.surj__ty_2Enum_2Enum _let_2)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_3 _let_1))) (@ _let_3 (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (or (= V0m V1n) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (= V1n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V2p))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (= V1n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V2p))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) tptp.fo__c_2Enum_2E0) (or (= V0m tptp.fo__c_2Enum_2E0) (= V1n tptp.fo__c_2Enum_2E0)))))
% 1.89/2.21 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y))) _let_1) (and (= V0x _let_1) (= V1y _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) V1n) (or (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (= V1n tptp.fo__c_2Enum_2E0)))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) _let_1))) (and (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (or (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EFACT) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EFACT))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EFACT) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)) (not (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1)) (not (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (or (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)) (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (not (and (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)) (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (= (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) _let_1))) (or (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (not (= (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) _let_1))) (and (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (and (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)) (exists ((V1m tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V1m)))))) (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1)) (exists ((V2m tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V2m)))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) (@ tptp.inj__ty_2Enum_2Enum V0n))) (exists ((V1m tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V1m))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) (@ tptp.inj__ty_2Enum_2Enum V0n))) (exists ((V1m tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V1m)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) _let_3))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_3)) (@ tptp.p (@ _let_2 _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ _let_3 _let_2))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (or (= V0n tptp.fo__c_2Enum_2E0) (@ tptp.p (@ _let_2 _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ _let_3 _let_2))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (= V0m V1n) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (not (= V0m V1n)) (or (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_1))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D) _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_4 _let_1)) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n))))) _let_1))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2p)))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (or (= V0m tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (or (= V1n tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_5 _let_2))) (@ _let_5 _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_6 (@ tptp.ap (@ _let_2 _let_3)))) (and (= (@ tptp.p (@ _let_6 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_4) (= (@ tptp.p (@ _let_6 (@ (@ tptp.ap (@ _let_5 _let_1)) _let_3))) _let_4))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) _let_1))))) (and (= (@ tptp.p (@ _let_5 _let_4)) (and (@ tptp.p (@ _let_3 _let_4)) (= V1n tptp.fo__c_2Enum_2E0))) (= (@ tptp.p (@ _let_5 _let_1)) (and (@ tptp.p (@ _let_3 _let_1)) (= V0m tptp.fo__c_2Enum_2E0)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (or (= V0m tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_3)))) (and (= (@ tptp.p (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) _let_2) (= (@ tptp.p (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_1)) _let_3))) _let_2)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_4))))) (and (= (@ tptp.p (@ _let_5 _let_2)) (or (= V0m tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)))) (= (@ tptp.p (@ _let_5 _let_4)) (or (= V1n tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) _let_3)) (@ (@ tptp.ap (@ _let_5 (@ _let_4 _let_2))) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_3)) _let_1))) _let_2)) (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ _let_4 _let_1)) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2))) _let_3)) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_3 (@ tptp.ap (@ _let_2 _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V2p))) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_5))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_5))) _let_4)) (@ tptp.p (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_3))) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_3))) _let_1)) (or (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3E))) (let ((_let_3 (@ tptp.ap (@ _let_2 _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V2p))) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_5))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_5))) _let_4)) (@ tptp.p (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3E))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1))) (or (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_4)) _let_1)) V1n) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_3)) V2p) (or (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))))
% 1.89/2.21 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (= V0n tptp.fo__c_2Enum_2E0))) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V1m))))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ tptp.p (@ _let_2 _let_3)) (or (= V1m (@ tptp.surj__ty_2Enum_2Enum _let_3)) (@ tptp.p (@ _let_2 _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0k tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V1n))) (exists ((V2r tptp.tp__ty_2Enum_2Enum) (V3q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2r))) (and (= V0k (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V3q))) _let_1))) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1k))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1))) (and (= V1k (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))) _let_1))) _let_3))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_3)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))
% 1.89/2.21 (assert (forall ((V0k tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V0k))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.21 (assert (forall ((V0k tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V0k))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1k))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0n)))) _let_1)))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum) (V2q tptp.tp__ty_2Enum_2Enum)) (=> (exists ((V3r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3r))) (and (= V1k (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2q))) _let_1))) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ tptp.inj__ty_2Enum_2Enum V1k))) (@ tptp.inj__ty_2Enum_2Enum V0n))) V2q))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (=> (exists ((V3q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2r))) (and (= V1k (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V3q))) _let_1))) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V1k))) (@ tptp.inj__ty_2Enum_2Enum V0n))) V2r))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1r tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1r))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V2q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2q))) _let_1))) (@ tptp.inj__ty_2Enum_2Enum V1r)))) _let_1)) V2q))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1k))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) V1k))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V1k))) _let_1))) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1r tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1r))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V2q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2q))) _let_1))) (@ tptp.inj__ty_2Enum_2Enum V1r)))) _let_1)) V1r))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1q tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2r))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V1q))) _let_1))) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2r))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1q))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_6 _let_1)) (@ tptp.p (@ _let_6 _let_5)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_5)) _let_1))) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1j tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2k))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1j))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_3 (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1k))) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum _let_3)))))))))
% 1.89/2.21 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0r))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V1q))) _let_1))) _let_1)) V1q)))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2r))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) _let_1))) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_4)) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (or (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 _let_2)) _let_1)) tptp.fo__c_2Enum_2E0)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m)))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2x))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0m))))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0q tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ tptp.inj__ty_2Enum_2Enum V0q))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) V0q)))
% 1.89/2.21 (assert (forall ((V0q tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ tptp.inj__ty_2Enum_2Enum V0q))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V0q)))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V2x))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1))) V0m)))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1d tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1d))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) _let_2))) _let_1))))))))
% 1.89/2.21 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V0m))) _let_1))) _let_1)))))))
% 1.89/2.21 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1p tptp.tp__ty_2Enum_2Enum) (V2q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2q))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ tptp.inj__ty_2Enum_2Enum V1p))) _let_1))) (exists ((V3k tptp.tp__ty_2Enum_2Enum) (V4r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3k))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2q))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4r))) (and (= V1p (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) _let_2))) _let_3))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_3)) _let_2)) (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ tptp.inj__ty_2Enum_2Enum V1m))) _let_1))) (forall ((V3q tptp.tp__ty_2Enum_2Enum) (V4r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4r))) (=> (and (= V1m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) _let_2))) _let_3))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_3)) _let_2))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1p tptp.tp__ty_2Enum_2Enum) (V2q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2q))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V1p))) _let_1))) (exists ((V3k tptp.tp__ty_2Enum_2Enum) (V4r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2q))) (and (= V1p (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V3k))) _let_2))) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V1m))) _let_1))) (forall ((V3q tptp.tp__ty_2Enum_2Enum) (V4r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (and (= V1m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V3q))) _let_2))) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1j tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2k))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1j))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1p tptp.tp__ty_2Enum_2Enum) (V2q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1p))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_6 _let_2)) (@ tptp.p (@ _let_6 _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ _let_3 _let_4))) (@ _let_3 _let_1)))))))))))))
% 1.89/2.21 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) V0x) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.21 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.21 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.21 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2z))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) _let_2))) _let_1))))))))))
% 1.89/2.21 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2z))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_2))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_3)) _let_1))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_3)) _let_1))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_4)) _let_1)) V0x) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2k))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_6 _let_1)) (@ tptp.p (@ _let_6 _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) _let_2)))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2z))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1y))) V2z) (and (= V1y (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (let ((_let_4 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2z)))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_4)))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_4)))) (let ((_let_7 (@ tptp.surj__ty_2Enum_2Enum _let_4))) (let ((_let_8 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_9 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_10 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) (and (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_9 _let_10)) _let_8)) _let_7) (and (= V1y (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_10))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 _let_10)) tptp.fo__c_2Enum_2E0))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_9 _let_3)) _let_8)) _let_7) (and (= V1y (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 _let_3)) tptp.fo__c_2Enum_2E0))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V1k))) _let_1)) tptp.fo__c_2Enum_2E0) (exists ((V2d tptp.tp__ty_2Enum_2Enum)) (= V1k (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2d))) (@ tptp.inj__ty_2Enum_2Enum V0n))))))))))
% 1.89/2.22 (assert (forall ((V0y tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_5 (@ _let_4 _let_2))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (not (= (@ tptp.surj__ty_2Enum_2Enum _let_5) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)))) _let_1))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_5)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0y tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1)))) (not (= (@ tptp.surj__ty_2Enum_2Enum _let_4) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)))) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0y tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0y))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_2))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1k))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_7 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_7 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_7 _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_5)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_6 _let_3)) _let_1))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 _let_5)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V2k))) (let ((_let_6 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_7 _let_2)) _let_5))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 _let_4)) _let_5))) (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) _let_4))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0v_27 $$unsorted)) (=> (@ (@ tptp.mem V0v_27) A_27a) (forall ((V1f_27 $$unsorted)) (=> (@ (@ tptp.mem V1f_27) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2M tptp.tp__ty_2Enum_2Enum) (V3M_27 tptp.tp__ty_2Enum_2Enum) (V4v $$unsorted)) (=> (@ (@ tptp.mem V4v) A_27a) (forall ((V5f $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Earithmetic_2Enum__CASE A_27a)))) (=> (@ (@ tptp.mem V5f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (=> (and (= V2M V3M_27) (=> (= V3M_27 tptp.fo__c_2Enum_2E0) (= V4v V0v_27)) (forall ((V6n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6n))) (=> (= V3M_27 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ (@ tptp.ap V5f) _let_1) (@ (@ tptp.ap V1f_27) _let_1)))))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2M))) V4v)) V5f) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3M_27))) V0v_27)) V1f_27)))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0P) (@ _let_1 (@ _let_1 tptp.bool))) (= (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) _let_1)))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 A_27a))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ (@ tptp.ap V1g) _let_2) (@ (@ tptp.ap (@ (@ tptp.ap V0f) _let_1)) _let_2))))) (and (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))))) (= (@ (@ tptp.ap V1g) _let_3) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_3)))))) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (= (@ (@ tptp.ap V1g) _let_3) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) _let_3))))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V1a))) (@ tptp.inj__ty_2Enum_2Enum V2b)))) (forall ((V3d tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3d))) (let ((_let_2 (@ tptp.ap V0P))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (and (=> (= V2b (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V1a))) _let_1))) (@ tptp.p (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (=> (= V1a (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V2b))) _let_1))) (@ tptp.p (@ _let_2 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.ap V0P))) (and (=> (= V1n tptp.fo__c_2Enum_2E0) (@ tptp.p (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (=> (= V1n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (@ tptp.p (@ _let_2 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0b))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (exists ((V2m tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0b))) (@ tptp.inj__ty_2Enum_2Enum V2m)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0n))) _let_1)) tptp.fo__c_2Enum_2E0) (and (= V0n tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1y)))) (or (@ tptp.p (@ _let_2 _let_1)) (= V1y tptp.fo__c_2Enum_2E0)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) V0n)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m))) _let_1) (or (= V0n _let_1) (= V1m tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0b))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0b))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0b))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0b))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0b))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0b))))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2m)))) (= V1n V2m)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ _let_3 _let_4))) (@ _let_3 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2b)))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_6 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_7 (= V0b tptp.fo__c_2Enum_2E0))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_4)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_8 _let_2))) (@ _let_8 _let_1))) (or (and _let_7 (= V2n tptp.fo__c_2Enum_2E0)) (and _let_7 (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2))) (= V0b (@ tptp.surj__ty_2Enum_2Enum _let_5)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_2)) _let_1))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) _let_3))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)) (= V0x tptp.fo__c_2Enum_2E0))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) (= V0n tptp.fo__c_2Enum_2E0))))))))))
% 1.89/2.22 (assert (forall ((V0b1 tptp.tp__ty_2Enum_2Enum) (V1b2 tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0b1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1b2))) _let_1))) (or (= V2x tptp.fo__c_2Enum_2E0) (= V0b1 V1b2)))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0p))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_4))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ _let_3 _let_4))) (@ _let_3 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_5)))) (let ((_let_7 (@ _let_6 _let_4))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_5)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_8 _let_7)) _let_5)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_8 (@ _let_6 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))))) _let_5)) (@ tptp.surj__ty_2Enum_2Enum _let_7))))))))))))))
% 1.89/2.22 (assert (forall ((V0z tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0z tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2))) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1))) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMAX))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMIN))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMAX))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMIN))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_2)) _let_1))) (= V0m V1n))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_2)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_2)) _let_1))) (not (= V0m V1n)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_2)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap V0P))) (=> (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1))) (and (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_2)) _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_5)) _let_1))) (and (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_6)) _let_2)) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_5)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (= (@ tptp.p (@ _let_4 _let_6)) (and (@ tptp.p (@ _let_4 _let_5)) (@ tptp.p (@ _let_4 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_4)) _let_2))) (let ((_let_6 (@ tptp.ap (@ _let_3 _let_1)))) (and (= (@ tptp.p (@ _let_6 _let_5)) (or (@ tptp.p (@ _let_6 _let_4)) (@ tptp.p (@ _let_6 _let_2)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_5)) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_5)) _let_1))) (and (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_6)) _let_2)) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_5)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (= (@ tptp.p (@ _let_4 _let_6)) (and (@ tptp.p (@ _let_4 _let_5)) (@ tptp.p (@ _let_4 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_4)) _let_2))) (let ((_let_6 (@ tptp.ap (@ _let_3 _let_1)))) (and (= (@ tptp.p (@ _let_6 _let_5)) (or (@ tptp.p (@ _let_6 _let_4)) (@ tptp.p (@ _let_6 _let_2)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_5)) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMIN))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) tptp.fo__c_2Enum_2E0)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMAX))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) V0n) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) V0n)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) tptp.fo__c_2Enum_2E0) (and (= V0m tptp.fo__c_2Enum_2E0) (= V1n tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) tptp.fo__c_2Enum_2E0) (or (= V0m tptp.fo__c_2Enum_2E0) (= V1n tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_1)) _let_1)) V0n))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_1)) _let_1)) V0n))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (and (exists ((V1x tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1x)))) (exists ((V2x tptp.tp__ty_2Enum_2Enum)) (forall ((V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2x))) (not (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))) (exists ((V4x tptp.tp__ty_2Enum_2Enum)) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V4x))) (forall ((V5y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V5y))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V4x))) (not (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (exists ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (or (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (exists ((V2m tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2m))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2n))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1c))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1c))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))) (and (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V1c))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1c))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (exists ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1c))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))) (or (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V1c))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Etransitive A_27a)) V0R)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.ap V1f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))) (forall ((V3m tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.ap V1f))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V3m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (=> (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.ap V0f))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (=> (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V0f))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V0f)) (forall ((V1b tptp.tp__ty_2Enum_2Enum)) (exists ((V2a tptp.tp__ty_2Enum_2Enum)) (forall ((V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap V0f) _let_1))) (@ tptp.inj__ty_2Enum_2Enum V1b))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2a)))))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V0f)) (forall ((V1b tptp.tp__ty_2Enum_2Enum)) (exists ((V2n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1b))) (@ (@ tptp.ap V0f) (@ tptp.inj__ty_2Enum_2Enum V2n))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (=> (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))) (forall ((V2b tptp.tp__ty_2Enum_2Enum)) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V2b))) (@ (@ tptp.ap V0f) (@ tptp.inj__ty_2Enum_2Enum V3n))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (not (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) _let_1)) _let_1)) tptp.fo__c_2Enum_2E0))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m))) tptp.fo__c_2Enum_2E0) (= V0n V1m))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) V0n) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) V0n)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1z))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) (@ tptp.inj__ty_2Enum_2Enum V0x))))) (let ((_let_3 (@ tptp.ap tptp.c_2Enum_2ESUC))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_2 (@ _let_3 _let_1)))) (@ _let_3 (@ _let_2 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1z tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1z))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) (@ tptp.inj__ty_2Enum_2Enum V0x))))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V2y))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_2 (@ _let_3 _let_1)))) (@ _let_3 (@ _let_2 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) _let_2)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) _let_2)) _let_1))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2z))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_4 _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ _let_4 _let_2))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_6 _let_2)) _let_5))) (@ (@ tptp.ap (@ _let_6 _let_1)) _let_5))) (or (@ tptp.p (@ _let_4 _let_5)) (@ tptp.p (@ _let_4 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_2))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0z tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0z))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_5 _let_1))) (@ _let_5 _let_4))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0z tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0z))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_6 _let_5))) (@ _let_6 _let_2))) (and (@ tptp.p (@ _let_4 _let_5)) (@ tptp.p (@ _let_4 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n1 tptp.tp__ty_2Enum_2Enum) (V1n2 tptp.tp__ty_2Enum_2Enum) (V2m1 tptp.tp__ty_2Enum_2Enum) (V3m2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3m2))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n2))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2m1))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0n1))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2))) (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1)))) (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_5)) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V0f)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) V2x) (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ _let_2 _let_1)) V2x))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V0f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V1x) V1x))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V0f)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2m))) (= (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) V1x) (@ (@ tptp.ap (@ _let_2 _let_3)) (@ (@ tptp.ap (@ _let_2 _let_1)) V1x))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V0f)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V1x) (@ (@ tptp.ap V0f) V1x)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V1x)) V2y)) (= V1x V2y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum) (V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5z $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)))) (=> (@ (@ tptp.mem V5z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_2)) V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_1)) V4y)) V5z))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) V3x)) V5z))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum) (V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4z $$unsorted)) (=> (@ (@ tptp.mem V4z) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V1m))) (@ tptp.inj__ty_2Enum_2Enum V2n)))) V3x)) V4z)) (exists ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)))) (and (@ (@ tptp.mem V5y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) V3x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) V5y)) V4z))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum) (V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4z $$unsorted)) (=> (@ (@ tptp.mem V4z) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V1m))) (@ tptp.inj__ty_2Enum_2Enum V2n)))) V3x)) V4z)) (exists ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)))) (and (@ (@ tptp.mem V5y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) V3x)) V5y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) V5y)) V4z))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1n)))) V2x)) V3y)) (exists ((V4z $$unsorted)) (and (@ (@ tptp.mem V4z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ tptp.inj__ty_2Enum_2Enum V1n))) V2x)) V4z)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V4z)) V3y)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ tptp.inj__ty_2Enum_2Enum V1n))) V2x)) V3y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V2x)) V3y)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V1x)) V2y))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V1x)) V2y)) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V1x)) V2y))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) V0R)) V1x)) V2y)) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2ENRC A_27a)) V0R)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V3n)))) V1x)) V2y))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.inj__ty_2Enum_2Enum V1n))) (exists ((V2k tptp.tp__ty_2Enum_2Enum)) (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.inj__ty_2Enum_2Enum V2k))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_3))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ tptp.ap tptp.c_2Enum_2ESUC))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_5 _let_4))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_5 _let_2))) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum) (V3p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V3p))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_6 _let_4)) _let_5))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_6 _let_2)) _let_5))) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap V0P))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ _let_3 _let_2)) (forall ((V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (@ tptp.p (@ _let_2 _let_1))))))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))) (let ((_let_4 (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V1q)))) (let ((_let_5 (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0p)))) (let ((_let_6 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_5)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_4)))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_4)) _let_2))) (@ _let_3 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) _let_2))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0p))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (=> (and (@ tptp.p (@ _let_4 _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))) (@ tptp.p (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_5 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) _let_4))) (or (and (@ tptp.p (@ _let_5 _let_1)) (@ tptp.p (@ _let_3 _let_4))) (and (@ tptp.p (@ _let_5 _let_4)) (@ tptp.p (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_4 (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (= (@ tptp.p (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_3)) _let_1))) (and (@ tptp.p (@ _let_4 _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))))))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 tptp.ty_2Enum_2Enum))) (let ((_let_3 (@ _let_1 _let_2))) (= tptp.c_2Earithmetic_2Efindq (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC _let_3) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Emeasure _let_3)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY tptp.ty_2Enum_2Enum) _let_2) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V0a $$unsorted)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1m $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) V1m)) V2n)))))))))))) (@ (@ tptp.lam (@ (@ tptp.arr _let_3) tptp.ty_2Enum_2Enum)) (lambda ((V3f $$unsorted)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4a $$unsorted)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V5m $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V6n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V6n)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) V4a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V7d $$unsorted)) (let ((_let_1 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) V5m)) V7d))) V4a)) (@ (@ tptp.ap V3f) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V4a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.ty_2Enum_2Enum)) V5m)) V7d))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) V6n)))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V1m))) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3d $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) V3d))) _let_3)) (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_3))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 tptp.ty_2Enum_2Enum)) _let_1)) V3d))))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V1m))) (@ tptp.inj__ty_2Enum_2Enum V2n))))) tptp.fo__c_2Enum_2E0) (= V0a tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_5 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 tptp.ty_2Enum_2Enum)) _let_1)) _let_4))))) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 tptp.ty_2Enum_2Enum))) (let ((_let_3 (@ _let_1 _let_2))) (= tptp.c_2Earithmetic_2EDIVMOD (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2EWFREC _let_3) _let_2)) (@ (@ tptp.ap (@ tptp.c_2Eprim__rec_2Emeasure _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo _let_3) tptp.ty_2Enum_2Enum) _let_2)) (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) _let_2))))) (@ (@ tptp.lam (@ (@ tptp.arr _let_3) _let_2)) (lambda ((V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY tptp.ty_2Enum_2Enum) _let_1) _let_1)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1a $$unsorted)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2m $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3n $$unsorted)) (let ((_let_1 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.ap (@ _let_1 tptp.ty_2Enum_2Enum)))) (let ((_let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_3)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V3n)) _let_5))) (@ (@ tptp.ap (@ _let_2 _let_5)) _let_5))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) V2m)) V3n))) (@ (@ tptp.ap (@ _let_2 V1a)) V2m))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) _let_3)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4q $$unsorted)) (let ((_let_1 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) V1a)) V4q))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) V2m)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) V3n)) V4q)))) V3n)))))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 _let_3)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ _let_2 V2m)) V3n))))))))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_4 (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)))) (let ((_let_5 (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1))) (let ((_let_6 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (let ((_let_7 (@ tptp.ap (@ _let_3 _let_6)))) (let ((_let_8 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_9 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_6)))) (let ((_let_10 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ _let_7 _let_8)) _let_5))) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_9 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) _let_10))) (@ (@ tptp.ap (@ _let_4 _let_10)) _let_10))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_9 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1))) (@ (@ tptp.ap (@ _let_4 _let_8)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) _let_6)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3q $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0a))) V3q))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V1m))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) V3q)))) _let_1))))))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_5)))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1q)))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_4)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_4))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1q tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_6)) _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_6))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_4 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_5 (@ tptp.ap (@ _let_4 tptp.ty_2Enum_2Enum)))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) _let_3)) (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1)))) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (and (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_4)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) _let_2)) _let_1)))))))))))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_4)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) _let_2)) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m1 tptp.tp__ty_2Enum_2Enum) (V2m2 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m1))) (@ tptp.inj__ty_2Enum_2Enum V2m2))) (exists ((V3a tptp.tp__ty_2Enum_2Enum) (V4b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V3a))) _let_1))) (@ tptp.inj__ty_2Enum_2Enum V1m1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V4b))) _let_1))) (@ tptp.inj__ty_2Enum_2Enum V2m2)))))))))))
% 1.89/2.22 (assert (forall ((V0m1 tptp.tp__ty_2Enum_2Enum) (V1m2 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0m1))) (@ tptp.inj__ty_2Enum_2Enum V1m2))) (= V0m1 V1m2))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m1 tptp.tp__ty_2Enum_2Enum) (V2m2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m2))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m1))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) _let_1)) _let_4)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m1 tptp.tp__ty_2Enum_2Enum) (V2m2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m2))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m1))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) _let_1)) _let_4)) _let_2)) (or (and (= V0n tptp.fo__c_2Enum_2E0) (= V1m1 V2m2)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1e0 tptp.tp__ty_2Enum_2Enum) (V2e1 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2e1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1e0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) _let_1)) _let_4)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x0 tptp.tp__ty_2Enum_2Enum) (V2x1 tptp.tp__ty_2Enum_2Enum) (V3y0 tptp.tp__ty_2Enum_2Enum) (V4y1 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4y1))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2x1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3y0))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1x0))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_5)) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x0 tptp.tp__ty_2Enum_2Enum) (V2x1 tptp.tp__ty_2Enum_2Enum) (V3y0 tptp.tp__ty_2Enum_2Enum) (V4y1 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4y1))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2x1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3y0))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1x0))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_5)) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))) _let_1)) _let_1)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum) (V3e tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3e))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2e tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2e))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum) (V3z tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3z))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2y))) (=> (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_1))) (@ tptp.p (@ _let_3 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_7 (@ _let_3 (@ _let_6 _let_5)))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_9 (@ tptp.ap (@ _let_8 _let_7)))) (let ((_let_10 (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ))) (let ((_let_11 (@ tptp.ap (@ _let_10 _let_4)))) (let ((_let_12 (@ _let_3 _let_5))) (let ((_let_13 (@ _let_3 _let_1))) (let ((_let_14 (@ _let_3 (@ _let_2 _let_5)))) (let ((_let_15 (@ tptp.ap (@ _let_8 _let_14)))) (let ((_let_16 (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_13)) _let_12)))) (let ((_let_17 (@ _let_3 (@ _let_6 _let_1)))) (let ((_let_18 (@ tptp.ap (@ _let_10 _let_17)))) (and (=> _let_16 (@ tptp.p (@ (@ tptp.ap (@ _let_18 _let_7)) (@ _let_9 _let_17)))) (=> _let_16 (@ tptp.p (@ (@ tptp.ap (@ _let_18 _let_14)) (@ _let_15 _let_17)))) (=> _let_16 (@ tptp.p (@ (@ tptp.ap (@ _let_11 _let_14)) (@ _let_15 _let_4)))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_13)) _let_12)) (@ tptp.p (@ (@ tptp.ap (@ _let_11 _let_7)) (@ _let_9 _let_4)))))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_2))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMODEQ) _let_2)) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n tptp.tp__ty_2Enum_2Enum) (V1zc $$unsorted)) (=> (@ (@ tptp.mem V1zc) A_27a) (forall ((V2sc $$unsorted)) (=> (@ (@ tptp.mem V2sc) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V3v $$unsorted)) (=> (@ (@ tptp.mem V3v) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2Enum__CASE A_27a)) (@ tptp.inj__ty_2Enum_2Enum V0n))) V1zc)) V2sc) V3v) (or (and (= V0n tptp.fo__c_2Enum_2E0) (= V1zc V3v)) (exists ((V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4x))) (and (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ (@ tptp.ap V2sc) _let_1) V3v)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0num $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0num) (@ _let_1 (@ (@ tptp.arr (@ _let_1 tptp.ty_2Enum_2Enum)) A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2EDATATYPE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap V0num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.c_2Enum_2ESUC)))))))
% 1.89/2.22 (declare-fun tptp.c_2Ewhile_2EHOARE__SPEC (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Ewhile_2EHOARE__SPEC A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Ewhile_2ELEAST () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Ewhile_2ELEAST) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-sort tptp.tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum 0)
% 1.89/2.22 (declare-fun tptp.inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (tptp.tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum) $$unsorted)
% 1.89/2.22 (declare-fun tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum ($$unsorted) tptp.tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X tptp.tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum)) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ tptp.inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum X)) X)))
% 1.89/2.22 (assert (forall ((X tptp.tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum)) (@ (@ tptp.mem (@ tptp.inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum X)) (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Enum_2Enum)) (= X (@ tptp.inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum X))))))
% 1.89/2.22 (declare-fun tptp.c_2Ewhile_2EOLEAST () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Ewhile_2EOLEAST) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Ewhile_2EOWHILE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ewhile_2EOWHILE A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ _let_1 A_27a)) (@ _let_1 (@ tptp.ty_2Eoption_2Eoption A_27a))))))))
% 1.89/2.22 (declare-fun tptp.c_2Ewhile_2EWHILE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ewhile_2EWHILE A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27a)) (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V3x $$unsorted)) (let ((_let_1 (@ tptp.ap V2f))) (=> (@ (@ tptp.mem V3x) A_27a) (= (@ _let_1 V3x) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.ap V0P) V3x))) V3x)) (@ _let_1 (@ (@ tptp.ap V1g) V3x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EWHILE A_27a)) V0P)) V1g)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ _let_1 V2x) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.ap V0P) V2x))) (@ _let_1 (@ (@ tptp.ap V1g) V2x)))) V2x))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0B $$unsorted)) (=> (@ (@ tptp.mem V0B) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1C $$unsorted)) (=> (@ (@ tptp.mem V1C) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V2R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V2R)) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0B) V3s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2R) (@ (@ tptp.ap V1C) V3s))) V3s)))))) (forall ((V4P $$unsorted)) (=> (@ (@ tptp.mem V4P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V5s $$unsorted)) (let ((_let_1 (@ tptp.ap V4P))) (=> (@ (@ tptp.mem V5s) A_27a) (=> (=> (@ tptp.p (@ (@ tptp.ap V0B) V5s)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap V1C) V5s)))) (@ tptp.p (@ _let_1 V5s)))))) (forall ((V6v $$unsorted)) (=> (@ (@ tptp.mem V6v) A_27a) (@ tptp.p (@ (@ tptp.ap V4P) V6v))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1C $$unsorted)) (=> (@ (@ tptp.mem V1C) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ewhile_2EHOARE__SPEC A_27a) A_27b)) V0P)) V1C)) V2Q)) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0P) V3s)) (@ tptp.p (@ (@ tptp.ap V2Q) (@ (@ tptp.ap V1C) V3s))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2B $$unsorted)) (=> (@ (@ tptp.mem V2B) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3C $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Ewhile_2EHOARE__SPEC A_27a) A_27a)))) (=> (@ (@ tptp.mem V3C) (@ (@ tptp.arr A_27a) A_27a)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) V1R)) (forall ((V4s $$unsorted)) (=> (@ (@ tptp.mem V4s) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V2B) V4s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) (@ (@ tptp.ap V3C) V4s))) V4s)))))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ _let_1 (lambda ((V5s $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V0P) V5s))) (@ (@ tptp.ap V2B) V5s)))))) V3C)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 V0P)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EWHILE A_27a)) V2B)) V3C))) (@ _let_1 (lambda ((V6s $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V0P) V6s))) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) (@ (@ tptp.ap V2B) V6s)))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0P)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EWHILE tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo tptp.ty_2Enum_2Enum) tptp.bool) tptp.bool)) tptp.c_2Ebool_2E_7E)) V0P))) tptp.c_2Enum_2ESUC)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0P)))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0P))) (not (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0P))) (let ((_let_3 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_3 _let_1)) (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0Q $$unsorted)) (=> (@ (@ tptp.mem V0Q) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (exists ((V2n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V1P) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (=> (and (forall ((V4m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V3n))) (not (@ tptp.p (@ (@ tptp.ap V1P) _let_1)))))) (@ tptp.p (@ (@ tptp.ap V1P) _let_1))) (@ tptp.p (@ (@ tptp.ap V0Q) _let_1)))))) (@ tptp.p (@ (@ tptp.ap V0Q) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V1P)))))))))
% 1.89/2.22 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (exists ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0p) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (and (@ tptp.p (@ (@ tptp.ap V0p) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0p))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0p))) (not (@ tptp.p (@ (@ tptp.ap V0p) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (exists ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0p) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (and (@ tptp.p (@ (@ tptp.ap V0p) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0p))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V0p))) (not (@ tptp.p (@ (@ tptp.ap V0p) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.lam tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.ap tptp.c_2Ewhile_2ELEAST))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_1 (lambda ((V1n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V1n)) (@ tptp.inj__ty_2Enum_2Enum V0x)))))) V0x) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_1 (lambda ((V2n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V0x))) V2n))))) V0x))))))
% 1.89/2.22 (assert (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET)))) tptp.fo__c_2Enum_2E0))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.lam tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2EOLEAST) V0P)) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F tptp.ty_2Enum_2Enum)) (@ _let_1 (lambda ((V1n $$unsorted)) (@ (@ tptp.ap V0P) V1n)))))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) (@ _let_1 (lambda ((V2n $$unsorted)) (@ (@ tptp.ap V0P) V2n))))))) (@ tptp.c_2Eoption_2ENONE tptp.ty_2Enum_2Enum))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.ap V1Q))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption tptp.ty_2Enum_2Enum)) tptp.bool)) (=> (and (=> (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (not (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V2n))))) (@ tptp.p (@ _let_1 (@ tptp.c_2Eoption_2ENONE tptp.ty_2Enum_2Enum)))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) _let_1)) (forall ((V4m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V3n))) (not (@ tptp.p (@ (@ tptp.ap V0P) _let_1))))))) (@ tptp.p (@ (@ tptp.ap V1Q) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Enum_2Enum)) _let_1))))))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap tptp.c_2Ewhile_2EOLEAST) V0P))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Enum_2Enum)))) (let ((_let_2 (@ tptp.lam tptp.ty_2Enum_2Enum))) (let ((_let_3 (@ tptp.ap tptp.c_2Ewhile_2EOLEAST))) (let ((_let_4 (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))))) (and (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ _let_3 (@ _let_2 (lambda ((V1n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V1n)) (@ tptp.inj__ty_2Enum_2Enum V0x)))))) _let_4) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ _let_3 (@ _let_2 (lambda ((V2n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V0x))) V2n))))) _let_4) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ _let_3 (@ _let_2 (lambda ((V3n $$unsorted)) tptp.c_2Ebool_2EF)))) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ tptp.c_2Eoption_2ENONE tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ _let_3 (@ _let_2 (lambda ((V4n $$unsorted)) tptp.c_2Ebool_2ET)))) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2EOLEAST) V0P)) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ tptp.c_2Eoption_2ENONE tptp.ty_2Enum_2Enum))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (not (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V1n)))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (= (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2EOLEAST) V0P)) (@ tptp.surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME tptp.ty_2Enum_2Enum)) _let_1))) (and (@ tptp.p (@ (@ tptp.ap V0P) _let_1)) (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n))) (not (@ tptp.p (@ (@ tptp.ap V0P) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0G $$unsorted)) (=> (@ (@ tptp.mem V0G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.lam tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2s) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V0G)) V1f)) V2s) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F tptp.ty_2Enum_2Enum)) (@ _let_1 (lambda ((V3n $$unsorted)) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) (@ (@ tptp.ap V0G) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V1f)) V3n)) V2s)))))))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V1f)) (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) (@ _let_1 (lambda ((V4n $$unsorted)) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) (@ (@ tptp.ap V0G) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V1f)) V4n)) V2s)))))))) V2s)))) (@ tptp.c_2Eoption_2ENONE A_27a)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0G $$unsorted)) (=> (@ (@ tptp.mem V0G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V0G)) V1f)))) (=> (@ (@ tptp.mem V2s) A_27a) (= (@ _let_1 V2s) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.ap V0G) V2s))) (@ _let_1 (@ (@ tptp.ap V1f) V2s)))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0G $$unsorted)) (=> (@ (@ tptp.mem V0G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V0G)) V1f)) V2s) (@ tptp.c_2Eoption_2ENONE A_27a)) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0G) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V1f)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V2s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0G $$unsorted)) (=> (@ (@ tptp.mem V0G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) A_27a) (forall ((V3s_27 $$unsorted)) (=> (@ (@ tptp.mem V3s_27) A_27a) (=> (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V0G)) V1f)) V2s) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3s_27)) (not (@ tptp.p (@ (@ tptp.ap V0G) V3s_27)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0G $$unsorted)) (=> (@ (@ tptp.mem V0G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) A_27a) (forall ((V3s_27 $$unsorted)) (=> (@ (@ tptp.mem V3s_27) A_27a) (=> (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V0G)) V1f)) V2s) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3s_27)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EWHILE A_27a)) V0G)) V1f)) V2s) V3s_27)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1G $$unsorted)) (=> (@ (@ tptp.mem V1G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) V3s)) (forall ((V4x $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V4x) A_27a) (=> (and (@ tptp.p (@ _let_1 V4x)) (@ tptp.p (@ (@ tptp.ap V1G) V4x))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap V2f) V4x)))))))) (forall ((V5s_27 $$unsorted)) (=> (@ (@ tptp.mem V5s_27) A_27a) (=> (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V1G)) V2f)) V3s) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V5s_27)) (@ tptp.p (@ (@ tptp.ap V0P) V5s_27)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0P) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1G $$unsorted)) (=> (@ (@ tptp.mem V1G) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (=> (and (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) A_27a) (=> (not (@ tptp.p (@ (@ tptp.ap V1G) V3s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V3s)) V3s))))) (forall ((V4s1 $$unsorted)) (=> (@ (@ tptp.mem V4s1) A_27a) (forall ((V5s2 $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V5s2) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap V1G) V4s1)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap V2f) V4s1))) V5s2))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4s1)) V5s2))))))))) (forall ((V6s1 $$unsorted)) (=> (@ (@ tptp.mem V6s1) A_27a) (forall ((V7s2 $$unsorted)) (=> (@ (@ tptp.mem V7s2) A_27a) (=> (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewhile_2EOWHILE A_27a)) V1G)) V2f)) V6s1) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V7s2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V6s1)) V7s2))))))))))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2Eexactlog () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral_2Eexactlog) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2Eexactlog (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral_2Eexactlog X0)) (@ (@ tptp.ap tptp.c_2Enumeral_2Eexactlog) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2EiBIT__cases (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr (@ _let_1 A_27a)))) (@ (@ tptp.mem (@ tptp.c_2Enumeral_2EiBIT__cases A_27a)) (@ _let_1 (@ (@ tptp.arr A_27a) (@ _let_2 (@ _let_2 A_27a)))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2EiDUB () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2EiDUB (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral_2EiDUB X0)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2EiSQR () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral_2EiSQR) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2EiSQR (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral_2EiSQR X0)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiSQR) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2EiSUB () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral_2EiSUB) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2EiZ () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral_2EiZ) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2EiZ (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral_2EiZ X0)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiZ) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2EiiSUC () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral_2EiiSUC) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2EiiSUC (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral_2EiiSUC X0)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiiSUC) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2Einternal__mult () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral_2Einternal__mult) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2Einternal__mult (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumeral_2Einternal__mult X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Einternal__mult) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2Eonecount () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral_2Eonecount) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2Eonecount (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumeral_2Eonecount X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Eonecount) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral_2Etexp__help () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral_2Etexp__help) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumeral_2Etexp__help (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumeral_2Etexp__help X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Etexp__help) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2EiZ) (@ tptp.inj__ty_2Enum_2Enum V0x))) V0x)))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2EiiSUC) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_2 _let_1))))))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) V0n)) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V1n)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap tptp.c_2Enumeral_2EiZ) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V4n))) tptp.fo__c_2Enum_2E0)) (forall ((V5n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V5n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V6n tptp.tp__ty_2Enum_2Enum) (V7m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V7m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V6n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))) (forall ((V8n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V8n))) tptp.fo__c_2Enum_2E0)) (forall ((V9n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V9n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V9n)) (forall ((V10n tptp.tp__ty_2Enum_2Enum) (V11m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V11m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V10n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))) (forall ((V12n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V12n))))) tptp.fo__c_2Enum_2E0)) (forall ((V13n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V13n))))) tptp.fo__c_2Enum_2E0)) (forall ((V14n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V14n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (forall ((V15n tptp.tp__ty_2Enum_2Enum) (V16m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V16m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V15n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V17n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V17n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_2 _let_1)))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)) tptp.fo__c_2Enum_2E0) (forall ((V18n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V18n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_2 _let_1)))))))) (forall ((V19n tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ tptp.inj__ty_2Enum_2Enum V19n))) tptp.fo__c_2Enum_2E0) (= V19n tptp.fo__c_2Earithmetic_2EZERO))) (forall ((V20n tptp.tp__ty_2Enum_2Enum)) (= (= tptp.fo__c_2Enum_2E0 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ tptp.inj__ty_2Enum_2Enum V20n)))) (= V20n tptp.fo__c_2Earithmetic_2EZERO))) (forall ((V21n tptp.tp__ty_2Enum_2Enum) (V22m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V21n))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V22m)))) (= V21n V22m)))) (forall ((V23n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V23n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) false)) (forall ((V24n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V24n))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) _let_1)))))) (forall ((V25n tptp.tp__ty_2Enum_2Enum) (V26m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V26m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V25n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))) (forall ((V27n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V27n))) false)) (forall ((V28n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V28n))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) _let_1))))) (forall ((V29n tptp.tp__ty_2Enum_2Enum) (V30m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V29n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V30m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E) (@ _let_3 _let_1))) (@ _let_3 _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1))))))) (forall ((V31n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V31n))) true)) (forall ((V32n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V32n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (forall ((V33n tptp.tp__ty_2Enum_2Enum) (V34m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V34m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V33n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))) (forall ((V35n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D) (@ tptp.inj__ty_2Enum_2Enum V35n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) true)) (forall ((V36n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V36n))) (= V36n tptp.fo__c_2Enum_2E0))) (forall ((V37n tptp.tp__ty_2Enum_2Enum) (V38m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V37n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V38m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3E_3D) (@ _let_3 _let_1))) (@ _let_3 _let_2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))))))) (forall ((V39n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V39n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) _let_1))) (@ tptp.p (@ _let_2 _let_1)))))) (forall ((V40n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V40n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) _let_1))) (@ tptp.p (@ _let_2 _let_1)))))) (not (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1))) (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EEVEN) _let_1)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumeral_2EiiSUC))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_6)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_6))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_5 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_2))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ _let_4 _let_1))) (let ((_let_6 (@ tptp.ap tptp.c_2Enumeral_2EiiSUC))) (let ((_let_7 (@ _let_6 _let_5))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_9 (@ _let_8 _let_1))) (let ((_let_10 (@ tptp.ap (@ _let_3 (@ _let_8 _let_2))))) (let ((_let_11 (@ _let_10 _let_9))) (let ((_let_12 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_13 (@ tptp.surj__ty_2Enum_2Enum (@ _let_12 _let_7)))) (let ((_let_14 (@ _let_12 _let_1))) (let ((_let_15 (@ _let_10 _let_14))) (let ((_let_16 (@ tptp.ap (@ _let_3 (@ _let_12 _let_2))))) (let ((_let_17 (@ _let_16 _let_9))) (let ((_let_18 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_19 (@ _let_18 _let_5))) (let ((_let_20 (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 _let_19)))) (let ((_let_21 (@ _let_16 _let_14))) (let ((_let_22 (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_2)))) (let ((_let_23 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_24 (@ _let_4 _let_23))) (let ((_let_25 (@ (@ tptp.ap (@ _let_3 _let_23)) _let_2))) (let ((_let_26 (@ tptp.surj__ty_2Enum_2Enum (@ _let_12 _let_19)))) (let ((_let_27 (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_2)))) (let ((_let_28 (@ tptp.ap tptp.c_2Enumeral_2EiZ))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_28 _let_25)) V0n) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_28 _let_24)) V0n) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_28 _let_21)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ _let_28 _let_5)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_28 _let_17)) _let_26) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_28 _let_15)) _let_26) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_28 _let_11)) _let_20) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_25)) _let_27) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_24)) _let_27) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_21)) _let_26) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_17)) _let_20) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_15)) _let_20) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_18 _let_11)) _let_13) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_25)) _let_22) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_24)) _let_22) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_21)) _let_20) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_17)) _let_13) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_15)) _let_13) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_11)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 _let_7))))))))))))))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (= V0n V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_4 (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_6 (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_5)))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_8 (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_2)))) (let ((_let_9 (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_5)))) (and (= (= tptp.fo__c_2Earithmetic_2EZERO _let_9) false) (= (= _let_9 tptp.fo__c_2Earithmetic_2EZERO) false) (= (= tptp.fo__c_2Earithmetic_2EZERO _let_6) false) (= (= _let_6 tptp.fo__c_2Earithmetic_2EZERO) false) (= (= _let_9 _let_4) false) (= (= _let_6 _let_8) false) (= (= _let_9 _let_8) _let_1) (= (= _let_6 _let_4) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.p (@ _let_4 _let_1)))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_7 (@ _let_6 _let_1))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_9 (@ _let_8 _let_2))) (let ((_let_10 (@ tptp.ap (@ _let_3 _let_9)))) (let ((_let_11 (@ _let_8 _let_1))) (let ((_let_12 (@ _let_6 _let_2))) (let ((_let_13 (@ tptp.ap (@ _let_3 _let_12)))) (let ((_let_14 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_15 (@ tptp.ap (@ _let_3 _let_14)))) (and (= (@ tptp.p (@ _let_15 _let_12)) true) (= (@ tptp.p (@ _let_15 _let_9)) true) (= (@ tptp.p (@ _let_4 _let_14)) false) (= (@ tptp.p (@ _let_13 _let_7)) _let_5) (= (@ tptp.p (@ _let_10 _let_11)) _let_5) (= (@ tptp.p (@ _let_13 _let_11)) (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (= (@ tptp.p (@ _let_10 _let_7)) _let_5)))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_6 (@ _let_5 _let_1))) (let ((_let_7 (@ tptp.ap (@ _let_3 (@ _let_5 _let_2))))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_9 (@ _let_8 _let_1))) (let ((_let_10 (@ tptp.ap (@ _let_3 (@ _let_8 _let_2))))) (let ((_let_11 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (and (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_11)) _let_2)) true) (= (@ tptp.p (@ _let_10 _let_11)) false) (= (@ tptp.p (@ _let_7 _let_11)) false) (= (@ tptp.p (@ _let_10 _let_9)) _let_4) (= (@ tptp.p (@ _let_10 _let_6)) _let_4) (= (@ tptp.p (@ _let_7 _let_9)) (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (= (@ tptp.p (@ _let_7 _let_6)) _let_4)))))))))))))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) tptp.fo__c_2Earithmetic_2EZERO) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0n)))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_1 _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ _let_3 _let_2)))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) (@ _let_2 (@ _let_3 _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_2 _let_1)))))))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0zf $$unsorted)) (=> (@ (@ tptp.mem V0zf) A_27a) (forall ((V1b1f $$unsorted)) (=> (@ (@ tptp.mem V1b1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) A_27a))) (forall ((V2b2f $$unsorted)) (=> (@ (@ tptp.mem V2b2f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) A_27a))) (exists ((V3f $$unsorted)) (and (@ (@ tptp.mem V3f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap V3f) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)) V0zf) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.ap V3f))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap V1b1f) _let_1)) (@ _let_2 _let_1)))))) (forall ((V5n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V5n))) (let ((_let_2 (@ tptp.ap V3f))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap V2b2f) _let_1)) (@ _let_2 _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0zf $$unsorted)) (=> (@ (@ tptp.mem V0zf) A_27a) (forall ((V1bf1 $$unsorted)) (=> (@ (@ tptp.mem V1bf1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2bf2 $$unsorted)) (=> (@ (@ tptp.mem V2bf2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumeral_2EiBIT__cases A_27a)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) V0zf)) V1bf1)) V2bf2) V0zf))))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4zf $$unsorted)) (=> (@ (@ tptp.mem V4zf) A_27a) (forall ((V5bf1 $$unsorted)) (=> (@ (@ tptp.mem V5bf1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V6bf2 $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (=> (@ (@ tptp.mem V6bf2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumeral_2EiBIT__cases A_27a)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) V4zf)) V5bf1)) V6bf2) (@ (@ tptp.ap V5bf1) _let_1))))))))) (forall ((V7n tptp.tp__ty_2Enum_2Enum) (V8zf $$unsorted)) (=> (@ (@ tptp.mem V8zf) A_27a) (forall ((V9bf1 $$unsorted)) (=> (@ (@ tptp.mem V9bf1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V10bf2 $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V7n))) (=> (@ (@ tptp.mem V10bf2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumeral_2EiBIT__cases A_27a)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) V8zf)) V9bf1)) V10bf2) (@ (@ tptp.ap V10bf2) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_1))))))
% 1.89/2.22 (assert (and (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) V0b)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ tptp.inj__ty_2Enum_2Enum V1x))) tptp.fo__c_2Earithmetic_2EZERO)))) (forall ((V2b $$unsorted)) (=> (@ (@ tptp.mem V2b) tptp.bool) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.lam tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4x))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumeral_2EiBIT__cases tptp.ty_2Enum_2Enum)) _let_3)))) (let ((_let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) V2b)) _let_5)) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) V2b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_5)) (@ _let_1 (lambda ((V5m $$unsorted)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2ET)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V5m)))))) (@ _let_1 (lambda ((V6m $$unsorted)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2EF)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V6m))))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_2))) (@ _let_1 (lambda ((V7m $$unsorted)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2EF)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V7m)))))) (@ _let_1 (lambda ((V8m $$unsorted)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2EF)) (@ tptp.inj__ty_2Enum_2Enum V3n))) V8m)))))))))))))))) (forall ((V9b $$unsorted)) (=> (@ (@ tptp.mem V9b) tptp.bool) (forall ((V10n tptp.tp__ty_2Enum_2Enum) (V11x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.lam tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V10n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V11x))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumeral_2EiBIT__cases tptp.ty_2Enum_2Enum)) _let_3)))) (let ((_let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) V9b)) _let_5)) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) V9b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_5)) (@ _let_1 (lambda ((V12m $$unsorted)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2ET)) (@ tptp.inj__ty_2Enum_2Enum V10n))) V12m)))))) (@ _let_1 (lambda ((V13m $$unsorted)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2ET)) (@ tptp.inj__ty_2Enum_2Enum V10n))) V13m))))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))) (@ _let_1 (lambda ((V14m $$unsorted)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2ET)) (@ tptp.inj__ty_2Enum_2Enum V10n))) V14m)))))) (@ _let_1 (lambda ((V15m $$unsorted)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2EF)) (@ tptp.inj__ty_2Enum_2Enum V10n))) V15m))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V3n))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) tptp.bool) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumeral_2EiSUB))) (let ((_let_4 (@ tptp.ap (@ _let_3 tptp.c_2Ebool_2EF)))) (let ((_let_5 (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_7 (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_5)))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_9 (@ _let_8 _let_1))) (let ((_let_10 (@ _let_8 _let_2))) (let ((_let_11 (@ tptp.ap (@ _let_4 _let_10)))) (let ((_let_12 (@ tptp.ap (@ _let_3 tptp.c_2Ebool_2ET)))) (let ((_let_13 (@ tptp.ap (@ _let_12 _let_2)))) (let ((_let_14 (@ _let_13 _let_1))) (let ((_let_15 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (let ((_let_16 (@ tptp.surj__ty_2Enum_2Enum (@ _let_15 _let_14)))) (let ((_let_17 (@ tptp.ap (@ _let_12 _let_10)))) (let ((_let_18 (@ _let_6 _let_1))) (let ((_let_19 (@ _let_6 _let_2))) (let ((_let_20 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_21 (@ tptp.ap (@ _let_4 _let_19)))) (let ((_let_22 (@ tptp.ap (@ _let_12 _let_19)))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 V1b)) _let_20)) (@ tptp.inj__ty_2Enum_2Enum V0x))) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_13 _let_20)) V2n) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_21 _let_20)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_15 _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_22 _let_18)) _let_16) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_21 _let_18)) _let_7) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_22 _let_9)) _let_7) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_21 _let_9)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_15 _let_5))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_11 _let_20)) (@ tptp.surj__ty_2Enum_2Enum _let_19)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_17 _let_18)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_14))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_11 _let_18)) _let_16) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_17 _let_9)) _let_16) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_11 _let_9)) _let_7))))))))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2))) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2EiSUB) tptp.c_2Ebool_2ET)) _let_2)) _let_1)))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_1 _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ _let_4 _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) tptp.fo__c_2Earithmetic_2EZERO))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ _let_4 _let_1))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral_2EiZ))) (let ((_let_8 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_9)) _let_2)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_9)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 (@ (@ tptp.ap (@ _let_6 (@ _let_8 _let_5))) _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ _let_7 (@ (@ tptp.ap (@ _let_6 _let_5)) _let_1)))))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2EiSQR) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) _let_1))))))
% 1.89/2.22 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ tptp.inj__ty_2Enum_2Enum V0n))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiSQR) (@ _let_3 _let_1))))))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumeral_2EiSQR))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_4 _let_2))) (@ _let_4 (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (let ((_let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (and (@ tptp.p (@ _let_6 _let_5)) (@ tptp.p (@ _let_6 _let_4)) (not (@ tptp.p (@ _let_6 _let_2))) (not (@ tptp.p (@ _let_3 _let_5))) (not (@ tptp.p (@ _let_3 _let_4))) (@ tptp.p (@ _let_3 _let_2)))))))))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EFACT) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EFACT))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EFACT))) (let ((_let_4 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) (@ _let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap V0f) V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2)))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW A_27a)) V0f)))) (let ((_let_6 (@ tptp.ap (@ _let_5 _let_4)))) (and (= (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V1x) V1x) (= (@ _let_6 V1x) (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_4))) _let_1)) (= (@ (@ tptp.ap (@ _let_5 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2)))) V1x) (@ _let_6 _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMIN))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_5)) _let_2)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_2)) _let_5)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1))) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMAX))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_5)) _let_1)) V0x) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_1)) _let_5)) V0x) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_1))) (@ _let_3 _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2))) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (let ((_let_4 (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)))) (let ((_let_5 (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1))) (let ((_let_6 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (let ((_let_7 (@ tptp.ap (@ _let_3 _let_6)))) (let ((_let_8 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_9 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_9 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ _let_7 _let_8)) _let_5))) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_6)) (@ (@ tptp.ap (@ _let_9 _let_2)) _let_1))) (@ (@ tptp.ap (@ _let_4 _let_8)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) _let_6)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3q $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V0a))) V3q))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum V1m))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) V3q)))) _let_1))))))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2Efindq) (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_5))))))))))))))))))
% 1.89/2.22 (assert (and (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V1n)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) _let_2)) _let_1)))))))))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V3n)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) _let_2)) _let_1)))))))))) (forall ((V4m tptp.tp__ty_2Enum_2Enum) (V5n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V5n)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V4m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) _let_2)) _let_1)))))))))) (forall ((V6m tptp.tp__ty_2Enum_2Enum) (V7n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V7n)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V6m))) (let ((_let_3 (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIVMOD) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 tptp.ty_2Enum_2Enum)) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1)))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))))
% 1.89/2.22 (assert (and (forall ((V0acc tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0acc))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Etexp__help) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2acc tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2acc))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumeral_2Etexp__help))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V1a))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Etexp__help) _let_4)) _let_6)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ _let_5 _let_6)) _let_3))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ (@ tptp.ap (@ _let_5 _let_4)) _let_3)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Etexp__help) _let_3)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0acc tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0acc))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_5 (@ _let_2 _let_4))) (let ((_let_6 (@ tptp.ap tptp.c_2Enumeral_2Etexp__help))) (let ((_let_7 (@ tptp.ap (@ _let_6 _let_5)))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_5))) _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 (@ _let_8 _let_4))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_3))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral_2Etexp__help))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_6 (@ _let_7 _let_1)))))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 (@ _let_3 _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ _let_6 _let_4))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_4))) _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ _let_6 (@ _let_7 _let_2)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)))))))))))))))
% 1.89/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Eonecount) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ tptp.inj__ty_2Enum_2Enum V0x))) V0x)) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumeral_2Eonecount))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Eonecount) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V3n)))) (@ tptp.inj__ty_2Enum_2Enum V4x))) tptp.fo__c_2Earithmetic_2EZERO))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2Eexactlog) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) tptp.fo__c_2Earithmetic_2EZERO) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2Eexactlog) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V0n)))) tptp.fo__c_2Earithmetic_2EZERO)) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2Eexactlog) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2x $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V2x)) _let_1))) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) V2x))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Eonecount) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Eonecount) _let_4)) _let_3))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_7 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_7 _let_5)) (@ tptp.p (@ _let_7 _let_4))) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ (@ tptp.ap (@ _let_6 _let_5)) _let_3)))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1m))) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2Eexactlog) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_4))) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_4)) (@ _let_3 (@ _let_2 _let_1)))))))))))))
% 1.89/2.22 (assert (= tptp.c_2Enumeral_2Einternal__mult tptp.c_2Earithmetic_2E_2A))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V0x)))) V0x)))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumeral_2Eexactlog))) (let ((_let_5 (@ _let_4 _let_3))) (let ((_let_6 (@ tptp.lam tptp.ty_2Enum_2Enum))) (let ((_let_7 (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (let ((_let_8 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_9 (@ _let_2 _let_8))) (let ((_let_10 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_11 (@ tptp.ap (@ _let_10 _let_3)))) (let ((_let_12 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_13 (@ _let_12 _let_8))) (let ((_let_14 (@ _let_12 _let_1))) (let ((_let_15 (@ tptp.ap (@ _let_10 _let_14)))) (let ((_let_16 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_17 (@ tptp.inj__ty_2Enum_2Enum V0n))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_10 _let_16)) _let_17)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_10 _let_17)) _let_16)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_15 _let_13)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Einternal__mult) _let_14)) _let_13))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_15 _let_9)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 (@ _let_6 (lambda ((V3n $$unsorted)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V1x)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) V3n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Etexp__help) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) V3n))) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Einternal__mult) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V2y))))))))) (@ _let_4 _let_9)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_11 _let_13)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 (@ _let_6 (lambda ((V4m $$unsorted)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V2y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) V4m))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Etexp__help) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) V4m))) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Einternal__mult) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V1x)))) _let_1))))))) _let_5))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_11 _let_9)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 (@ _let_6 (lambda ((V5m $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V6n $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2y)))) (let ((_let_3 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1x)))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2EPRE))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EDIV2))) (let ((_let_6 (@ tptp.ap tptp.c_2Enumeral_2Etexp__help))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (let ((_let_8 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_8 (@ _let_7 V5m))) (@ (@ tptp.ap (@ _let_6 (@ _let_5 V5m))) (@ _let_4 _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_8 (@ _let_7 V6n))) (@ (@ tptp.ap (@ _let_6 (@ _let_5 V6n))) (@ _let_4 _let_3)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral_2Einternal__mult) _let_3)) _let_2))))))))))))))) (@ (@ tptp.ap tptp.c_2Enumeral_2Eexactlog) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V2y)))))))) _let_5)))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumeral_2Einternal__mult))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ _let_4 _let_1))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral_2EiZ))) (let ((_let_8 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_9)) _let_2)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_9)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 (@ (@ tptp.ap (@ _let_6 (@ _let_8 _let_5))) _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ _let_7 (@ (@ tptp.ap (@ _let_6 _let_5)) _let_1)))))))))))))))))
% 1.89/2.22 (declare-fun tptp.c_2Edivides_2EPRIMES () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Edivides_2EPRIMES) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Edivides_2EPRIMES (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Edivides_2EPRIMES X0)) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Edivides_2Edivides () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Edivides_2Edivides) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Edivides_2Eprime () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Edivides_2Eprime) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.inj__ty_2Enum_2Enum V1b))) (exists ((V2q tptp.tp__ty_2Enum_2Enum)) (= V1b (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2q))) (@ tptp.inj__ty_2Enum_2Enum V0a))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0m))) (= V0m tptp.fo__c_2Enum_2E0))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_1)) _let_1)))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.ap tptp.c_2Edivides_2Edivides))) (let ((_let_3 (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1b))) (=> (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_4)) _let_1))) (@ tptp.p (@ _let_3 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0a)))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0x))) _let_1)) (= V0x (@ tptp.surj__ty_2Enum_2Enum _let_1))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0a))))) (=> (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0a))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1b))) (=> (and (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1)))) (@ tptp.p (@ _let_2 _let_1))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0a))))) (=> (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_1)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)) (= V1n tptp.fo__c_2Enum_2E0)))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Edivides_2Edivides))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (= V0a V1b)))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V0a))))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2c)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V0n))) _let_1))) _let_1)) (or (= V1m tptp.fo__c_2Enum_2E0) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0b))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EFACT) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EFACT) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ tptp.inj__ty_2Enum_2Enum V0a))) (and (not (= V0a (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (forall ((V1b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V1b))) (@ tptp.inj__ty_2Enum_2Enum V0a))) (or (= V1b V0a) (= V1b (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))
% 1.89/2.22 (assert (not (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (not (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))
% 1.89/2.22 (assert (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ _let_1 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0p))) (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0p))) (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Edivides_2Eprime))) (=> (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_1))) (= V0m V1n)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (not (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (exists ((V1p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1p))) (and (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0n)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (exists ((V1p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1p))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) _let_1)) (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_1)))))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) V1p))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V0n)))) V1p))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Edivides_2EPRIMES))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Edivides_2EPRIMES))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Edivides_2EPRIMES))) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (= V0m V1n)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) _let_1))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (exists ((V1i tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V1i)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (exists ((V1i tptp.tp__ty_2Enum_2Enum)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V1i)))) (forall ((V2j tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2j))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1i))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) _let_1))) (@ tptp.inj__ty_2Enum_2Enum V0n))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Edivides_2EPRIMES))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_1)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2)))) (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_1))) false)))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ tptp.inj__ty_2Enum_2Enum V0p))) (exists ((V1i tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V1i))) V0p)))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) (@ tptp.inj__ty_2Enum_2Enum V0p))) (exists ((V1i tptp.tp__ty_2Enum_2Enum)) (= V0p (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V1i))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Edivides_2EPRIMES) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)))) (let ((_let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) (let ((_let_6 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)))) (let ((_let_7 (@ tptp.ap (@ _let_4 _let_2)))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ _let_7 _let_1))) _let_5)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ _let_7 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) tptp.c_2Ebool_2ET)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 _let_5)) tptp.c_2Ebool_2ET)) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_3)) _let_2))) _let_1)))))))))))))))
% 1.89/2.22 (declare-fun tptp.ty_2Eind__type_2Erecspace (tptp.del) tptp.del)
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EBOTTOM (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EBOTTOM A_27a)) (@ tptp.ty_2Eind__type_2Erecspace A_27a))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ECONSTR (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (let ((_let_2 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2ECONSTR A_27a)) (@ _let_2 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr (@ _let_2 _let_1)) _let_1))))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EFCONS (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EFCONS A_27a)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr _let_1) _let_1))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EFNIL (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EFNIL A_27a)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EINJA (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EINJA A_27a)) (@ _let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ _let_1 tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EINJF (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EINJF A_27a)) (@ (@ tptp.arr (@ _let_1 _let_2)) _let_2))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EINJN (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EINJN A_27a)) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EINJP (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EINJP A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EISO (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eind__type_2EISO A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27a)) tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ENUMFST () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Eind__type_2ENUMFST) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Eind__type_2ENUMFST (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Eind__type_2ENUMFST X0)) (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMFST) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ENUMLEFT () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Eind__type_2ENUMLEFT) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ENUMPAIR () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Eind__type_2ENUMPAIR) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Eind__type_2ENUMPAIR (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Eind__type_2ENUMPAIR X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMPAIR) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ENUMRIGHT () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Eind__type_2ENUMRIGHT) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Eind__type_2ENUMRIGHT (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Eind__type_2ENUMRIGHT X0)) (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMRIGHT) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ENUMSND () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Eind__type_2ENUMSND) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Eind__type_2ENUMSND (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Eind__type_2ENUMSND X0)) (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMSND) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2ENUMSUM () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Eind__type_2ENUMSUM) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EZBOT (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EZBOT A_27a)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EZCONSTR (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_3 (@ _let_2 (@ _let_1 tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) (@ _let_2 (@ _let_1 (@ (@ tptp.arr (@ _let_2 _let_3)) _let_3)))))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2EZRECSPACE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) tptp.bool))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2Edest__rec (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2Edest__rec A_27a)) (@ (@ tptp.arr (@ tptp.ty_2Eind__type_2Erecspace A_27a)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Eind__type_2Emk__rec (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eind__type_2Emk__rec A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (@ tptp.ty_2Eind__type_2Erecspace A_27a)))))
% 1.89/2.22 (assert (forall ((A_27A tptp.del) (A_27B tptp.del) (A_27C tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27A) (@ (@ tptp.arr A_27B) A_27C))) (=> (forall ((V1x1 $$unsorted)) (=> (@ (@ tptp.mem V1x1) A_27A) (forall ((V2y1 $$unsorted)) (=> (@ (@ tptp.mem V2y1) A_27B) (forall ((V3x2 $$unsorted)) (=> (@ (@ tptp.mem V3x2) A_27A) (forall ((V4y2 $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V4y2) A_27B) (= (= (@ (@ tptp.ap (@ _let_1 V1x1)) V2y1) (@ (@ tptp.ap (@ _let_1 V3x2)) V4y2)) (and (= V1x1 V3x2) (= V2y1 V4y2)))))))))))) (exists ((V5X $$unsorted)) (and (@ (@ tptp.mem V5X) (@ (@ tptp.arr A_27C) A_27A)) (exists ((V6Y $$unsorted)) (and (@ (@ tptp.mem V6Y) (@ (@ tptp.arr A_27C) A_27B)) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27A) (forall ((V8y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap V0P) V7x)) V8y))) (=> (@ (@ tptp.mem V8y) A_27B) (and (= (@ (@ tptp.ap V5X) _let_1) V7x) (= (@ (@ tptp.ap V6Y) _let_1) V8y)))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_4 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMPAIR) _let_6)) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_4)) _let_6))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ _let_5 _let_4)) _let_3))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0x1 tptp.tp__ty_2Enum_2Enum) (V1y1 tptp.tp__ty_2Enum_2Enum) (V2x2 tptp.tp__ty_2Enum_2Enum) (V3y2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Eind__type_2ENUMPAIR))) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0x1))) (@ tptp.inj__ty_2Enum_2Enum V1y1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2x2))) (@ tptp.inj__ty_2Enum_2Enum V3y2)))) (= V0x1 V2x2)))))
% 1.89/2.22 (assert (forall ((V0x1 tptp.tp__ty_2Enum_2Enum) (V1y1 tptp.tp__ty_2Enum_2Enum) (V2x2 tptp.tp__ty_2Enum_2Enum) (V3y2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Eind__type_2ENUMPAIR))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0x1))) (@ tptp.inj__ty_2Enum_2Enum V1y1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2x2))) (@ tptp.inj__ty_2Enum_2Enum V3y2)))) (and (= V0x1 V2x2) (= V1y1 V3y2))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMPAIR) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y)))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMFST) _let_1)) V0x) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMSND) _let_1)) V1y)))))
% 1.89/2.22 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMSUM) V0b)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) V0b)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_2)))))))))
% 1.89/2.22 (assert (forall ((V0b1 $$unsorted)) (=> (@ (@ tptp.mem V0b1) tptp.bool) (forall ((V1x1 tptp.tp__ty_2Enum_2Enum) (V2b2 $$unsorted)) (=> (@ (@ tptp.mem V2b2) tptp.bool) (forall ((V3x2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Eind__type_2ENUMSUM))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 V0b1)) (@ tptp.inj__ty_2Enum_2Enum V1x1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 V2b2)) (@ tptp.inj__ty_2Enum_2Enum V3x2)))) (and (= (@ tptp.p V0b1) (@ tptp.p V2b2)) (= V1x1 V3x2))))))))))
% 1.89/2.22 (assert (forall ((V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMSUM) V0x)) (@ tptp.inj__ty_2Enum_2Enum V1y)))) (and (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMLEFT) _let_1)) (@ tptp.p V0x)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMRIGHT) _let_1)) V1y)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0m tptp.tp__ty_2Enum_2Enum)) (= (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJN A_27a)) (@ tptp.inj__ty_2Enum_2Enum V0m)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1n $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2a $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V1n)) (@ tptp.inj__ty_2Enum_2Enum V0m)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n1 tptp.tp__ty_2Enum_2Enum) (V1n2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2EINJN A_27a)))) (= (= (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0n1)) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n2))) (= V0n1 V1n2)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJA A_27a)) V0a) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1n $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2b $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V2b)) V0a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0a1 $$unsorted)) (=> (@ (@ tptp.mem V0a1) A_27a) (forall ((V1a2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2EINJA A_27a)))) (=> (@ (@ tptp.mem V1a2) A_27a) (= (= (@ _let_1 V0a1) (@ _let_1 V1a2)) (= V0a1 V1a2))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (= (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJF A_27a)) V0f) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMFST) V1n))) (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMSND) V1n)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f1 $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0f1) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (forall ((V1f2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2EINJF A_27a)))) (let ((_let_2 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V1f2) (@ _let_2 (@ _let_2 (@ (@ tptp.arr A_27a) tptp.bool)))) (= (= (@ _let_1 V0f1) (@ _let_1 V1f2)) (= V0f1 V1f2))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f1 $$unsorted)) (=> (@ (@ tptp.mem V0f1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1f2 $$unsorted)) (=> (@ (@ tptp.mem V1f2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJP A_27a)) V0f1)) V1f2) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2n $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V3a $$unsorted)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMRIGHT) V2n))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) (@ (@ tptp.ap tptp.c_2Eind__type_2ENUMLEFT) V2n))) (@ (@ tptp.ap (@ (@ tptp.ap V0f1) _let_1)) V3a))) (@ (@ tptp.ap (@ (@ tptp.ap V1f2) _let_1)) V3a)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f1 $$unsorted)) (=> (@ (@ tptp.mem V0f1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1f1_27 $$unsorted)) (=> (@ (@ tptp.mem V1f1_27) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V2f2 $$unsorted)) (=> (@ (@ tptp.mem V2f2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V3f2_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2EINJP A_27a)))) (=> (@ (@ tptp.mem V3f2_27) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (= (= (@ (@ tptp.ap (@ _let_1 V0f1)) V2f2) (@ (@ tptp.ap (@ _let_1 V1f1_27)) V3f2_27)) (and (= V0f1 V1f1_27) (= V2f2 V3f2_27)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0c tptp.tp__ty_2Enum_2Enum) (V1i $$unsorted)) (=> (@ (@ tptp.mem V1i) A_27a) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2EINJP A_27a)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0c))) (let ((_let_3 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2r) (@ _let_3 (@ _let_3 (@ (@ tptp.arr A_27a) tptp.bool)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) _let_2)) V1i)) V2r) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJN A_27a)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2)))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJA A_27a)) V1i))) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJF A_27a)) V2r))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))) (= (@ tptp.c_2Eind__type_2EZBOT A_27a) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJP A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EINJN A_27a)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V0z $$unsorted)) tptp.c_2Ebool_2ET))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0c tptp.tp__ty_2Enum_2Enum) (V1i $$unsorted)) (=> (@ (@ tptp.mem V1i) A_27a) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2r) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (not (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V0c))) V1i)) V2r) (@ tptp.c_2Eind__type_2EZBOT A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Eind__type_2EZRECSPACE A_27a) (@ (@ tptp.lam (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (lambda ((V0a0 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) tptp.bool))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V1ZRECSPACE_27 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2a0 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))) V2a0)) (@ tptp.c_2Eind__type_2EZBOT A_27a)))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3c $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4i $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool))))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F _let_2)) (@ (@ tptp.lam _let_2) (lambda ((V5r $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))) V2a0)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) V3c)) V4i)) V5r)))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V6n $$unsorted)) (@ (@ tptp.ap V1ZRECSPACE_27) (@ (@ tptp.ap V5r) V6n)))))))))))))))))))) (@ (@ tptp.ap V1ZRECSPACE_27) V2a0))))))) (@ (@ tptp.ap V1ZRECSPACE_27) V0a0))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) (@ tptp.c_2Eind__type_2EZBOT A_27a))) (forall ((V0c tptp.tp__ty_2Enum_2Enum) (V1i $$unsorted)) (=> (@ (@ tptp.mem V1i) A_27a) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2r) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (=> (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) (@ (@ tptp.ap V2r) (@ tptp.inj__ty_2Enum_2Enum V3n))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V0c))) V1i)) V2r))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0ZRECSPACE_27 $$unsorted)) (=> (@ (@ tptp.mem V0ZRECSPACE_27) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) (@ tptp.c_2Eind__type_2EZBOT A_27a))) (forall ((V1c tptp.tp__ty_2Enum_2Enum) (V2i $$unsorted)) (=> (@ (@ tptp.mem V2i) A_27a) (forall ((V3r $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V3r) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (=> (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) (@ (@ tptp.ap V3r) (@ tptp.inj__ty_2Enum_2Enum V4n))))) (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V1c))) V2i)) V3r)))))))))) (forall ((V5a0 $$unsorted)) (=> (@ (@ tptp.mem V5a0) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) V5a0)) (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) V5a0)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0ZRECSPACE_27 $$unsorted)) (=> (@ (@ tptp.mem V0ZRECSPACE_27) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) (@ tptp.c_2Eind__type_2EZBOT A_27a))) (forall ((V1c tptp.tp__ty_2Enum_2Enum) (V2i $$unsorted)) (=> (@ (@ tptp.mem V2i) A_27a) (forall ((V3r $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V3r) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (=> (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap V3r) (@ tptp.inj__ty_2Enum_2Enum V4n)))) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) _let_1)) (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) _let_1))))) (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V1c))) V2i)) V3r)))))))))) (forall ((V5a0 $$unsorted)) (=> (@ (@ tptp.mem V5a0) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) V5a0)) (@ tptp.p (@ (@ tptp.ap V0ZRECSPACE_27) V5a0)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0a0 $$unsorted)) (=> (@ (@ tptp.mem V0a0) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) V0a0)) (or (= V0a0 (@ tptp.c_2Eind__type_2EZBOT A_27a)) (exists ((V1c tptp.tp__ty_2Enum_2Enum) (V2i $$unsorted)) (and (@ (@ tptp.mem V2i) A_27a) (exists ((V3r $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (and (@ (@ tptp.mem V3r) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) tptp.bool)))) (= V0a0 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V1c))) V2i)) V3r)) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) (@ (@ tptp.ap V3r) (@ tptp.inj__ty_2Enum_2Enum V4n)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (exists ((V0rep $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (let ((_let_2 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool)))) (and (@ (@ tptp.mem V0rep) (@ (@ tptp.arr _let_1) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION _let_2) _let_1)) (@ tptp.c_2Eind__type_2EZRECSPACE A_27a))) V0rep))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ tptp.ty_2Eind__type_2Erecspace A_27a)) (= (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Emk__rec A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Edest__rec A_27a)) V0a)) V0a))) (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)) V1r)) (= (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Edest__rec A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Emk__rec A_27a)) V1r)) V1r)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Eind__type_2EBOTTOM A_27a) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Emk__rec A_27a)) (@ tptp.c_2Eind__type_2EZBOT A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0c tptp.tp__ty_2Enum_2Enum) (V1i $$unsorted)) (=> (@ (@ tptp.mem V1i) A_27a) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0c))) (=> (@ (@ tptp.mem V2r) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2ECONSTR A_27a)) _let_1)) V1i)) V2r) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Emk__rec A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EZCONSTR A_27a)) _let_1)) V1i)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3n $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Eind__type_2Edest__rec A_27a)) (@ (@ tptp.ap V2r) V3n)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2EZRECSPACE A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Eind__type_2Emk__rec A_27a)))) (=> (@ (@ tptp.mem V1y) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (=> (= (@ _let_2 V0x) (@ _let_2 V1y)) (=> (and (@ tptp.p (@ _let_1 V0x)) (@ tptp.p (@ _let_1 V1y))) (= V0x V1y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ tptp.ty_2Eind__type_2Erecspace A_27a)) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2Edest__rec A_27a)))) (=> (@ (@ tptp.mem V1y) (@ tptp.ty_2Eind__type_2Erecspace A_27a)) (= (= (@ _let_1 V0x) (@ _let_1 V1y)) (= V0x V1y))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0c tptp.tp__ty_2Enum_2Enum) (V1i $$unsorted)) (=> (@ (@ tptp.mem V1i) A_27a) (forall ((V2r $$unsorted)) (=> (@ (@ tptp.mem V2r) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (not (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2ECONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V0c))) V1i)) V2r) (@ tptp.c_2Eind__type_2EBOTTOM A_27a))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0c1 tptp.tp__ty_2Enum_2Enum) (V1i1 $$unsorted)) (=> (@ (@ tptp.mem V1i1) A_27a) (forall ((V2r1 $$unsorted)) (=> (@ (@ tptp.mem V2r1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (forall ((V3c2 tptp.tp__ty_2Enum_2Enum) (V4i2 $$unsorted)) (=> (@ (@ tptp.mem V4i2) A_27a) (forall ((V5r2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eind__type_2ECONSTR A_27a)))) (=> (@ (@ tptp.mem V5r2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0c1))) V1i1)) V2r1) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3c2))) V4i2)) V5r2)) (and (= V0c1 V3c2) (= V1i1 V4i2) (= V2r1 V5r2)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ tptp.ty_2Eind__type_2Erecspace A_27a)) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Eind__type_2EBOTTOM A_27a))) (forall ((V1c tptp.tp__ty_2Enum_2Enum) (V2i $$unsorted)) (=> (@ (@ tptp.mem V2i) A_27a) (forall ((V3r $$unsorted)) (=> (@ (@ tptp.mem V3r) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (=> (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap V3r) (@ tptp.inj__ty_2Enum_2Enum V4n))))) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2ECONSTR A_27a)) (@ tptp.inj__ty_2Enum_2Enum V1c))) V2i)) V3r))))))))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) (@ tptp.ty_2Eind__type_2Erecspace A_27a)) (@ tptp.p (@ (@ tptp.ap V0P) V5x))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0Fn $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0Fn) (@ _let_1 (@ (@ tptp.arr A_27a) (@ (@ tptp.arr (@ _let_1 (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (@ (@ tptp.arr (@ _let_1 A_27b)) A_27b))))) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr (@ tptp.ty_2Eind__type_2Erecspace A_27a)) A_27b)) (forall ((V2c tptp.tp__ty_2Enum_2Enum) (V3i $$unsorted)) (=> (@ (@ tptp.mem V3i) A_27a) (forall ((V4r $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (=> (@ (@ tptp.mem V4r) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eind__type_2Erecspace A_27a))) (= (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2ECONSTR A_27a)) _let_1)) V3i)) V4r)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap V0Fn) _let_1)) V3i)) V4r)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V5n $$unsorted)) (@ (@ tptp.ap V1f) (@ (@ tptp.ap V4r) V5n)))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EFCONS A_27a)) V0a)) V1f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V0a))))) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (forall ((V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EFCONS A_27a)) V2a)) V3f)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap V3f) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n tptp.tp__ty_2Enum_2Enum)) (= (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EFNIL A_27a)) (@ tptp.inj__ty_2Enum_2Enum V0n)) (@ tptp.c_2Ebool_2EARB A_27a))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eind__type_2EFCONS A_27a)) V0a)) V1f)) _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) V0a)) (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27a)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eind__type_2EISO A_27a) A_27b)) V0f)) V1g)) (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27b) (= (@ (@ tptp.ap V0f) (@ (@ tptp.ap V1g) V2x)) V2x))) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (= (@ (@ tptp.ap V1g) (@ (@ tptp.ap V0f) V3y)) V3y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.lam A_27a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eind__type_2EISO A_27a) A_27a)) (@ _let_1 (lambda ((V0x $$unsorted)) V0x)))) (@ _let_1 (lambda ((V1x $$unsorted)) V1x)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (A_27d tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27c)) (forall ((V1f_27 $$unsorted)) (=> (@ (@ tptp.mem V1f_27) (@ (@ tptp.arr A_27c) A_27a)) (forall ((V2g $$unsorted)) (=> (@ (@ tptp.mem V2g) (@ (@ tptp.arr A_27b) A_27d)) (forall ((V3g_27 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27c) A_27d))) (let ((_let_2 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V3g_27) (@ (@ tptp.arr A_27d) A_27b)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eind__type_2EISO A_27a) A_27c)) V0f)) V1f_27)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eind__type_2EISO A_27b) A_27d)) V2g)) V3g_27))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eind__type_2EISO _let_2) _let_1)) (@ (@ tptp.lam _let_2) (lambda ((V4h $$unsorted)) (@ (@ tptp.lam A_27c) (lambda ((V5a_27 $$unsorted)) (@ (@ tptp.ap V2g) (@ (@ tptp.ap V4h) (@ (@ tptp.ap V1f_27) V5a_27))))))))) (@ (@ tptp.lam _let_1) (lambda ((V6h $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V7a $$unsorted)) (@ (@ tptp.ap V3g_27) (@ (@ tptp.ap V6h) (@ (@ tptp.ap V0f) V7a)))))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eind__type_2EISO A_27a) A_27b)) V0f)) V1g)) (and (forall ((V2P $$unsorted)) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap V2P) V3x)))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27b) (@ tptp.p (@ (@ tptp.ap V2P) (@ (@ tptp.ap V1g) V4x)))))))) (forall ((V5P $$unsorted)) (=> (@ (@ tptp.mem V5P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V6x $$unsorted)) (and (@ (@ tptp.mem V6x) A_27a) (@ tptp.p (@ (@ tptp.ap V5P) V6x)))) (exists ((V7x $$unsorted)) (and (@ (@ tptp.mem V7x) A_27b) (@ tptp.p (@ (@ tptp.ap V5P) (@ (@ tptp.ap V1g) V7x)))))))) (forall ((V8a $$unsorted)) (=> (@ (@ tptp.mem V8a) A_27a) (forall ((V9b $$unsorted)) (=> (@ (@ tptp.mem V9b) A_27b) (= (= V8a (@ (@ tptp.ap V1g) V9b)) (= (@ (@ tptp.ap V0f) V8a) V9b)))))))))))))
% 1.89/2.22 (declare-fun tptp.c_2EbasicSize_2Ebool__size () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2EbasicSize_2Ebool__size) (@ (@ tptp.arr tptp.bool) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.c_2EbasicSize_2Eone__size () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2EbasicSize_2Eone__size) (@ (@ tptp.arr tptp.ty_2Eone_2Eone) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2EbasicSize_2Eone__size (tptp.tp__ty_2Eone_2Eone) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Eone_2Eone)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2EbasicSize_2Eone__size X0)) (@ (@ tptp.ap tptp.c_2EbasicSize_2Eone__size) (@ tptp.inj__ty_2Eone_2Eone X0)))))
% 1.89/2.22 (declare-fun tptp.c_2EbasicSize_2Eoption__size (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2EbasicSize_2Eoption__size A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ tptp.ty_2Eoption_2Eoption A_27a)) tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.c_2EbasicSize_2Epair__size (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2EbasicSize_2Epair__size A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2EbasicSize_2Esum__size (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2EbasicSize_2Esum__size A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b)) tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2EbasicSize_2Ebool__size) V0b)) tptp.fo__c_2Enum_2E0))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) tptp.ty_2Enum_2Enum)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EbasicSize_2Epair__size A_27a) A_27b)) V0f)) V1g) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap V0f) V2x))) (@ (@ tptp.ap V1g) V3y)))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Eone_2Eone)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2EbasicSize_2Eone__size) (@ tptp.inj__ty_2Eone_2Eone V0x))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) tptp.ty_2Enum_2Enum)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EbasicSize_2Esum__size A_27a) A_27b)) V0f)) V1g)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V2x))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap V0f) V2x))))))))) (forall ((V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V4g $$unsorted)) (=> (@ (@ tptp.mem V4g) (@ (@ tptp.arr A_27b) tptp.ty_2Enum_2Enum)) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27b) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EbasicSize_2Esum__size A_27a) A_27b)) V3f)) V4g)) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b)) V5y))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap V4g) V5y))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EbasicSize_2Eoption__size A_27a)) V0f)) (@ tptp.c_2Eoption_2ENONE A_27a))) tptp.fo__c_2Enum_2E0))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EbasicSize_2Eoption__size A_27a)) V1f)) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V2x))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap V1f) V2x)))))))))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2ELOG () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Elogroot_2ELOG) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Elogroot_2ELOG (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Elogroot_2ELOG X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2EROOT () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Elogroot_2EROOT) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Elogroot_2EROOT (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Elogroot_2EROOT X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2ESQRTd () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Elogroot_2ESQRTd) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2EiSQRT0 () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Elogroot_2EiSQRT0) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2EiSQRT1 () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Elogroot_2EiSQRT1) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2EiSQRT2 () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Elogroot_2EiSQRT2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Elogroot_2EiSQRT3 () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Elogroot_2EiSQRT3) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (assert (forall ((V0e tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0e))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ _let_3 _let_4))) (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0e tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0e))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ _let_3 _let_4))) (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0r))) (exists ((V2rt tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2rt))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_4)) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) _let_1)) _let_2))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_2)) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0r))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) _let_2)) _let_1)) V2p))))))))
% 1.89/2.22 (assert (exists ((V0f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (and (@ (@ tptp.mem V0f) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))) (forall ((V1a tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap V0f) _let_2)) _let_1))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_4 _let_3))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_1)) (@ _let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)) _let_1))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_4 _let_3))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_1)) (@ _let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3)))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_4 _let_3))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ _let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)) _let_1)) V2p))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_3)))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_3)))) (let ((_let_7 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_8 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_9 (@ tptp.ap (@ _let_8 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_9 _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_8 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_3)) (@ tptp.p (@ _let_9 _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 (@ (@ tptp.ap (@ _let_5 (@ _let_4 (@ _let_7 _let_2)))) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 (@ _let_6 (@ (@ tptp.ap (@ _let_5 (@ _let_4 _let_2))) _let_1)))))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_4))) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_4)) (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_1)))) (let ((_let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_4)) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2c)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) V2c))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_6 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_4))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ _let_3 _let_4))) (@ _let_3 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1))) _let_4)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_1)) _let_2)) tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ _let_3 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))) _let_4))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) _let_1)))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_6 _let_1)) (@ tptp.p (@ _let_6 _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_5 _let_3))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0r))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ _let_3 _let_4))) (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EEXP))) (let ((_let_4 (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2r tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2r))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_3)))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_6 (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_3)) (@ tptp.p (@ _let_6 _let_2)) (@ tptp.p (@ _let_6 _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) _let_1)) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ _let_4 _let_2))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_2)) _let_1)))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_3))))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0r))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) _let_1)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_5)) _let_1)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_5)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2x $$unsorted)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V2x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0r))))) V2x)) _let_1)))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_2)) _let_1))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2ESQRTd) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_2)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT0) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET _let_2) _let_2)) (@ (@ tptp.lam _let_2) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2d $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_6 (@ tptp.ap (@ _let_5 (@ _let_3 (@ _let_4 _let_2)))))) (let ((_let_7 (@ (@ tptp.ap (@ _let_5 (@ _let_3 (@ _let_4 _let_1)))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p)))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V2d)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ (@ tptp.ap (@ _let_8 _let_7)) (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p))))) (@ (@ tptp.ap (@ _let_8 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_7))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ _let_6 V2d))) (@ _let_3 _let_2)))))))))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p))))))) (@ (@ tptp.ap tptp.c_2Elogroot_2ESQRTd) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT1) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET _let_2) _let_2)) (@ (@ tptp.lam _let_2) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2d $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_6 (@ tptp.ap (@ _let_5 (@ _let_3 (@ _let_4 _let_2)))))) (let ((_let_7 (@ (@ tptp.ap (@ _let_5 (@ _let_3 (@ _let_4 _let_1)))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p)))) (let ((_let_8 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_9 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V2d)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ (@ tptp.ap (@ _let_9 _let_7)) (@ _let_8 (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p)))))) (@ (@ tptp.ap (@ _let_9 (@ _let_8 _let_7))) (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) V2d)) (@ _let_3 _let_2)))))))))))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p)))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p))))))) (@ (@ tptp.ap tptp.c_2Elogroot_2ESQRTd) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT2) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET _let_2) _let_2)) (@ (@ tptp.lam _let_2) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2d $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3c $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4e $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V4e)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ (@ tptp.ap (@ _let_4 V2d)) (@ _let_3 V3c)))) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V2d))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ _let_3 V4e))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) V3c)) V2d)))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p)))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p))))))) (@ (@ tptp.ap tptp.c_2Elogroot_2ESQRTd) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT3) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET _let_2) _let_2)) (@ (@ tptp.lam _let_2) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2d $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3c $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4e $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) V4e)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ (@ tptp.ap (@ _let_5 V2d)) (@ _let_4 (@ _let_3 V3c))))) (@ (@ tptp.ap (@ _let_5 (@ _let_4 V2d))) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) V4e)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) V3c))) V2d)))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p)))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) V1p))))))) (@ (@ tptp.ap tptp.c_2Elogroot_2ESQRTd) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.ap tptp.c_2Elogroot_2EiSQRT3))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_6 (@ _let_5 _let_1))) (let ((_let_7 (@ _let_5 _let_6))) (let ((_let_8 (@ tptp.ap tptp.c_2Elogroot_2ESQRTd))) (let ((_let_9 (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT2) _let_3)))) (let ((_let_10 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_11 (@ _let_10 _let_6))) (let ((_let_12 (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT1) _let_3)))) (let ((_let_13 (@ _let_10 _let_1))) (let ((_let_14 (@ _let_5 _let_13))) (let ((_let_15 (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Elogroot_2EiSQRT0) _let_3)))) (let ((_let_16 (@ _let_10 _let_13))) (let ((_let_17 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_18 (@ _let_10 _let_17))) (let ((_let_19 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) _let_18))) (let ((_let_20 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (let ((_let_21 (@ tptp.ap (@ _let_20 _let_19)))) (let ((_let_22 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (and (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 _let_17)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_20 _let_22)) _let_22))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 _let_18)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_21 _let_22))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 (@ _let_5 _let_17))) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_21 _let_19))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 _let_16)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_4 _let_1))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 _let_14)) _let_15) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 _let_11)) _let_12) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 _let_7)) _let_9) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 (@ _let_2 _let_16))) _let_15) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 (@ _let_2 _let_14))) _let_12) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 (@ _let_2 _let_11))) _let_9) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_8 (@ _let_2 _let_7))) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ _let_4 _let_3))))))))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2EROOT) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ _let_2 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Elogroot_2ESQRTd) _let_1))))))))
% 1.89/2.22 (declare-fun tptp.c_2Egcd_2Egcd () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Egcd_2Egcd) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Egcd_2Egcd (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Egcd_2Egcd X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Egcd_2Eis__gcd () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Egcd_2Eis__gcd) (@ _let_1 (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Egcd_2Elcm () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Egcd_2Elcm) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Egcd_2Elcm (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Egcd_2Elcm X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Elcm) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0a))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) _let_4)) _let_1)) _let_2)) (and (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ _let_3 _let_1)) (forall ((V3d tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V3d))))) (=> (and (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1b)))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum) (V3d tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.inj__ty_2Enum_2Enum V1b))))) (=> (and (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3d)))) (= V2c V3d)))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) _let_1)) _let_1)) _let_1)))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_4 (@ tptp.ap tptp.c_2Egcd_2Eis__gcd))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_2)) _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) _let_1)))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0p))) (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_2)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) _let_2)) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_4 (@ tptp.ap tptp.c_2Egcd_2Eis__gcd))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) _let_3)))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_3)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_3))) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V1y tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V1y)))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2x)))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (forall ((V3x tptp.tp__ty_2Enum_2Enum) (V4y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4y))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_5 (@ tptp.ap V0P))) (let ((_let_6 (@ tptp.ap (@ _let_5 (@ _let_2 _let_4))))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_8 (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_4)))) (=> (and (=> (not _let_8) (@ tptp.p (@ _let_6 (@ (@ tptp.ap (@ _let_7 _let_1)) _let_4)))) (=> _let_8 (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_7 _let_4)) _let_1))) _let_3)))) (@ tptp.p (@ _let_6 _let_3))))))))))))) (forall ((V5v tptp.tp__ty_2Enum_2Enum) (V6v1 tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V5v))) (@ tptp.inj__ty_2Enum_2Enum V6v1)))))))))
% 1.89/2.22 (assert (and (forall ((V0y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0y))) V0y)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1x)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum _let_1)))) (forall ((V2y tptp.tp__ty_2Enum_2Enum) (V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_5 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_6 (@ tptp.ap (@ _let_5 (@ _let_4 _let_1))))) (let ((_let_7 (@ _let_4 _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_7)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) _let_7))) (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))))
% 1.89/2.22 (assert (and (forall ((V0y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0y))) V0y)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V1x))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum _let_1)))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V2x))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.surj__ty_2Enum_2Enum _let_1)))) (forall ((V3y tptp.tp__ty_2Enum_2Enum) (V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_4 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V4x))))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_6 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_3))) (let ((_let_7 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))))) (let ((_let_8 (@ (@ tptp.ap (@ _let_5 _let_7)) _let_3))) (let ((_let_9 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_10 (@ tptp.ap (@ _let_9 _let_4)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_10 _let_7)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_8)) _let_6))) (@ (@ tptp.ap (@ _let_9 (@ (@ tptp.ap (@ _let_5 _let_6)) _let_8))) _let_7))) (@ _let_10 (@ (@ tptp.ap (@ _let_5 _let_8)) _let_6)))))))))))))))) (forall ((V5y tptp.tp__ty_2Enum_2Enum) (V6x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V5y))))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_7 (@ (@ tptp.ap (@ _let_6 _let_5)) (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (let ((_let_8 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_9 (@ tptp.ap (@ _let_8 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_9 _let_5)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_7)) _let_4))) (@ (@ tptp.ap (@ _let_8 (@ (@ tptp.ap (@ _let_6 _let_4)) _let_7))) _let_5))) (@ _let_9 (@ (@ tptp.ap (@ _let_6 _let_7)) _let_4))))))))))))))) (forall ((V7y tptp.tp__ty_2Enum_2Enum) (V8x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V8x))))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V7y))) (let ((_let_7 (@ _let_2 (@ _let_1 _let_6)))) (let ((_let_8 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_9 (@ tptp.ap (@ _let_8 _let_3)))) (let ((_let_10 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_6)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_9 _let_10)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_7)) _let_5))) (@ (@ tptp.ap (@ _let_8 (@ (@ tptp.ap (@ _let_4 _let_5)) _let_7))) _let_10))) (@ _let_9 (@ (@ tptp.ap (@ _let_4 _let_7)) _let_5)))))))))))))))) (forall ((V9y tptp.tp__ty_2Enum_2Enum) (V10x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V10x))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V9y))) (let ((_let_6 (@ _let_3 (@ _let_2 _let_5)))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_9 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_10 (@ tptp.ap (@ _let_9 (@ _let_3 (@ _let_8 _let_1)))))) (let ((_let_11 (@ _let_3 (@ _let_8 _let_5)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_10 _let_11)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_6)) _let_4))) (@ (@ tptp.ap (@ _let_9 (@ (@ tptp.ap (@ _let_7 _let_4)) _let_6))) _let_11))) (@ _let_10 (@ (@ tptp.ap (@ _let_7 _let_6)) _let_4)))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Eis__gcd) _let_2)) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) _let_1))))) (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1)) (forall ((V2d tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V2d))))) (=> (and (@ tptp.p (@ _let_3 _let_2)) (@ tptp.p (@ _let_3 _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_1)) _let_1)) V0a))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0a)))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0a))) V0a)))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1))))))))
% 1.89/2.22 (assert (and (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1))))))) (forall ((V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (and (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))) (forall ((V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_2))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m))) tptp.fo__c_2Enum_2E0) (and (= V0n tptp.fo__c_2Enum_2E0) (= V1m tptp.fo__c_2Enum_2E0)))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.surj__ty_2Enum_2Enum _let_1))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_4 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_1)) _let_3)) _let_2) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) _let_2))))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0p))) (=> (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_2)) (or (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2c tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2c))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0a))) (=> (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_4)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) _let_1)))) (@ tptp.p (@ _let_3 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0p tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0p))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (=> (and (@ tptp.p (@ (@ tptp.ap tptp.c_2Edivides_2Eprime) _let_2)) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) _let_1)))) (or (@ tptp.p (@ _let_3 _let_4)) (@ tptp.p (@ _let_3 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (=> (and (not (= V0n tptp.fo__c_2Enum_2E0)) (not (= V1m tptp.fo__c_2Enum_2E0))) (exists ((V2p tptp.tp__ty_2Enum_2Enum) (V3q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3q))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_4 (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1m)))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (and (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4))) (= V1m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V1y tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V1y)))) (forall ((V2x tptp.tp__ty_2Enum_2Enum) (V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3y))) (let ((_let_3 (@ tptp.ap V0P))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))) (forall ((V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4x))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) _let_1)) _let_1)))) (forall ((V5x tptp.tp__ty_2Enum_2Enum) (V6y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V5x))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap V0P) _let_2)))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_4 _let_2)) (@ tptp.p (@ _let_4 _let_1)) (@ tptp.p (@ _let_3 _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1)))))))))) (forall ((V7m tptp.tp__ty_2Enum_2Enum) (V8n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V7m))) (@ tptp.inj__ty_2Enum_2Enum V8n)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (=> (not (= V0n tptp.fo__c_2Enum_2E0)) (exists ((V2p tptp.tp__ty_2Enum_2Enum) (V3q tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V2p))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V3q))) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) _let_2)) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Elcm) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap (@ _let_4 _let_2)) _let_3))) (@ (@ tptp.ap (@ _let_4 _let_1)) _let_3)))) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Elcm) _let_2)) _let_1))) (let ((_let_4 (@ tptp.ap tptp.c_2Edivides_2Edivides))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_2)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_1)) _let_3)) (forall ((V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Edivides_2Edivides))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Elcm) _let_3)) _let_2))) _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Elcm))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) tptp.fo__c_2Enum_2E0)))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Elcm))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) V0x) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)) V0x)))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Elcm))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Elcm))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_5 _let_1)) (@ tptp.p (@ _let_5 _let_2))) (and (@ tptp.p (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2))) (@ tptp.p (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (forall ((V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2p))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Edivides_2Edivides))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Elcm) _let_4)) _let_2)))) (or (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_4)) _let_1))) (not (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2k))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) (@ tptp.inj__ty_2Enum_2Enum V0m))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2k))) (=> (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_5 (@ tptp.ap tptp.c_2Egcd_2Egcd))) (let ((_let_6 (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))))) (let ((_let_7 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1)))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EEVEN))) (let ((_let_9 (@ tptp.p (@ _let_8 _let_3)))) (and (=> (and _let_9 (@ tptp.p (@ _let_8 _let_1))) (= _let_7 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) (@ _let_6 (@ (@ tptp.ap (@ _let_4 _let_1)) _let_2)))))) (=> (and _let_9 (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1))) (= _let_7 (@ tptp.surj__ty_2Enum_2Enum (@ _let_6 _let_1))))))))))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Einvtri () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumpair_2Einvtri) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Einvtri (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumpair_2Einvtri X0)) (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Einvtri0 () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumpair_2Einvtri0) (@ _let_1 (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enapp () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumpair_2Enapp) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Enapp (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumpair_2Enapp X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enapp) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Encons () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumpair_2Encons) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Encons (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumpair_2Encons X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enfoldl (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Enumpair_2Enfoldl A_27a)) (@ (@ tptp.arr (@ _let_1 (@ _let_2 A_27a))) (@ _let_2 (@ _let_1 A_27a))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enfst () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumpair_2Enfst) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Enfst (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumpair_2Enfst X0)) (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enlen () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumpair_2Enlen) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Enlen (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumpair_2Enlen X0)) (@ (@ tptp.ap tptp.c_2Enumpair_2Enlen) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enlistrec (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Enumpair_2Enlistrec A_27a)) (@ _let_2 (@ (@ tptp.arr (@ _let_1 (@ _let_1 (@ _let_2 A_27a)))) (@ _let_1 A_27a))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enmap () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumpair_2Enmap) (@ (@ tptp.arr _let_1) _let_1))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Enpair () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumpair_2Enpair) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Enpair (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumpair_2Enpair X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Ensnd () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumpair_2Ensnd) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Ensnd (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumpair_2Ensnd X0)) (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Enumpair_2Etri () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumpair_2Etri) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Enumpair_2Etri (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumpair_2Etri X0)) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (let ((_let_4 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_4)) (@ _let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) _let_3))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (= V0n tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (and (= (= _let_2 tptp.fo__c_2Enum_2E0) _let_1) (= (= tptp.fo__c_2Enum_2E0 _let_2) _let_1))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0m))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (= V0m V1n)))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V0P) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap V0P))) (let ((_let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (=> (=> (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_4))) _let_4))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))) (forall ((V3v tptp.tp__ty_2Enum_2Enum) (V4v1 tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V3v))) (@ tptp.inj__ty_2Enum_2Enum V4v1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumpair_2Einvtri0))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_3)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_3)) _let_1))) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_2))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri0) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri0) _let_3)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_5)))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_5))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_3)) (@ _let_2 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri0) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum V1a)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_1))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1)))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ tptp.inj__ty_2Enum_2Enum V0n)))) V0n)))
% 1.89/2.22 (assert (forall ((V0y tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0y))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumpair_2Etri))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_3 _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1)) V0y)))))))
% 1.89/2.22 (assert (forall ((V0y tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) _let_2))) _let_1))) V1x))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) _let_1))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) _let_2))) _let_2))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Enumpair_2Etri) (@ (@ tptp.ap tptp.c_2Enumpair_2Einvtri) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y)))) V0x)))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y)))) V1y)))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (exists ((V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.inj__ty_2Enum_2Enum V2y)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) _let_1))) (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) _let_1))) V0n))))
% 1.89/2.22 (assert (forall ((V0x1 tptp.tp__ty_2Enum_2Enum) (V1y1 tptp.tp__ty_2Enum_2Enum) (V2x2 tptp.tp__ty_2Enum_2Enum) (V3y2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enumpair_2Enpair))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0x1))) (@ tptp.inj__ty_2Enum_2Enum V1y1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2x2))) (@ tptp.inj__ty_2Enum_2Enum V3y2)))) (and (= V0x1 V2x2) (= V1y1 V3y2))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) _let_1))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) _let_1))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1t))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) _let_2)) _let_1))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum) (V2h tptp.tp__ty_2Enum_2Enum) (V3t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Enumpair_2Encons))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2h))) (@ tptp.inj__ty_2Enum_2Enum V3t)))) (and (= V0x V2h) (= V1y V3t))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (not (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y))) tptp.fo__c_2Enum_2E0))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0P) (@ _let_2 (@ (@ tptp.arr (@ _let_1 (@ _let_1 (@ _let_2 A_27a)))) (@ _let_1 tptp.bool)))) (=> (forall ((V1n $$unsorted)) (=> (@ (@ tptp.mem V1n) A_27a) (forall ((V2f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2f) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) A_27a)))) (forall ((V3l tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3l))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1n)) V2f)))) (=> (=> (not (= V3l tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))) (@ tptp.p (@ _let_2 _let_1))))))))))) (forall ((V4v $$unsorted)) (=> (@ (@ tptp.mem V4v) A_27a) (forall ((V5v1 $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V5v1) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) A_27a)))) (forall ((V6v2 tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap V0P) V4v)) V5v1)) (@ tptp.inj__ty_2Enum_2Enum V6v2)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n $$unsorted)) (=> (@ (@ tptp.mem V0n) A_27a) (forall ((V1l tptp.tp__ty_2Enum_2Enum) (V2f $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) _let_2))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enlistrec A_27a)) V0n)) V2f)))) (let ((_let_5 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2f) (@ _let_5 (@ _let_5 (@ (@ tptp.arr A_27a) A_27a)))) (= (@ _let_4 _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) V0n)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap V2f) (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) _let_2))) _let_3)) (@ _let_4 _let_3))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n $$unsorted)) (=> (@ (@ tptp.mem V0n) A_27a) (forall ((V1f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V1f) (@ _let_1 (@ _let_1 (@ (@ tptp.arr A_27a) A_27a)))) (forall ((V2h tptp.tp__ty_2Enum_2Enum) (V3t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3t))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enlistrec A_27a)) V0n)) V1f)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2h))) (and (= (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V0n) (= (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) _let_3)) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap V1f) _let_3)) _let_1)) (@ _let_2 _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (forall ((V1h tptp.tp__ty_2Enum_2Enum) (V2t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2t))) (let ((_let_2 (@ tptp.ap V0P))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ tptp.inj__ty_2Enum_2Enum V1h))) _let_1)))))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.inj__ty_2Enum_2Enum V3n))))))))
% 1.89/2.22 (assert (= tptp.c_2Enumpair_2Enlen (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enlistrec tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V0n $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1t $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2r $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) V2r)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1t))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumpair_2Enlen))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ tptp.inj__ty_2Enum_2Enum V0h))) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ _let_2 _let_1))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (= (@ (@ tptp.ap tptp.c_2Enumpair_2Enmap) V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enlistrec tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1n $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2t $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3r $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ (@ tptp.ap V0f) V1n))) V3r))))))))))))
% 1.89/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (forall ((V1h tptp.tp__ty_2Enum_2Enum) (V2t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2t))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enmap) V0f)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1h))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumpair_2Encons))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap V0f) _let_3))) (@ _let_2 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) A_27a))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2l tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2l))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enfoldl A_27a)) V0f)) V1a)) _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enlistrec (@ (@ tptp.arr A_27a) A_27a))) (@ (@ tptp.lam A_27a) (lambda ((V3a $$unsorted)) V3a)))) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4n $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V5t $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27a)) (lambda ((V6r $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V7a $$unsorted)) (@ (@ tptp.ap V6r) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V4n)) V7a)))))))))))) _let_1)) V1a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) A_27a))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2h tptp.tp__ty_2Enum_2Enum) (V3t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3t))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2h))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enfoldl A_27a)) V0f)))) (let ((_let_4 (@ tptp.ap (@ _let_3 V1a)))) (and (= (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V1a) (= (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) _let_2)) _let_1)) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap V0f) _let_2)) V1a))) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0l1 tptp.tp__ty_2Enum_2Enum) (V1l2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0l1))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enapp) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Enumpair_2Enlistrec tptp.ty_2Enum_2Enum)) _let_2)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V2n $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3t $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4r $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) V2n)) V4r))))))))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0nlist tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2t tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0nlist))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2t))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumpair_2Enapp))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ tptp.inj__ty_2Enum_2Enum V1h))))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) V0nlist) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (or (= V0n tptp.fo__c_2Enum_2E0) (exists ((V1h tptp.tp__ty_2Enum_2Enum) (V2t tptp.tp__ty_2Enum_2Enum)) (= V0n (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Encons) (@ tptp.inj__ty_2Enum_2Enum V1h))) (@ tptp.inj__ty_2Enum_2Enum V2t))))))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EBIT () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EBIT) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EBITS () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EBITS) (@ _let_1 (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2EBITS (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum) (X2 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ (@ tptp.fo__c_2Ebit_2EBITS X0) X1) X2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1))) (@ tptp.inj__ty_2Enum_2Enum X2)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EBITV () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EBITV) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2EBITV (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Ebit_2EBITV X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITV) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EBITWISE () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebit_2EBITWISE) (@ _let_1 (@ (@ tptp.arr (@ _let_2 (@ _let_2 tptp.bool))) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EBIT__MODIFY () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EBIT__MODIFY) (@ _let_1 (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr tptp.bool) tptp.bool))) (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EBIT__REVERSE () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EBIT__REVERSE) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2EBIT__REVERSE (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Ebit_2EBIT__REVERSE X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EDIVMOD__2EXP () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EDIVMOD__2EXP) (@ _let_1 (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EDIV__2EXP () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EDIV__2EXP) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2EDIV__2EXP (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Ebit_2EDIV__2EXP X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2ELOG2 () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Ebit_2ELOG2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2ELOG2 (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Ebit_2ELOG2 X0)) (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2ELOWEST__SET__BIT () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Ebit_2ELOWEST__SET__BIT) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2ELOWEST__SET__BIT (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Ebit_2ELOWEST__SET__BIT X0)) (@ (@ tptp.ap tptp.c_2Ebit_2ELOWEST__SET__BIT) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EMOD__2EXP () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EMOD__2EXP) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2EMOD__2EXP (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Ebit_2EMOD__2EXP X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EMOD__2EXP__EQ () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EMOD__2EXP__EQ) (@ _let_1 (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2EMOD__2EXP__MAX () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2EMOD__2EXP__MAX) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2ESBIT () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Ebit_2ESBIT) (@ (@ tptp.arr tptp.bool) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2ESIGN__EXTEND () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2ESIGN__EXTEND) (@ _let_1 (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2ESIGN__EXTEND (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum) (X2 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ (@ tptp.fo__c_2Ebit_2ESIGN__EXTEND X0) X1) X2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESIGN__EXTEND) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1))) (@ tptp.inj__ty_2Enum_2Enum X2)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2ESLICE () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2ESLICE) (@ _let_1 (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2ESLICE (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum) (X2 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ (@ tptp.fo__c_2Ebit_2ESLICE X0) X1) X2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1))) (@ tptp.inj__ty_2Enum_2Enum X2)))))
% 1.89/2.22 (declare-fun tptp.c_2Ebit_2ETIMES__2EXP () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Ebit_2ETIMES__2EXP) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (declare-fun tptp.fo__c_2Ebit_2ETIMES__2EXP (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Ebit_2ETIMES__2EXP X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ETIMES__2EXP) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ETIMES__2EXP) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIVMOD__2EXP) _let_1)) _let_3)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_3)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_3)) _let_2)))))))))
% 1.89/2.22 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) V0b)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) V0b)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_3)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITV) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0h))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_4)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_4))) _let_1))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (= tptp.c_2Ebit_2ELOG2 (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOWEST__SET__BIT) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1i $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) V1i)) (@ tptp.inj__ty_2Enum_2Enum V0n)))))))))
% 1.89/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0x))) tptp.fo__c_2Enum_2E0)) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))))
% 1.89/2.22 (assert (and (forall ((V0op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V0op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0op)) (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.inj__ty_2Enum_2Enum V2y))) tptp.fo__c_2Enum_2E0))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V4op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V5x tptp.tp__ty_2Enum_2Enum) (V6y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V6y))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V5x))) (let ((_let_5 (@ tptp.ap tptp.c_2Ebit_2EBITWISE))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) V4op)) _let_4)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 _let_1)) V4op)) _let_4)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap V4op) (@ _let_3 _let_4))) (@ _let_3 _let_2)))) _let_1)))))))))))))))
% 1.89/2.22 (assert (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__MODIFY) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0f)) (@ tptp.inj__ty_2Enum_2Enum V1x))) tptp.fo__c_2Enum_2E0)))) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V4x))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EBIT__MODIFY))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) V3f)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_1)) V3f)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap V3f) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)) _let_2)))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0l tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESIGN__EXTEND) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1h))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3m $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2)))))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ (@ tptp.ap (@ _let_5 _let_1)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))))) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ _let_5 (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum V1h)))) (@ _let_4 _let_1)))) V3m))) V3m)))))))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__EQ) _let_2)) _let_4)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__MAX) _let_3)) _let_4)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) _let_3)) _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) _let_3))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum) (V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_6 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_3 _let_5)) _let_4))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1p))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_3 _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_1)) V1p)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n)))) V0n)))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIVMOD__2EXP) _let_2)) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) _let_2)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))
% 1.89/2.22 (assert (forall ((V0r tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0r))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (=> (not (= V0m tptp.fo__c_2Enum_2E0)) (exists ((V1p tptp.tp__ty_2Enum_2Enum)) (= V0m (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V1p))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.inj__ty_2Enum_2Enum V0n))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (not (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n))) tptp.fo__c_2Enum_2E0))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V1k))) _let_1))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1k))) (= V1k (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_4 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1b))))) (@ _let_2 _let_1)))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1b))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_2))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_1)) _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_4)) (@ _let_3 _let_1)))) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1l))) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_3)) _let_1)) _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_4)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))))) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.inj__ty_2Enum_2Enum V1l))) _let_1))) _let_1)))))
% 1.89/2.22 (assert (forall ((V0h1 tptp.tp__ty_2Enum_2Enum) (V1l1 tptp.tp__ty_2Enum_2Enum) (V2h2 tptp.tp__ty_2Enum_2Enum) (V3l2 tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l1))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V3l2))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V2h2))) (let ((_let_6 (@ (@ tptp.ap (@ _let_4 _let_5)) _let_2))) (let ((_let_7 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (let ((_let_8 (@ tptp.inj__ty_2Enum_2Enum V0h1))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_6)) _let_8)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_5)) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_8)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_6)) (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0h))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_4)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_4)) _let_1)) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_3)) (@ _let_2 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2n))) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.inj__ty_2Enum_2Enum V1l))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_3)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1)) V1a))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_1))) _let_2)) _let_1)) V0n))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ tptp.inj__ty_2Enum_2Enum V0b))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0b))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V1m)))) (= V1m V0n))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (=> (not (= V0a V1b)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V1b))))))))
% 1.89/2.22 (assert (forall ((V0h1 tptp.tp__ty_2Enum_2Enum) (V1l1 tptp.tp__ty_2Enum_2Enum) (V2h2 tptp.tp__ty_2Enum_2Enum) (V3l2 tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l1))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V3l2))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V2h2))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V0h1))) (let ((_let_7 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_5)) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_6)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_6)) (@ (@ tptp.ap (@ _let_4 _let_5)) _let_2)))) (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))) (= (not (= _let_3 tptp.fo__c_2Enum_2E0)) (= _let_3 (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))))) (= (not (= _let_3 (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))) (= _let_3 tptp.fo__c_2Enum_2E0)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_3)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_3)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0x)))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.inj__ty_2Enum_2Enum V1b))) (exists ((V2p tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2p))) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0a))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1h))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_3)) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_3)) _let_1)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1l))) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_3)) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_3)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1h2 tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1h2))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_3)) _let_5)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_5)) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_3)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1h))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_3)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_3)) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1h))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V0n))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2l))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ _let_3 (@ _let_2 _let_4)))) (@ _let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2ESLICE))) (let ((_let_5 (@ tptp.ap (@ _let_4 _let_3)))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_7 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_6))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_8 _let_7)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_8 _let_2)) _let_6))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ _let_5 _let_7)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_6)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1m_27 tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum) (V3l tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2ESLICE))) (let ((_let_5 (@ tptp.ap (@ _let_4 _let_3)))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_6)) (= V1m_27 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 _let_6)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_6)) _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap (@ _let_5 (@ tptp.inj__ty_2Enum_2Enum V1m_27))) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_6)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_2)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2n))) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0l tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) (@ tptp.inj__ty_2Enum_2Enum V1h))) (@ tptp.inj__ty_2Enum_2Enum V0l))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2a))) _let_2))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) _let_1)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V3b))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_5)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_5))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 _let_3)))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) (@ tptp.inj__ty_2Enum_2Enum V1l))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V2a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))))) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum) (V3y tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2ESLICE))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2)))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V3y))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_8 _let_3)) _let_7)) (@ tptp.p (@ (@ tptp.ap (@ _let_8 _let_6)) _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_7)) _let_6)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_5 _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2A))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 (@ _let_4 _let_2))) (@ _let_4 _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (let ((_let_5 (@ tptp.ap (@ _let_4 _let_3)))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_7 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_6))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_8 _let_7)) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_8 _let_2)) _let_6))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ _let_5 _let_7)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_7)) _let_2))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_6)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_1)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1a))))) (= (not (= _let_2 tptp.fo__c_2Enum_2E0)) (= _let_2 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_1)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1a))))) (= (not (= _let_2 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (= _let_2 tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_2)) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)))) (= (= (@ tptp.p (@ _let_5 _let_4)) (@ tptp.p (@ _let_5 _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0y tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_3)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_3)) _let_3)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_2)) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_1)) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_2)) _let_2)) _let_1)) tptp.fo__c_2Enum_2E0))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1h))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V2l))) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESLICE) _let_4)) _let_6)) _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_6)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_2)) _let_4)) (@ tptp.p (@ _let_3 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) V0b)))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) _let_2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ _let_3 _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))) (let ((_let_5 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_4)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_4)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 _let_3)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 _let_4)) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (let ((_let_5 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_5)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_5)) _let_2))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_5)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_5)) _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0h))) (@ tptp.inj__ty_2Enum_2Enum V1l))))) (= (forall ((V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4x))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V1l))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0h)))) (= (@ tptp.p (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2a))) (@ tptp.p (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V3b))))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2a))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3b))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (=> (forall ((V2i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2i))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0n))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1m))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V1m))) tptp.fo__c_2Enum_2E0))))
% 1.89/2.22 (assert (= (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) tptp.c_2Earithmetic_2EODD))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITV) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_1))) (not (= (@ tptp.p (@ _let_2 _let_3)) (@ tptp.p (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EBITS))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_2)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_7 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_7)) _let_7)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_8 (@ (@ tptp.ap (@ _let_6 _let_5)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_6 (@ _let_8 _let_5))) (@ _let_8 _let_1)))) (@ _let_8 (@ (@ tptp.ap (@ _let_6 (@ _let_4 _let_5))) (@ _let_4 _let_1)))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_5 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) (@ _let_3 _let_4))) (@ _let_3 _let_1)))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ _let_7 _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) (@ _let_3 (@ (@ tptp.ap (@ _let_7 (@ _let_6 _let_4))) (@ _let_6 _let_1))))) _let_5)) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) _let_5)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V1op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_1)) V1op)) (@ tptp.inj__ty_2Enum_2Enum V2a))) (@ tptp.inj__ty_2Enum_2Enum V3b)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V2op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V3a tptp.tp__ty_2Enum_2Enum) (V4b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_5)) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_5)) V2op)) _let_4)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2op) (@ _let_3 _let_4))) (@ _let_3 _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V2op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V3a tptp.tp__ty_2Enum_2Enum) (V4b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V4b))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_4)))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_4)) _let_7)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2op) (@ _let_8 _let_6))) (@ _let_8 _let_5))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_7)) V2op)) _let_6)) _let_5))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_3)) _let_4)))) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V2op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V3a tptp.tp__ty_2Enum_2Enum) (V4b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4b))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_5)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2op) (@ _let_6 _let_4))) (@ _let_6 _let_3)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_5)) V2op)) _let_4)) _let_3))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) _let_1)) _let_2)))) _let_1)) tptp.fo__c_2Enum_2E0))))))))))))))
% 1.89/2.22 (assert (forall ((V0wl tptp.tp__ty_2Enum_2Enum) (V1op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V1op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0wl))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_3))) V1op)))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_3)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_5 _let_2))) (@ _let_5 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0i tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0i))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0i tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0i))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2))) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_5)) (@ (@ tptp.lam tptp.bool) (lambda ((V3x $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) V3x))))))) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2b))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_3)))) _let_5))) (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_3))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1i tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) _let_3))) (let ((_let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum V2a))) _let_4))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum V1i))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_7)))) (let ((_let_9 (= (@ tptp.surj__ty_2Enum_2Enum _let_5) tptp.fo__c_2Enum_2E0))) (= (@ tptp.p (@ _let_8 (@ (@ tptp.ap (@ _let_6 _let_4)) _let_5))) (or (and _let_9 (= V1i V0n)) (and (not _let_9) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_7)) _let_3)) (not (@ tptp.p (@ _let_8 (@ (@ tptp.ap (@ _let_6 _let_5)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2l tptp.tp__ty_2Enum_2Enum) (V3a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2l))) (let ((_let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V1h))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_4)) _let_6)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_6)) _let_3)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2s tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2s))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_4))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_4)))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2s tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2s))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_3)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_2))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum) (V2s tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2s))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ tptp.inj__ty_2Enum_2Enum V1a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0h tptp.tp__ty_2Enum_2Enum) (V1l tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1l))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0h))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2x))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) _let_3))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITS) _let_2)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V3n)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1i))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1i tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1i))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2)))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3)) _let_2))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_6 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_4)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_6 _let_5)) _let_3))) (@ tptp.p (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_5)) (@ _let_2 _let_4)))) _let_3)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1a))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (=> (and (not (= V1a tptp.fo__c_2Enum_2E0)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) _let_2)) tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2)) (@ tptp.p (@ _let_3 _let_1))) (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.inj__ty_2Enum_2Enum V1b)))) (let ((_let_4 (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V0a))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_3)) _let_5)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_5)) _let_3)) tptp.fo__c_2Enum_2E0)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_7 _let_5)) _let_3))) _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap (@ _let_6 _let_5)) _let_4))) _let_3)))))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0b))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_3)))) _let_1))) (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_3))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum) (V2i tptp.tp__ty_2Enum_2Enum) (V3a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2)))))) (let ((_let_5 (@ _let_4 _let_1))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_8 (@ tptp.ap (@ _let_7 _let_6)))) (let ((_let_9 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_5)))) (let ((_let_10 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_11 (@ tptp.inj__ty_2Enum_2Enum V2i))) (let ((_let_12 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_13 (@ (@ tptp.ap (@ _let_12 _let_11)) _let_10))) (let ((_let_14 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (let ((_let_15 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_16 (@ _let_4 _let_10))) (let ((_let_17 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_17 _let_13)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_17 _let_6)) _let_5))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_14 _let_11)) (@ _let_9 (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap (@ _let_12 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_6)) _let_16))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) (@ _let_8 _let_16))) _let_15))) _let_15)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2)))))) _let_5)))) (@ tptp.p (@ (@ tptp.ap (@ _let_14 _let_13)) (@ _let_9 (@ _let_8 _let_5)))))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) tptp.bool) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) V0b)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ _let_3 _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V1op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2a tptp.tp__ty_2Enum_2Enum) (V3b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3b))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EDIV))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_7 (@ tptp.ap tptp.c_2Ebit_2EBITWISE))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_6))) V1op)) _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_6)) V1op)) (@ (@ tptp.ap (@ _let_5 _let_3)) _let_4))) (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap (@ (@ tptp.ap V1op) (@ _let_2 _let_3))) (@ _let_2 _let_1)))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1j tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2k))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum V1j))))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 (@ (@ tptp.ap (@ _let_4 _let_2)) _let_1)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 _let_2))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1j tptp.tp__ty_2Enum_2Enum) (V2k tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1j))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2k))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_2)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1)) V0n)))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EMOD))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_5 _let_3)) _let_1))) _let_2)))) (=> (not (= _let_6 tptp.fo__c_2Enum_2E0)) (= _let_6 (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 _let_3)) _let_2))) _let_1))))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_5 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_3)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE) _let_3)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_4 _let_3)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_2))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.ap tptp.c_2Ebit_2ELOG2))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_3)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_3)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))))
% 1.89/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_2))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_1)))))))) (forall ((V2y tptp.tp__ty_2Enum_2Enum) (V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) _let_2)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_2))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((V0i tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0i))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_1))) _let_2)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) _let_1))))))))
% 1.89/2.22 (assert (forall ((V0i tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2op $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V2op) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V3a tptp.tp__ty_2Enum_2Enum) (V4b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0i))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_2)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_1)) V2op)) (@ tptp.inj__ty_2Enum_2Enum V3a))) (@ tptp.inj__ty_2Enum_2Enum V4b)))))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))) (or (= V0x tptp.fo__c_2Enum_2E0) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_2))) _let_1)))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum) (V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V3a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V1n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_4)) (= (@ tptp.p (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__MODIFY) _let_4)) V2f)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2f) _let_2)) (@ _let_3 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((V0l tptp.tp__ty_2Enum_2Enum) (V1h tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum) (V3i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0l))) (let ((_let_5 (@ tptp.ap tptp.c_2Ebit_2EBIT))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V1h))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum V3i))) (let ((_let_8 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_7)))) (let ((_let_9 (@ tptp.ap (@ _let_5 _let_7)))) (=> (not (= V0l tptp.fo__c_2Enum_2E0)) (= (@ tptp.p (@ _let_9 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESIGN__EXTEND) _let_4)) _let_6)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_4)) _let_6))) (@ _let_8 _let_4)))) (@ _let_9 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2)))) _let_4))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_8 _let_6))) (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))))) _let_1)))))))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (=> (not (= V0n tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) _let_1))) _let_1))))))
% 1.89/2.22 (assert (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (and (not (= V2n tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0a)))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))))) (exists ((V3i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3i))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V0a))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1b))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2n)))))))))))
% 1.89/2.22 (assert (forall ((V0b tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (=> (and (not (= V1n tptp.fo__c_2Enum_2E0)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ tptp.inj__ty_2Enum_2Enum V1n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.inj__ty_2Enum_2Enum V0b))))) (exists ((V2i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2i))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0b))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V1n)))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (forall ((V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V0n))) (not (@ tptp.p (@ (@ tptp.ap V1P) _let_1)))))) (@ tptp.p (@ (@ tptp.ap V1P) (@ tptp.inj__ty_2Enum_2Enum V0n)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ewhile_2ELEAST) V1P)) V0n)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EBIGINTER (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr _let_1) tptp.bool)) _let_1)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EBIGUNION (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr _let_1) tptp.bool)) _let_1)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EBIJ (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ECARD (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2ECARD A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ECHOICE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2ECHOICE A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ECOMPL (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2ECOMPL A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ECROSS (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EDELETE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EDELETE A_27a)) (@ (@ tptp.arr _let_2) (@ _let_1 _let_2)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EDFUNSET (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EDFUNSET A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.arr (@ _let_1 A_27b)) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EDIFF (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EDIFF A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EDISJOINT (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EEMPTY (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (@ (@ tptp.arr A_27a) tptp.bool))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EFINITE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EFUNSET (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.arr (@ _let_1 A_27b)) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EGSPEC (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) tptp.bool))) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EIMAGE (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr A_27b) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EINJ (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EINSERT (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EINSERT A_27a)) (@ _let_1 (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EINTER (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EITSET (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27b) A_27b))) (let ((_let_2 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) (@ (@ tptp.arr (@ _let_2 _let_1)) (@ (@ tptp.arr (@ _let_2 tptp.bool)) _let_1)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ELINV (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2ELINV A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr A_27b) A_27a)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ELINV__OPT (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr A_27b) (@ tptp.ty_2Eoption_2Eoption A_27a))))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EMAX__SET () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Epred__set_2EMAX__SET) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EMIN__SET () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Epred__set_2EMIN__SET) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EPOW (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EPOW A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EPREIMAGE (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ _let_1 tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EPROD__IMAGE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EPROD__IMAGE A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EPROD__SET () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Epred__set_2EPROD__SET) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EPSUBSET (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EREL__RESTRICT (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) (@ (@ tptp.arr _let_3) (@ (@ tptp.arr _let_2) _let_3))))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EREST (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EREST A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ERINV (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2ERINV A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr A_27b) A_27a)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ESING (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2ESING A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ESUBSET (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ESUM__IMAGE (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) tptp.ty_2Enum_2Enum))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ESUM__SET () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Epred__set_2ESUM__SET) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2ESURJ (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EUNION (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2EUNIV (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2EUNIV A_27a)) (@ (@ tptp.arr A_27a) tptp.bool))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Echooser (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Echooser A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Ecount () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Epred__set_2Ecount) (@ _let_1 (@ _let_1 tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Ecountable (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Eenumerate (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Eenumerate A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Eequiv__on (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) (@ (@ tptp.arr (@ _let_1 _let_2)) (@ (@ tptp.arr _let_2) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Eis__measure__maximal (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Eis__measure__maximal A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Enum__to__pair () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Epred__set_2Enum__to__pair) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Epair__to__num () $$unsorted)
% 1.89/2.22 (assert (@ (@ tptp.mem tptp.c_2Epred__set_2Epair__to__num) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (declare-fun tptp.fo__c_2Epred__set_2Epair__to__num (tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 1.89/2.22 (assert (forall ((X0 tptp.tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Epred__set_2Epair__to__num X0)) (@ (@ tptp.ap tptp.c_2Epred__set_2Epair__to__num) (@ tptp.inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum X0)))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Epairwise (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Epairwise A_27a)) (@ (@ tptp.arr (@ _let_1 _let_2)) (@ (@ tptp.arr _let_2) tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Epartition (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ tptp.arr _let_2))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Epartition A_27a)) (@ (@ tptp.arr (@ _let_1 _let_2)) (@ _let_3 (@ _let_3 tptp.bool)))))))))
% 1.89/2.22 (declare-fun tptp.c_2Epred__set_2Eschroeder__close (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Epred__set_2Eschroeder__close A_27a)) (@ (@ tptp.arr (@ _let_1 A_27a)) (@ (@ tptp.arr _let_2) _let_2)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0P)) (@ tptp.p (@ (@ tptp.ap V0P) V1x))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1P)) (@ tptp.p (@ (@ tptp.ap V1P) V0x))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1P) V2x))))) (@ tptp.p (@ (@ tptp.ap V1P) V0x))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (= V0s V1t) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (= V0s V1t)) (exists ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (and (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ _let_1 V1t)) (not (@ tptp.p (@ _let_1 V0s)))))))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (exists ((V1n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V1n))) V0s))) (exists ((V2n tptp.tp__ty_2Enum_2Enum)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V2n))) V0s)) (forall ((V3m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3m))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V2n))) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) tptp.bool))) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1v)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27b)) V0f))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1v)) tptp.c_2Ebool_2ET) (@ (@ tptp.ap V0f) V2x))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) tptp.bool))) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27b)) V0f)) V1v)) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1v)) tptp.c_2Ebool_2ET) (@ (@ tptp.ap V0f) V2x))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap V0P) V1x))))) V0P))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_2) _let_2)) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ty_2Epair_2Eprod _let_2) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))) (@ (@ tptp.ap (@ (@ tptp.ap V0P) V1x)) V2y)))))))) (@ (@ tptp.ap (@ _let_1 tptp.bool)) V0P)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27a) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0y)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap V1P) V2x))))))) (@ tptp.p (@ (@ tptp.ap V1P) V0y))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (forall ((V2P $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V1y))) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V3x)) V4y))) (@ (@ tptp.ap (@ (@ tptp.ap V2P) V3x)) V4y)))))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V2P) V0x)) V1y)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27b) (forall ((V3P $$unsorted)) (=> (@ (@ tptp.mem V3P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V3P) V1y)) (= V2x (@ (@ tptp.ap V0f) V1y))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V2x)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27b) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) tptp.bool)) (@ (@ tptp.ap V0f) V4x))) (@ (@ tptp.ap V3P) V4x)))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) A_27b) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27b) (forall ((V3P $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V3P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0a)) V1b))) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V4y)) V2x))) (@ (@ tptp.ap V3P) V4y))))))) (and (@ tptp.p (@ (@ tptp.ap V3P) V0a)) (= V1b V2x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) A_27b) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3P $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V3P) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0a)) V1b))) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2x)) V4y))) (@ (@ tptp.ap V3P) V4y))))))) (and (@ tptp.p (@ (@ tptp.ap V3P) V1b)) (= V0a V2x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) A_27a) (forall ((V2P $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V0a)) V1b))) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V3x)) V3x))) (@ (@ tptp.ap V2P) V3x))))))) (and (@ tptp.p (@ (@ tptp.ap V2P) V0a)) (= V0a V1b)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1M $$unsorted)) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (= (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0s)))) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V0s)) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1M))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4y)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V3x))) (@ _let_1 V4y)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Epred__set_2EEMPTY A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2EF)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)))) (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EEMPTY A_27a)) V0x)) false))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Epred__set_2EUNIV A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ tptp.c_2Epred__set_2EUNIV A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNIV A_27a)) V0x)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (not (= (@ tptp.c_2Epred__set_2EUNIV A_27a) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (not (= (@ tptp.c_2Epred__set_2EEMPTY A_27a) (@ tptp.c_2Epred__set_2EUNIV A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)))) (= V0s (@ tptp.c_2Epred__set_2EUNIV A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (= V0s (@ tptp.c_2Epred__set_2EUNIV A_27a)) (forall ((V1v $$unsorted)) (=> (@ (@ tptp.mem V1v) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1v)) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0P)) V1Q)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ _let_1 V0P)) (@ tptp.p (@ _let_1 V1Q))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap V0s) V2x)) (@ tptp.p (@ (@ tptp.ap V1t) V2x)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V2u))) (@ tptp.p (@ _let_2 V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V0s))) (= V0s V1t))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) _let_1)) (= V0s _let_1))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) (@ tptp.c_2Epred__set_2EUNIV A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EUNIV A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) _let_1)) V0s)) (= V0s _let_1))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (= V0s V1t) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V0s))) (= V0s V1t))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2d tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap V0f))) (=> (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_2 (@ tptp.ap V0f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2d))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) tptp.bool) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1y) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK tptp.bool) A_27a)) V0x))) V1y)) (or (not (@ tptp.p V0x)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ tptp.c_2Epred__set_2EUNIV A_27a))) V1y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0x)))) (=> (@ (@ tptp.mem V1y) tptp.bool) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK tptp.bool) A_27a)) V1y))) (or (@ tptp.p (@ _let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (@ tptp.p V1y)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) V1t)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (not (= V0s V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V2u))) (@ tptp.p (@ _let_2 V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ _let_1 V0s))) (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) (or (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t)) V2x)) (or (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1t)) V2u)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1t))) V2u)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V0s) V0s))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 V0s)) V1t) (@ (@ tptp.ap (@ _let_1 V1t)) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))))))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V3t)) V2s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) V2u)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V2u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t) V1t)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V0s) V0s))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1s)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) V1s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EUNIV A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) _let_1)) V0s) _let_1)))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EUNIV A_27a))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1s)) _let_1) _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t) _let_1) (and (= V0s _let_1) (= V1t _let_1)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1s)) V2t))) (@ tptp.p (@ (@ tptp.ap V0P) V3x))))) (and (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V1s)) (@ tptp.p (@ (@ tptp.ap V0P) V4x))))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V5x)) V2t)) (@ tptp.p (@ (@ tptp.ap V0P) V5x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V0s))) (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t))) (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t)) V2x)) (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1t)) V2u)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1t))) V2u)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V0s) V0s))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 V0s)) V1t) (@ (@ tptp.ap (@ _let_1 V1t)) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t))) V0s)))))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V3t)) V2s))) V2s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1t)) V2u))) (and (@ tptp.p (@ _let_1 V1t)) (@ tptp.p (@ _let_1 V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1t)) V0s) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) _let_1)) V0s) _let_1)))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) _let_1) _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) V0s) V0s))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) (@ tptp.c_2Epred__set_2EUNIV A_27a)) V1s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ _let_2 V1t)) V2u)) (@ (@ tptp.ap (@ _let_2 (@ _let_1 V1t))) (@ _let_1 V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ _let_2 V1t)) V2u)) (@ (@ tptp.ap (@ _let_2 (@ _let_1 V1t))) (@ _let_1 V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s)) V1t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s)) V1t)) (not (exists ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s)) V1t)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ _let_1 V0s)) (not (@ tptp.p (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V0s)) _let_1))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s)) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s)) V0s)) (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) V2u)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V2u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (let ((_let_2 (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V2u)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V2u))))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 _let_3)) V2u)) _let_2) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2u)) _let_3)) _let_2))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V1t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2u)) V1t))) (@ tptp.p (@ _let_1 V2u)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V0s))) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) (@ _let_1 V1t))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t))) (and (@ tptp.p (@ _let_1 V0s)) (not (@ tptp.p (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t)) V2x)) (and (@ tptp.p (@ _let_1 V0s)) (not (@ tptp.p (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) V0s))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) _let_1)) V0s) _let_1)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) (@ tptp.c_2Epred__set_2EUNIV A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V0s)) V1t))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 _let_2)) V1t) _let_2))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V0s) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t))) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V1t)) V0s))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (and (= (@ (@ tptp.ap (@ _let_2 V0s)) _let_1) V1t) (= (@ (@ tptp.ap (@ _let_2 _let_1)) V0s) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s)) (= (@ _let_1 (@ _let_1 V1t)) V1t))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0x)))) (=> (@ (@ tptp.mem V2z) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1y)) V2z)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1y))) V2z)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0x)))) (=> (@ (@ tptp.mem V2z) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1y))) V2z) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V2z))) V1y)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0x)) V1y))))) (=> (@ (@ tptp.mem V1y) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (@ _let_2 V0x) (@ (@ tptp.ap (@ _let_1 V1y)) V0x)) (= (@ _let_2 V1y) (@ (@ tptp.ap (@ _let_1 V0x)) V1y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2g $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (=> (@ (@ tptp.mem V2g) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_2 V0s)) V1t))) V2g) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V0s)) V2g))) V1t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1t)) V0s)) (@ _let_1 V1t))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V1t)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0g $$unsorted)) (=> (@ (@ tptp.mem V0g) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap V0g))) (=> (and (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.ap V1f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))) (forall ((V5n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V5n))) (let ((_let_2 (@ tptp.ap V1f))) (= (@ (@ tptp.ap V0g) _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))) (@ _let_2 _let_1)))))) (not (= V2m V3n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2m)))) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2y)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V2y)) V0x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2y)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1y)) V2s))) (or (= V0x V1y) (@ tptp.p (@ _let_1 V2s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1y)) V2s)) V0x)) (or (= V0x V1y) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (or (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (exists ((V2t $$unsorted)) (and (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= V0s (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V2t)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)) (exists ((V2t $$unsorted)) (and (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= V0s (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V2t)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s) V1s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s) V1s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)))) (let ((_let_2 (@ _let_1 V1s))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 _let_2) _let_2))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0x)))) (let ((_let_3 (@ tptp.ap (@ _let_1 V1y)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_2 (@ _let_3 V2s)) (@ _let_3 (@ _let_2 V2s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EUNIV A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) _let_1) _let_1)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (= (@ tptp.c_2Epred__set_2EEMPTY A_27a) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V1s)) V2t))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)))) (let ((_let_4 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_4) (= (@ (@ tptp.ap (@ _let_1 (@ _let_3 V1s))) V2t) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2t))) _let_2)) (@ _let_3 _let_2))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1s))) V2t) (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1s)) V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V1s)) V2t))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)))) (let ((_let_4 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_4) (= (@ (@ tptp.ap (@ _let_1 (@ _let_3 V1s))) V2t) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2t))) (@ _let_3 _let_2))) _let_2)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))) V2t)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s)) V2t)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V2t)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))) (and (@ tptp.p (@ _let_1 V1s)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))) V2t)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s)) V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s))) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V2t))) (@ tptp.p (@ _let_1 V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V0s)) V1t))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ _let_1 (@ _let_3 V0s))) V1t) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1t))) _let_2)) (@ _let_3 _let_2)))))))))))))
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.bool)))) (= (@ tptp.c_2Epred__set_2EUNIV tptp.bool) (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2ET)) (@ (@ tptp.ap (@ _let_1 tptp.c_2Ebool_2EF)) (@ tptp.c_2Epred__set_2EEMPTY tptp.bool))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1a)) V2s))) (@ tptp.p (@ (@ tptp.ap V0P) V3x))))) (and (@ tptp.p (@ (@ tptp.ap V0P) V1a)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V2s)) (@ tptp.p (@ (@ tptp.ap V0P) V4x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1a)) V2s))) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))) (or (@ tptp.p (@ (@ tptp.ap V0P) V1a)) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V2s)) (@ tptp.p (@ (@ tptp.ap V0P) V4x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V1x) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V2y))) (and (@ tptp.p (@ _let_1 V0s)) (not (= V1x V2y))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V2y)) V1x)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)) (not (= V1x V2y)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V0x) V1s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (=> (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V1x) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2x_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (let ((_let_3 (@ tptp.ap (@ _let_2 V2x_27)))) (let ((_let_4 (@ tptp.ap (@ _let_2 V1x)))) (=> (@ (@ tptp.mem V2x_27) A_27a) (= (= (@ tptp.p (@ _let_4 V0s)) (@ tptp.p (@ _let_3 V0s))) (= (@ tptp.p (@ _let_4 (@ _let_1 V2x_27))) (@ tptp.p (@ _let_3 (@ _let_1 V1x))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) _let_1)) V0x) _let_1)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V0x)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V1s)) V0x))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 _let_2)) V0x) _let_2))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V2s)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 (@ _let_2 V0x))) V1y) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1y))) V0x)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V0x))) V1s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V2t)) V0x))) (and (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s))) (@ tptp.p (@ _let_1 V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V2t))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V0x))) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ _let_1 V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2x)) V1t)) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V2x))) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) V1t)) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2x)) V0s))) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) V1t)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (exists ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2y)))) (and (@ (@ tptp.mem V2y) A_27a) (@ tptp.p (@ _let_1 V1t)) (not (@ tptp.p (@ _let_1 V0s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V2s)) V1y))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)))) (let ((_let_4 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2s) _let_4) (= (@ (@ tptp.ap (@ _let_1 (@ _let_3 V2s))) V1y) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V0x)) V1y))) _let_2)) (@ _let_3 _let_2))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V0x)) V1s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_2 V0s)) V2x))) V1t) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V0s)) V1t))) V2x)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V0s)) V2x))) V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1t)) V2x))) V0s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s))) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V1s))) (and (@ tptp.p (@ _let_1 V1s)) (not (= V0x (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V1s)) V0x)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (not (= V0x (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) V0s)) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (= V0s (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) false)))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) (@ _let_2 V1s))) (or (= V1s _let_1) (= V1s (@ _let_2 _let_1)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)))) (let ((_let_2 (@ tptp.p (@ _let_1 V1t)))) (let ((_let_3 (@ tptp.p (@ _let_1 V0s)))) (let ((_let_4 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) (or (and _let_3 (= V1t _let_4)) (and _let_2 (= V0s _let_4)) (and _let_3 _let_2 (= V0s V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1y)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (= V0x V1y)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1y)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V0x)) (= V0x V1y)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (not (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) _let_1) _let_1))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (not (= _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)))) (=> (@ (@ tptp.mem V1y) A_27a) (= (= (@ (@ tptp.ap (@ _let_2 V0x)) _let_1) (@ (@ tptp.ap (@ _let_2 V1y)) _let_1)) (= V0x V1y)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) _let_1))) _let_1))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)))) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ _let_1 V0s) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ _let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) _let_1))) V0x) _let_1)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V1x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V1x) _let_1) (= V0s (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V0x))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) _let_1)) _let_1)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) V0s)) (and (not (= V0s _let_1)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s) _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27b) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) tptp.bool)) (@ (@ tptp.ap V0f) V2x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27b) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V0y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V2f)) V1s))) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (= V0y (@ (@ tptp.ap V2f) V3x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27b) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V2f)) V1s)) V0y)) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (= V0y (@ (@ tptp.ap V2f) V3x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V2f) V0x))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V2f)) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27b)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) V1x)))) V0s) V0s))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27a)) (@ tptp.c_2Ecombin_2EI A_27a))) V0s) V0s))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27a)) (@ tptp.c_2Ecombin_2EI A_27a)) (@ tptp.c_2Ecombin_2EI (@ (@ tptp.arr A_27a) tptp.bool)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EIMAGE A_27a))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)) V0f)) V1g))) V2s) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) A_27c)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V1g)) V2s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V2s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27b)) (@ (@ tptp.ap V0f) V1x))) (@ _let_1 V2s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V1f)) V0s) (@ tptp.c_2Epred__set_2EEMPTY A_27b)) (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V2s))) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V2s)) V1x)) (@ _let_1 V2s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1s)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27b)) (@ _let_1 V1s))) (@ _let_1 V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (forall ((V2f $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V2f)))) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ _let_1 V0s))) (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) V2t)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27b)) (@ _let_1 V1s))) (@ _let_1 V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s1 $$unsorted)) (=> (@ (@ tptp.mem V1s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2s2) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V4y) A_27a) (= (= (@ _let_1 V3x) (@ _let_1 V4y)) (= V3x V4y))))))) (= (= (@ _let_1 V1s1) (@ _let_1 V2s2)) (= V1s1 V2s2)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s1 $$unsorted)) (=> (@ (@ tptp.mem V1s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2s2) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V4y) A_27a) (= (= (@ _let_1 V3x) (@ _let_1 V4y)) (= V3x V4y))))))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27b)) (@ _let_1 V1s1))) (@ _let_1 V2s2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V1s1)) V2s2))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f_27 $$unsorted)) (=> (@ (@ tptp.mem V2f_27) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V3s_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)))) (=> (@ (@ tptp.mem V3s_27) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (= V1s V3s_27) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V3s_27)) (= (@ (@ tptp.ap V0f) V4x) (@ (@ tptp.ap V2f_27) V4x)))))) (= (@ (@ tptp.ap (@ _let_1 V0f)) V1s) (@ (@ tptp.ap (@ _let_1 V2f_27)) V3s_27)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) tptp.bool))) (let ((_let_2 (@ tptp.c_2Ecombin_2Eo A_27b))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) _let_1)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27b)) V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_2 A_27a) _let_1)) (@ (@ tptp.c_2Epair_2EFST A_27a) tptp.bool))) V0f))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_2 tptp.bool) _let_1)) (@ (@ tptp.c_2Epair_2ESND A_27a) tptp.bool))) V0f))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27c) A_27a)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EIMAGE A_27c))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27c) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27a)) V1g)) V2s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27c) A_27b) A_27a)) V0f)) V1g))) V2s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) A_27a)) V1f)) V2s))) (@ tptp.p (@ (@ tptp.ap V0P) V3y))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V4x)) V2s)) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap V1f) V4x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) A_27a)) V1f)) V2s))) (@ tptp.p (@ (@ tptp.ap V0P) V3y)))) (exists ((V4x $$unsorted)) (and (@ (@ tptp.mem V4x) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V4x)) V2s)) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap V1f) V4x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) V2t))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V5y)) V1s))) (=> (= (@ _let_1 V4x) (@ _let_1 V5y)) (= V4x V5y))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) V2t))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V5y)) V1s))) (= (= (@ _let_1 V4x) (@ _let_1 V5y)) (= V4x V5y))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) V1x)))) V0s)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V4u $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EINJ A_27a))) (=> (@ (@ tptp.mem V4u) (@ (@ tptp.arr A_27c) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V0f)) V2s)) V3t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27b) A_27c)) V1g)) V3t)) V4u))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)) V1g)) V0f))) V2s)) V4u)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (and (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V1s)))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V2s)) (@ tptp.c_2Epred__set_2EEMPTY A_27b))) (= V2s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V2f)) V0s)) V1t)) (forall ((V3e $$unsorted)) (=> (@ (@ tptp.mem V3e) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3e)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V2f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V3e))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27b)) V1t)) (@ (@ tptp.ap V2f) V3e)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V2s))) V3t)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2s)) V3t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V1x))) V3t)) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4y)) V2s)) (= (@ _let_1 V1x) (@ _let_1 V4y))) (= V1x V4y)))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0b $$unsorted)) (=> (@ (@ tptp.mem V0b) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)))) (=> (@ (@ tptp.mem V4y) A_27b) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0b)) V1s)) V2t)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V4y)) V2t)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EUPDATE A_27a) A_27b)) V3x)) V4y)) V0b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V3x)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27b)) V4y)) V2t))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V3s0 $$unsorted)) (=> (@ (@ tptp.mem V3s0) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4t0 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V4t0) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V3s0)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) V2t)) V4t0))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3s0)) V4t0)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ _let_1 V2t)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))) V2t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) V2t))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V4x)) V2t)) (exists ((V5y $$unsorted)) (and (@ (@ tptp.mem V5y) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V5y)) V1s)) (= (@ (@ tptp.ap V0f) V5y) V4x)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) V1x)))) V0s)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V4u $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2ESURJ A_27a))) (=> (@ (@ tptp.mem V4u) (@ (@ tptp.arr A_27c) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V0f)) V2s)) V3t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27b) A_27c)) V1g)) V3t)) V4u))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)) V1g)) V0f))) V2s)) V4u)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (and (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V1s)) (= V1s (@ tptp.c_2Epred__set_2EEMPTY A_27b))))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V2s)) (@ tptp.c_2Epred__set_2EEMPTY A_27b))) (= V2s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) V2t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s) V2t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V2f)) V0s)) V1t)))) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27b) A_27a)) V3g)) V1t)) V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) V1x)))) V0s)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (@ tptp.c_2Epred__set_2EUNIV A_27b))) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2y) A_27a) (= (= (@ _let_1 V1x) (@ _let_1 V2y)) (= V1x V2y)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (and (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V1s)) (= V1s (@ tptp.c_2Epred__set_2EEMPTY A_27b))))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V2s)) (@ tptp.c_2Epred__set_2EEMPTY A_27b))) (= V2s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V4u $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EBIJ A_27a))) (=> (@ (@ tptp.mem V4u) (@ (@ tptp.arr A_27c) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V0f)) V2s)) V3t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27b) A_27c)) V1g)) V3t)) V4u))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)) V1g)) V0f))) V2s)) V4u)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V2f)) V0s)) V1t)) (forall ((V3e $$unsorted)) (=> (@ (@ tptp.mem V3e) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3e)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V2f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V3e))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27b)) V1t)) (@ (@ tptp.ap V2f) V3e)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (=> (exists ((V2t $$unsorted)) (and (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V1f)) V0s)) V2t)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V1f)) V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V1f)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s0 $$unsorted)) (=> (@ (@ tptp.mem V0s0) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s0)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V2f)) V1s)) V3t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V2f)) V0s0)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V2f)) V0s0)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V2f)) V0s)) V1t)))) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27b) A_27a)) V3g)) V1t)) V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V2f)) V0s)) V1t)))) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27b) A_27a)) V3g)) V1t)) V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27c) tptp.bool)) (forall ((V2u $$unsorted)) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (exists ((V3f $$unsorted)) (and (@ (@ tptp.mem V3f) (@ (@ tptp.arr A_27a) A_27c)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27c)) V3f)) V0s)) V1t)))) (exists ((V4g $$unsorted)) (and (@ (@ tptp.mem V4g) (@ (@ tptp.arr A_27c) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27c) A_27b)) V4g)) V1t)) V2u))))) (exists ((V5h $$unsorted)) (and (@ (@ tptp.mem V5h) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V5h)) V0s)) V2u))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27b) A_27a)) V3g)) V2t)) V1s)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V1s)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27a) A_27b)) V3g)) V0f)) V4x) V4x)))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V5x)) V2t)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) A_27b) A_27a)) V0f)) V3g)) V5x) V5x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V0P)) V1Q) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V2f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V0P))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V2f) V3x))) V1Q)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1Q) (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EDFUNSET A_27a) A_27b)) V0P)) V1Q) (@ (@ tptp.lam (@ _let_1 A_27b)) (lambda ((V2f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V0P))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V2f) V3x))) (@ (@ tptp.ap V1Q) V3x)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.arr A_27a) A_27b))) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V1P)) V2Q))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) V2Q)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V1P)) V2Q)) V0f)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) V2Q)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Q $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V2Q) (@ _let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ _let_1 A_27b))) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EDFUNSET A_27a) A_27b)) V1P)) V2Q))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) (@ (@ tptp.ap V2Q) V3x)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Q $$unsorted)) (=> (@ (@ tptp.mem V2Q) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EDFUNSET A_27a) A_27b)) V1P)) V2Q)) V0f)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) (@ (@ tptp.ap V2Q) V3x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.arr A_27a) A_27b))) V2f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V0s)) V1t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V0s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V2f) V3x))) V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (@ tptp.c_2Epred__set_2EUNIV A_27b)) (@ tptp.c_2Epred__set_2EUNIV (@ (@ tptp.arr A_27a) A_27b)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1y $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27b) tptp.bool))) (=> (@ (@ tptp.mem V1y) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V0x)) V1y) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EDFUNSET A_27a) A_27b)) V0x)) (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK _let_1) A_27a)) V1y)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V0s) (@ tptp.c_2Epred__set_2EUNIV (@ (@ tptp.arr A_27a) A_27b))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (=> (@ (@ tptp.mem V1f) _let_1) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V1f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V0s)) (@ tptp.c_2Epred__set_2EEMPTY A_27b)))) (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2c $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V0a)))) (=> (@ (@ tptp.mem V2c) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27b)) V1b)) V2c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER (@ (@ tptp.arr A_27a) A_27b))) (@ _let_1 V1b))) (@ _let_1 V2c)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eschroeder__close A_27a)) V0f)) V1s)) V2x)) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27a)) V0f))) (@ tptp.inj__ty_2Enum_2Enum V3n))) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eschroeder__close A_27a)) V1f)) V2s))) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27a)) V1f))) (@ tptp.inj__ty_2Enum_2Enum V3n))) V2s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eschroeder__close A_27a)) V0f)) V1s))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27a)) V0f)) _let_1))) _let_1))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eschroeder__close A_27a)) V0f)) V1s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V2t) (@ _let_2 tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ _let_2 A_27a))) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27a)) V1s)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2t)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eschroeder__close A_27a)) V0f)) V2t))) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s)) (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27a)) V2f)) V0s)) V1t))))) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27a) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27a)) V3g)) V0s)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V2f)) V0s)) V1t)))) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27b) A_27a)) V3g)) V1t)) V0s))))) (exists ((V4h $$unsorted)) (and (@ (@ tptp.mem V4h) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V4h)) V0s)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (exists ((V2f $$unsorted)) (and (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V2f)) V0s)) V1t)))) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V3g)) V0s)) V1t))))) (exists ((V4h $$unsorted)) (and (@ (@ tptp.mem V4h) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V4h)) V0s)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.arr A_27a) A_27b))) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EFUNSET A_27a) A_27b)) V1s)) V2t))) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V3y)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V3y)) (@ (@ tptp.ap V0f) V4x)))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1e)) V2s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) V2s))) V3t))) (exists ((V4u $$unsorted)) (let ((_let_1 (@ (@ tptp.ap V0f) V1e))) (and (@ (@ tptp.mem V4u) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27b)) _let_1)) V4u) V3t) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) _let_1)) V4u))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V2s)) V4u)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (= V2t (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27a) A_27b)) V0f)) V1s)) V2y) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ tptp.ty_2Eoption_2Eoption A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V2y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s)))) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) (@ (@ tptp.ap V0f) V3x))) V2y)))))))) (@ tptp.c_2Eoption_2ENONE A_27a))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27a) A_27b)) V0f)) V1s)) V2y) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (= (@ (@ tptp.ap V0f) V3x) V2y))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ty_2Eoption_2Eoption A_27b))) (let ((_let_2 (@ tptp.c_2Epred__set_2EIMAGE A_27b))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27b) A_27a)) V0f)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 A_27a)) V0f)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 _let_1)) (@ tptp.c_2Eoption_2ESOME A_27b))) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27b) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27a) A_27b)) V0f)) V1s)) V4y) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ESOME A_27a)) V3x)) (and (= V4y (@ (@ tptp.ap V0f) V3x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V4y)) V2t))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV A_27a) A_27b)) V0f)) V1s)) V2y) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27a) A_27b)) V0f)) V1s)) V2y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV A_27a) A_27b)) V0f)) V1s)) (@ (@ tptp.ap V0f) V3x)) V3x))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V3x)) V2t)) (= (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV A_27a) A_27b)) V0f)) V1s)) V3x)) V3x))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27b) A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV A_27a) A_27b)) V0f)) V1s))) V2t)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V3x))) V2t))))) (exists ((V4g $$unsorted)) (and (@ (@ tptp.mem V4g) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V5x)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap V4g) V5x))) V1s))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V6x)) V1s)) (= (@ (@ tptp.ap V4g) (@ (@ tptp.ap V0f) V6x)) V6x)))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V7x)) V2t)) (= (@ (@ tptp.ap V0f) (@ (@ tptp.ap V4g) V7x)) V7x)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V2s)))) (let ((_let_3 (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1e)) V2s)))) (let ((_let_4 (@ (@ tptp.ap V0f) V1e))) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) V2s))) V3t)) (or (and (not _let_3) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) _let_4)) V3t)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27b)) V3t)) _let_4)))) (and _let_3 (@ tptp.p (@ _let_2 V3t))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ERINV A_27a) A_27b)) V0f)) V1s)) V2y) (@ (@ tptp.ap (@ tptp.c_2Eoption_2ETHE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ELINV__OPT A_27a) A_27b)) V0f)) V1s)) V2y))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) V2t)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V3x)) V2t)) (= (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ERINV A_27a) A_27b)) V0f)) V1s)) V3x)) V3x))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) V2t)) (exists ((V3g $$unsorted)) (and (@ (@ tptp.mem V3g) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27b) A_27a)) V3g)) V2t)) V1s)) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V4y)) V2t)) (= (@ (@ tptp.ap V0f) (@ (@ tptp.ap V3g) V4y)) V4y))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap V1P) V2s)) (forall ((V3e $$unsorted)) (=> (@ (@ tptp.mem V3e) A_27a) (@ tptp.p (@ (@ tptp.ap V1P) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V3e)) V2s))))))))) (@ tptp.p (@ _let_1 V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap V0P) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap V0P) V1s))) (forall ((V2e $$unsorted)) (=> (@ (@ tptp.mem V2e) A_27a) (=> (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2e)) V1s))) (@ tptp.p (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2e)) V1s)))))))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V3s)) (@ tptp.p (@ (@ tptp.ap V0P) V3s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))) (@ tptp.p (@ _let_1 V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V0x))) (@ tptp.p (@ _let_1 V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))) (@ tptp.p (@ _let_1 V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s))) (@ tptp.p (@ _let_1 V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V1t)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0P)) V1Q))) (@ tptp.p (@ _let_1 V1Q))) (@ tptp.p (@ _let_1 V0P)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V1f)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27b) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V1x)) (@ (@ tptp.ap V0f) V2y)))))))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V3s))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V3s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2y) A_27a) (= (= (@ _let_1 V1x) (@ _let_1 V2y)) (= V1x V2y))))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V3s))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V3s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) V0R)) V1s)) V2x)) V3y)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V3y)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) V0R)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (@ tptp.c_2Erelation_2EEMPTY__REL A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2R $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) V2R)))) (let ((_let_2 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V2R) (@ _let_2 (@ _let_2 tptp.bool))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s1)) V1s2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)) (@ _let_1 V0s1))) (@ _let_1 V1s2)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) tptp.fo__c_2Enum_2E0) (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ _let_1 V0s))) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V0s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s))) _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) tptp.fo__c_2Enum_2E0)))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ _let_1 V0s))) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V0s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s))) _let_2)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0s)) tptp.fo__c_2Enum_2E0) (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ _let_1 V0s))) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V1x))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_2)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t)))) (@ _let_1 V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1t)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t)))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 (@ _let_1 V0s))) (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V0s)) (@ tptp.p (@ _let_2 V1t))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ _let_1 V0s))) (@ _let_1 V1t)))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V1t))) (@ _let_1 V0s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V1t)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_1 V1t))) (@ _let_1 V0s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1t)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 V0s)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 V1t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t))) (= V0s V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESING A_27a)) V0s)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0t)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V1s)) V0t))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ _let_1 V1s))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) V0t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V1s)) V0t))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ _let_1 V1s))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) V0t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0t)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V0t))) (@ _let_1 V1s))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V1s)) V0t))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) V0f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2t)) V1s))) (exists ((V3N tptp.tp__ty_2Enum_2Enum)) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V3N))) _let_1)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap V0f) _let_1))) V2t)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t))) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V0f)) V1s)) V2t))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0S $$unsorted)) (=> (@ (@ tptp.mem V0S) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0S)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) A_27b)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V2f)) V0S)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V1t))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0S)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V3y) A_27a) (= (= (@ _let_1 V2x) (@ _let_1 V3y)) (= V2x V3y))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s)))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V0f)) V1s)) V2t)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V2t))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V1f)) V0s)) V2t))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27b)) V1f)) V0s)) V2t)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V2t)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0s)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27b)) V1f)) V0s)) V2t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V2y)) V1x)) (@ tptp.p (@ (@ tptp.ap V0P) V2y))))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1x)) (@ tptp.p (@ (@ tptp.ap V0P) V1x)))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V3x)) (@ tptp.p (@ (@ tptp.ap V0P) V3x)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V2s)) V1t)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V2s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V2s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V2t))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s)))) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V0n)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.bool)) V1m)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) V1m)) (@ tptp.inj__ty_2Enum_2Enum V0n)))))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_2)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) _let_1)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (= (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum)))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Epred__set_2Ecount))) (= (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_1)) (@ _let_2 _let_1)))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V0n)))) V0n)))
% 1.89/2.22 (assert (forall ((V0n1 tptp.tp__ty_2Enum_2Enum) (V1n2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2Ecount))) (= (= (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V0n1)) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n2))) (= V0n1 V1n2)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a)))) (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0P))) (exists ((V1x $$unsorted)) (and (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0P))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (= (@ _let_1 V1x) (@ _let_1 V2y)) (= V1x V2y))))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V3s))) (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V3s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (not (@ tptp.p (@ _let_1 V0s))) (@ tptp.p (@ _let_1 V1t))) (exists ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ _let_1 V0s)) (not (@ tptp.p (@ _let_1 V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)))) (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27a)) V1f)) V0s)) V0s)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) A_27a)) V1f)) V0s)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a)))) (exists ((V0f $$unsorted)) (and (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27a)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (= (@ _let_1 V1x) (@ _let_1 V2y)) (= V1x V2y))))))) (exists ((V3y $$unsorted)) (and (@ (@ tptp.mem V3y) A_27a) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (not (= (@ (@ tptp.ap V0f) V4x) V3y)))))))))))
% 1.89/2.22 (assert (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1t)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V1t)) V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a)))) (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)) (@ tptp.c_2Epred__set_2EUNIV A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (not (@ tptp.p (@ _let_1 V0s))) (@ tptp.p (@ _let_1 V1t))) (not (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (exists ((V1c $$unsorted)) (and (@ (@ tptp.mem V1c) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (exists ((V2n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) V1c)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V2n)))) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (exists ((V2b tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V2b)))) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3m))) (let ((_let_2 (@ tptp.ap V1f))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_4 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0s))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_3)) _let_4)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_1)) _let_4))) (=> (= (@ _let_2 _let_3) (@ _let_2 _let_1)) (= V2n V3m))))))))) (= V0s (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V4n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) (@ (@ tptp.ap V1f) V4n))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) V4n)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (exists ((V2b tptp.tp__ty_2Enum_2Enum)) (forall ((V3e $$unsorted)) (=> (@ (@ tptp.mem V3e) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3e)) V0s)) (exists ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2b))) (= V3e (@ (@ tptp.ap V1f) _let_1)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) V0R)) V1s))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2Eirreflexive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Erelation_2ETC A_27a)) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) V0R)) V1s))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EStrongOrder A_27a)) _let_1))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) _let_1))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2s $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.arr A_27a) tptp.bool))) V2s)) V0P))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V2s))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1sos $$unsorted)) (=> (@ (@ tptp.mem V1sos) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1sos))) (exists ((V2s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (and (@ (@ tptp.mem V2s) _let_1) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2s)) V1sos)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1sos $$unsorted)) (=> (@ (@ tptp.mem V1sos) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1sos)) V0x)) (exists ((V2s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (and (@ (@ tptp.mem V2s) _let_1) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2s)) V1sos)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V2y)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) V0f)) V1s)))) (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V2y)) (@ (@ tptp.ap V0f) V3x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ tptp.c_2Epred__set_2EEMPTY (@ (@ tptp.arr A_27a) tptp.bool))) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.c_2Epred__set_2EEMPTY _let_1))) (let ((_let_3 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (let ((_let_4 (or (= V0P _let_2) (= V0P (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)) _let_3)) _let_2))))) (let ((_let_5 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V0P))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr _let_1) tptp.bool)) (and (= (= _let_5 _let_3) _let_4) (= (= _let_3 _let_5) _let_4))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0x) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY _let_1))) V0x)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)))) (=> (@ (@ tptp.mem V1t) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ _let_2 V0s)) (@ (@ tptp.ap (@ _let_2 V1t)) (@ tptp.c_2Epred__set_2EEMPTY _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (forall ((V1s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_2)) V0s1)) V1s2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ _let_1 V0s1))) (@ _let_1 V1s2))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V0s))) V1t)) (forall ((V2s_27 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2s_27) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2s_27)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V2s_27)) V1t))))))))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (forall ((V4t $$unsorted)) (=> (@ (@ tptp.mem V4t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V4t)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V3s))) (forall ((V5s_27 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V5s_27) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V5s_27)) V3s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V4t)) V5s_27))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_2)) V0s)) V1P)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) (@ _let_1 V1P))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0X $$unsorted)) (=> (@ (@ tptp.mem V0X) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1P))) V0X)) (forall ((V2Y $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2Y) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2Y)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2Y)) V0X))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1N tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) V0f)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)))) (=> (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V1N))) _let_1)) (= (@ (@ tptp.ap V0f) _let_1) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))) (= (@ _let_2 (@ _let_1 (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) (@ _let_2 (@ _let_1 (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V1N))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE _let_1)) V0P)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V1s)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V0P))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr _let_1) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V0P))) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE _let_1)) V0P)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V1s)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V0x)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0x)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1P))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE _let_1)) V1s)) (forall ((V2e $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2e) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2e)) V1s)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2e)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V2e)) V0n)))))) (forall ((V3e1 $$unsorted)) (=> (@ (@ tptp.mem V3e1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4e2 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)))) (=> (@ (@ tptp.mem V4e2) _let_1) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V3e1)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4e2)) V1s)) (not (= V3e1 V4e2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V3e1)) V4e2)))))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD _let_1)) V1s))) (@ tptp.inj__ty_2Enum_2Enum V0n)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) (=> (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap V0f))) (=> (not (= V1m V2n)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1m)))) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))))))) (forall ((V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3n))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ (@ tptp.ap V0f) _let_1))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE tptp.ty_2Enum_2Enum) (@ (@ tptp.arr A_27a) tptp.bool))) V0f)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) _let_1)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1s))) (@ tptp.p (@ (@ tptp.ap V0P) V2x))))) (forall ((V3t $$unsorted)) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.arr A_27a) tptp.bool))) V3t)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V3t))) (@ tptp.p (@ (@ tptp.ap V0P) V4x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V0P) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2s $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.arr A_27a) tptp.bool))) V2s)) V0P))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V2s))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V1B))) (forall ((V2P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2P) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2P)) V1B)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V2P))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0B $$unsorted)) (=> (@ (@ tptp.mem V0B) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V0B)) V1x)) (forall ((V2P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2P) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2P)) V0B)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V2P))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) (@ (@ tptp.arr A_27a) tptp.bool))) V1f)) V2s)))) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V3y)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap V1f) V3y))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_2)) V0P)) V1B)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0P)) (@ _let_1 V1B))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) (@ tptp.c_2Epred__set_2EEMPTY (@ (@ tptp.arr A_27a) tptp.bool))) (@ tptp.c_2Epred__set_2EUNIV A_27a))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)))) (=> (@ (@ tptp.mem V1Q) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) (@ (@ tptp.ap (@ _let_2 V0P)) (@ (@ tptp.ap (@ _let_2 V1Q)) (@ tptp.c_2Epred__set_2EEMPTY _let_1)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0P)) V1Q)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0P) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)) V0P)) (@ tptp.c_2Epred__set_2EEMPTY _let_1))) V0P)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0X $$unsorted)) (=> (@ (@ tptp.mem V0X) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0X)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V1P))) (forall ((V2Y $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2Y) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2Y)) V1P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0X)) V2Y))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0X $$unsorted)) (=> (@ (@ tptp.mem V0X) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Y $$unsorted)) (=> (@ (@ tptp.mem V1Y) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2P $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V2P))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)))) (let ((_let_3 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr _let_3) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_3)) V1Y)) V2P)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V1Y)) V0X))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V0X)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) V0X))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (forall ((V1s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_2)) V0s1)) V1s2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ _let_1 V0s1))) (@ _let_1 V1s2))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0sp $$unsorted)) (=> (@ (@ tptp.mem V0sp) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (and (forall ((V2t $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2t)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2t)) V0sp)))))) (not (= V1s (@ tptp.c_2Epred__set_2EEMPTY _let_1)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V1s))) V0sp)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0sp $$unsorted)) (=> (@ (@ tptp.mem V0sp) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_1) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0sp)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V1s)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2u $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0sp)) V2u))))) V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0sp $$unsorted)) (=> (@ (@ tptp.mem V0sp) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (and (forall ((V2t $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2t)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2t)) V0sp)))))) (not (= V1s (@ tptp.c_2Epred__set_2EEMPTY _let_1)))) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V1s) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0sp)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V3u $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0sp)) V3u))))) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) (=> (exists ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (and (@ (@ tptp.mem V1s) _let_1) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V1s)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) V0P)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) V1Q) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) V2p)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V2p))) V0P))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V2p))) V1Q)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V2x) _let_1) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) V1Q))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V2x))) V0P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V2x))) V1Q))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) V1Q)) V2x)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V2x))) V0P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V2x))) V1Q)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) (@ tptp.c_2Epred__set_2EEMPTY A_27b)) (@ tptp.c_2Epred__set_2EEMPTY (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27c) A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27c))) V0P) (@ tptp.c_2Epred__set_2EEMPTY (@ (@ tptp.ty_2Epair_2Eprod A_27c) A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0s)) V1t) (@ tptp.c_2Epred__set_2EEMPTY (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (or (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (= V1t (@ tptp.c_2Epred__set_2EEMPTY A_27b)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ _let_1 (@ _let_2 V0P))) V1Q) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ _let_1 (@ _let_2 (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) V1Q))) (@ (@ tptp.ap (@ _let_1 V0P)) V1Q))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27b)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27b) (= (@ _let_1 (@ _let_2 V1Q)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ _let_1 (@ _let_2 (@ tptp.c_2Epred__set_2EEMPTY A_27b))))) (@ _let_1 V1Q))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V1Q))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) V1Q)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V1y) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27b)) V1y)) (@ tptp.c_2Epred__set_2EEMPTY A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V1y))) (@ tptp.c_2Epred__set_2EEMPTY _let_1)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V1P)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) V1P))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V1P)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V1Q))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) V1Q))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0P))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27b)) V1Q))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2P0 $$unsorted)) (=> (@ (@ tptp.mem V2P0) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3Q0 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)))) (=> (@ (@ tptp.mem V3Q0) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ _let_1 V2P0)) V3Q0))) (@ (@ tptp.ap (@ _let_1 V0P)) V1Q))) (or (= V2P0 (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (= V3Q0 (@ tptp.c_2Epred__set_2EEMPTY A_27b)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2P0)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) V3Q0)) V1Q)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0P)) V1Q))) (or (= V0P (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (= V1Q (@ tptp.c_2Epred__set_2EEMPTY A_27b)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V1Q))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ tptp.c_2Epred__set_2EUNIV (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (@ tptp.c_2Epred__set_2EUNIV A_27b)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE _let_1)) (@ tptp.c_2Epred__set_2EUNIV _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) (@ tptp.c_2Epred__set_2EUNIV A_27b))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (= (@ tptp.c_2Epred__set_2EUNIV _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) _let_1)) (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b))) (@ tptp.c_2Epred__set_2EUNIV A_27a)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) _let_1)) (@ (@ tptp.c_2Esum_2EINR A_27a) A_27b))) (@ tptp.c_2Epred__set_2EUNIV A_27b)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b)) V2x))) V1t))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) _let_1)) (@ (@ tptp.c_2Esum_2EINL A_27a) A_27b))) V0s)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27b) A_27a))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Esum_2Esum A_27b) A_27a))) (@ (@ tptp.ap (@ (@ tptp.c_2Esum_2EINR A_27b) A_27a)) V2x))) V1t))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) _let_1)) (@ (@ tptp.c_2Esum_2EINR A_27b) A_27a))) V0s)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) V0P) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) V0P)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) V1s))) (not (@ tptp.p (@ _let_1 V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) V1s)) V0x)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ _let_1 V0s)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) V0s))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) _let_1)) V0s) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) _let_1)) V0s) (@ tptp.c_2Epred__set_2EUNIV A_27a)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (=> (@ (@ tptp.mem V1q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ (@ tptp.ap (@ _let_1 V0p)) V1q))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) V0p))) V1q)) V1q)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ _let_1 V0s))) (@ _let_1 V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (let ((_let_2 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) V0x))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (@ (@ tptp.ap (@ _let_3 V0x)) _let_2) _let_1) (= (@ (@ tptp.ap (@ _let_3 _let_2)) V0x) _let_1))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ _let_1 V0s))) (@ _let_1 V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr A_27b) tptp.bool))) (=> (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3b $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V3b) A_27b) (=> (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (not (= V2s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V2s))) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V2s))) V3b)))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2s)) V3b)))))))) (forall ((V4v $$unsorted)) (=> (@ (@ tptp.mem V4v) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V5v1 $$unsorted)) (=> (@ (@ tptp.mem V5v1) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V4v)) V5v1))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) V1f)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)))) (=> (@ (@ tptp.mem V2b) A_27b) (= (@ (@ tptp.ap (@ _let_1 V0s)) V2b) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V0s)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) V2b)) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s))) V2b))))) (@ tptp.c_2Ebool_2EARB A_27b))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V1P $$unsorted)) (=> (@ (@ tptp.mem V1P) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr A_27b) tptp.bool))) (=> (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3b $$unsorted)) (let ((_let_1 (@ tptp.ap V1P))) (=> (@ (@ tptp.mem V3b) A_27b) (=> (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (not (= V2s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V2s))) (@ (@ tptp.ap (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V2s))) V3b)))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2s)) V3b)))))))) (forall ((V4v $$unsorted)) (=> (@ (@ tptp.mem V4v) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V5v1 $$unsorted)) (=> (@ (@ tptp.mem V5v1) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1P) V4v)) V5v1))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V2b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) V1f)))) (=> (@ (@ tptp.mem V2b) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (= (@ (@ tptp.ap (@ _let_1 V0s)) V2b) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V0s)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) V2b)) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s))) V2b)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V1b $$unsorted)) (=> (@ (@ tptp.mem V1b) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V1b) V1b))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3b $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2x)) V0s))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) V1f)))) (=> (@ (@ tptp.mem V3b) A_27b) (= (@ (@ tptp.ap (@ _let_2 _let_1)) V3b) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) _let_1))) (@ (@ tptp.ap (@ (@ tptp.ap V1f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) _let_1))) V3b)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (forall ((V4z $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ _let_1 V2x)))) (let ((_let_3 (@ tptp.ap (@ _let_1 V3y)))) (=> (@ (@ tptp.mem V4z) A_27b) (= (@ _let_2 (@ _let_3 V4z)) (@ _let_3 (@ _let_2 V4z)))))))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V6b) A_27b) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V5x)) V1s))) V6b) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V5x))) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V5x)) V6b))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27b))) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (forall ((V2s $$unsorted)) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V3b) A_27b) (=> (and (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (forall ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (let ((_let_2 (@ tptp.ap (@ _let_1 V4x)))) (let ((_let_3 (@ tptp.ap (@ _let_1 V5y)))) (=> (@ (@ tptp.mem V6z) A_27b) (= (@ _let_2 (@ _let_3 V6z)) (@ _let_3 (@ _let_2 V6z)))))))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s))) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) V2s))) V3b) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V1e)) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V2s)) V1e))) V3b))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) V1s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam A_27a) (lambda ((V2e $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3acc $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap V0f) V2e))) V3acc))))))) V1s)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) tptp.fo__c_2Enum_2E0) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) V2s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap V0f) V1e))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V2s)) V1e)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap V0f) V1e))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2t)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V2t))) (@ _let_1 V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2e $$unsorted)) (=> (@ (@ tptp.mem V2e) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2e)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap V0f) V2e))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (forall ((V2e $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)))) (let ((_let_2 (@ _let_1 V1s))) (=> (@ (@ tptp.mem V2e) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V1s)) V2e))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2e)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) (@ (@ tptp.ap V0f) V2e)))) _let_2)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V1s)) (@ tptp.p (@ _let_2 V2t))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1s)) V2t))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ _let_1 V1s))) (@ _let_1 V2t)))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) V2t)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V2n))) (@ (@ tptp.ap V0f) V3x)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s))) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap V0f) V3x))) (@ tptp.inj__ty_2Enum_2Enum V2n)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V1s))) (@ tptp.inj__ty_2Enum_2Enum V2n))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0P)) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V2p $$unsorted)) (=> (@ (@ tptp.mem V2p) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2p)) V0P)) (forall ((V3q $$unsorted)) (let ((_let_1 (@ tptp.ap V1f))) (=> (@ (@ tptp.mem V3q) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3q)) V0P)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 V2p)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 V3q)))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V1f)) V0P)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0P))) (@ (@ tptp.ap V1f) V2p)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2f1 $$unsorted)) (=> (@ (@ tptp.mem V2f1) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V3f2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)))) (=> (@ (@ tptp.mem V3f2) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (=> (and (= V0s1 V1s2) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V1s2)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap V2f1) V4x)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap V3f2) V4x))))))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 V2f1)) V0s1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 V3f2)) V1s2))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (= (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V0f)) V1s)) tptp.fo__c_2Enum_2E0) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap V0f) V2x)) tptp.fo__c_2Enum_2E0)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) (@ (@ tptp.ap (@ _let_1 V0f)) V2s))) (@ (@ tptp.ap (@ _let_1 V1g)) V2s)))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EABS__DIFF) (@ (@ tptp.ap V0f) V3x))) (@ (@ tptp.ap V1g) V3x)))))) V2s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (=> (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap V0f) V3x))) (@ (@ tptp.ap V1g) V3x)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap (@ _let_1 V0f)) V2s))) (@ (@ tptp.ap (@ _let_1 V1g)) V2s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (=> (and (exists ((V3x $$unsorted)) (and (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap V0f) V3x))) (@ (@ tptp.ap V1g) V3x))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4x)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap V0f) V4x))) (@ (@ tptp.ap V1g) V4x))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ (@ tptp.ap (@ _let_1 V0f)) V2s))) (@ (@ tptp.ap (@ _let_1 V1g)) V2s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27b)) V0s)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27b) A_27a)) V1g)) V0s)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)) V2f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) A_27a)) V1g)) V0s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27b) tptp.ty_2Enum_2Enum) A_27a)) V2f)) V1g))) V0s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) A_27a)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ A_27a) A_27a)) V1g)) V0s)) V0s)) (forall ((V2f $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE A_27a)))) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) tptp.ty_2Enum_2Enum) A_27a)) V2f)) V1g))) V0s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 V2f)) V0s)))))))))))))
% 1.89/2.22 (assert (= tptp.c_2Epred__set_2ESUM__SET (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE tptp.ty_2Enum_2Enum)) (@ tptp.c_2Ecombin_2EI tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) tptp.fo__c_2Enum_2E0) (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_1)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE tptp.ty_2Enum_2Enum)) V1s)) _let_1))))))))))))
% 1.89/2.22 (assert (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) tptp.fo__c_2Enum_2E0))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum)))) V0n)))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET tptp.ty_2Enum_2Enum)) V0s)) V1t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V0s))) (@ _let_1 V1t))))))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET) V1s))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V0s)) (forall ((V1e tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET))) (let ((_let_2 (@ _let_1 V0s))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V1e))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE tptp.ty_2Enum_2Enum)) V0s)) _let_3))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_3)) V0s))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_2)) _let_3))) _let_2)))))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2ESUM__SET))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V0s)) (@ tptp.p (@ _let_2 V1t))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION tptp.ty_2Enum_2Enum)) V0s)) V1t))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ _let_1 V0s))) (@ _let_1 V1t)))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER tptp.ty_2Enum_2Enum)) V0s)) V1t)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPROD__IMAGE A_27a)) V0f)) V1s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EITSET A_27a) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam A_27a) (lambda ((V2e $$unsorted)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3acc $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap V0f) V2e))) V3acc))))))) V1s)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPROD__IMAGE A_27a)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPROD__IMAGE A_27a)) V0f)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) V2s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap V0f) V1e))) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V2s)) V1e)))))))))))))))
% 1.89/2.22 (assert (= tptp.c_2Epred__set_2EPROD__SET (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPROD__IMAGE tptp.ty_2Enum_2Enum)) (@ tptp.c_2Ecombin_2EI tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2EPROD__SET) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Epred__set_2EPROD__SET))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_1)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_1)) (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE tptp.ty_2Enum_2Enum)) V1s)) _let_1))))))))))))
% 1.89/2.22 (assert (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2EPROD__SET) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) tptp.ty_2Enum_2Enum)) V0f)))) (let ((_let_2 (@ _let_1 V1s))) (let ((_let_3 (@ tptp.ap tptp.c_2Epred__set_2EPROD__SET))) (let ((_let_4 (@ (@ tptp.ap V0f) V2x))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) _let_2)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_4)) _let_2)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2x)) V1s)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_4)) (@ _let_3 _let_2))))))))))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) V0s))) (let ((_let_2 (= V0s (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V0s)) (and (=> (not _let_2) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (forall ((V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) V0s)))))))) (=> _let_2 (= (@ tptp.surj__ty_2Enum_2Enum _let_1) tptp.fo__c_2Enum_2E0)))))))))
% 1.89/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) tptp.fo__c_2Enum_2E0) (forall ((V0e tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0e))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V1s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_2)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) _let_2)) (@ _let_1 V1s)))))))))))
% 1.89/2.22 (assert (forall ((V0e tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1)) tptp.fo__c_2Enum_2E0) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V0e))) _let_1))) V0e))))))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.ap V1Q))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V0P)) (=> (= V0P (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum)) (@ tptp.p (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (=> (and (forall ((V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ tptp.inj__ty_2Enum_2Enum V2x)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0P))) (@ tptp.p (@ (@ tptp.ap V1Q) _let_1)))))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) V0P))))))))))
% 1.89/2.22 (assert (= tptp.c_2Epred__set_2EMIN__SET tptp.c_2Ewhile_2ELEAST))
% 1.89/2.22 (assert (forall ((V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (not (= V0P (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (=> (and (forall ((V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0P)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ tptp.inj__ty_2Enum_2Enum V2x))) _let_1))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0P))) (@ tptp.p (@ (@ tptp.ap V1Q) _let_1)))))) (@ tptp.p (@ (@ tptp.ap V1Q) (@ (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET) V0P)))))))))
% 1.89/2.22 (assert (and (forall ((V0e tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V0e))) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum)))) V0e)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V2e1 tptp.tp__ty_2Enum_2Enum) (V3e2 tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V3e2))) V1s))) (let ((_let_3 (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2e1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_1 _let_4)) _let_2))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) _let_4)) (@ _let_3 _let_2)))))))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET) V0s))) V0s)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET) V0s))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0I $$unsorted)) (=> (@ (@ tptp.mem V0I) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1J $$unsorted)) (=> (@ (@ tptp.mem V1J) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V2n $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET))) (let ((_let_2 (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (=> (@ (@ tptp.mem V2n) A_27a) (=> (and (not (= V0I _let_2)) (not (= V1J _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET tptp.ty_2Enum_2Enum)) V0I)) V1J))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V1J))) (@ _let_1 V0I)))))))))))))
% 1.89/2.22 (assert (forall ((V0I $$unsorted)) (=> (@ (@ tptp.mem V0I) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1J $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)))) (=> (@ (@ tptp.mem V1J) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V0I)) (@ tptp.p (@ _let_2 V1J)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET tptp.ty_2Enum_2Enum)) V0I)) V1J))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V0I))) (@ _let_1 V1J)))))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V0s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET) V0s))) (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) V0s)))))))
% 1.89/2.22 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET))) (let ((_let_2 (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)))) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ _let_3 V0A)) (@ tptp.p (@ _let_3 V1B)) (not (= V0A _let_2)) (not (= V1B _let_2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION tptp.ty_2Enum_2Enum)) V0A)) V1B))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMIN) (@ _let_1 V0A))) (@ _let_1 V1B)))))))))))))
% 1.89/2.22 (assert (forall ((V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)))) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V0A)) (@ tptp.p (@ _let_2 V1B))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION tptp.ty_2Enum_2Enum)) V0A)) V1B))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMAX) (@ _let_1 V0A))) (@ _let_1 V1B))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0set $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0set) _let_1) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0set) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V1s $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)) V0set))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0set $$unsorted)) (=> (@ (@ tptp.mem V0set) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1e $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1e) _let_1) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V1e)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0set))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1e)) V0set)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Epred__set_2EUNIV (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s2) _let_2) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s1)) V1s2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_2)) (@ _let_1 V0s1))) (@ _let_1 V1s2)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (forall ((V1s1 $$unsorted)) (=> (@ (@ tptp.mem V1s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s1)))) (=> (@ (@ tptp.mem V2s2) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_1 V2s2)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0e)) V2s2))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 V0s1)) V1s2)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V0s1)) V2x))) (@ (@ tptp.ap (@ _let_1 V1s2)) V2x)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0s) _let_1) (not (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0s) (@ tptp.c_2Epred__set_2EEMPTY _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)))) (let ((_let_2 (@ _let_1 V1s))) (let ((_let_3 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0e))) (let ((_let_4 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_4) (= (@ _let_1 (@ (@ tptp.ap _let_3) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_4) _let_4)) _let_3)) _let_2))) _let_2)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (and (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) _let_2) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT _let_1)) _let_2)) (@ tptp.c_2Epred__set_2EEMPTY _let_1))) (forall ((V0e $$unsorted)) (=> (@ (@ tptp.mem V0e) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_3 (@ (@ tptp.arr _let_2) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_2) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0e)) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET _let_3) _let_3)) (@ (@ tptp.lam _let_3) (lambda ((V2ps $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_1) _let_1)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0e))) V2ps))) V2ps)))))) (@ _let_1 V1s)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0s) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE _let_1)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0s) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD _let_1)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EEXP) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V0x)) tptp.c_2Ebool_2EF)))) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V0x)) tptp.c_2Ebool_2ET)))) (@ tptp.c_2Epred__set_2EUNIV A_27a))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0y))))) V0y))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V0y))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0y)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V0y)) V1x))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0y)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.ty_2Epair_2Eprod A_27b) tptp.bool))) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27b) tptp.bool)) (@ (@ tptp.ap V0f) V1x)))))) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27b) A_27a)) V0f) (@ tptp.c_2Epred__set_2EEMPTY A_27b))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_2 (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap V0P) V2x))) (@ (@ tptp.ap V1Q) V2x)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ _let_2 (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V3x)) (@ (@ tptp.ap V0P) V3x))))))) (@ _let_2 (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V4x)) (@ (@ tptp.ap V1Q) V4x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1Q $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)))) (=> (@ (@ tptp.mem V1Q) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_2 (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap V0P) V2x))) (@ (@ tptp.ap V1Q) V2x)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ _let_2 (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V3x)) (@ (@ tptp.ap V0P) V3x))))))) (@ _let_2 (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V4x)) (@ (@ tptp.ap V1Q) V4x))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) V0R)) V1s)) (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V2x)) V2x))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4y)) V1s))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V3x)))))))))) (forall ((V5x $$unsorted)) (=> (@ (@ tptp.mem V5x) A_27a) (forall ((V6y $$unsorted)) (=> (@ (@ tptp.mem V6y) A_27a) (forall ((V7z $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (let ((_let_2 (@ tptp.ap (@ _let_1 V5x)))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V7z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 V5x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V6y)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V7z)) V1s)) (@ tptp.p (@ _let_2 V6y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V6y)) V7z))) (@ tptp.p (@ _let_2 V7z))))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) V2t)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3x)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V2t)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V4y)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V4y)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)))))))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) V0R)) V1s)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s)) V1s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) V0R)) V1s)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) V0R)) V1s)) (forall ((V2t1 $$unsorted)) (=> (@ (@ tptp.mem V2t1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t2 $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_2)))) (=> (@ (@ tptp.mem V3t2) _let_2) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 V2t1)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V3t2)) _let_1)) (not (= V2t1 V3t2))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V2t1)) V3t2)))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) V0R)) V1s)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V2t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) V3x)) V4y)))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2t)) V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s))) (forall ((V2t $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V2t) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V2t)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2ECARD A_27a))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_2) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eequiv__on A_27a)) V0R)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap _let_1) V1s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUM__IMAGE _let_2)) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epartition A_27a)) V0R)) V1s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0P) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epairwise A_27a)) V0P)) V1s)) (forall ((V2e1 $$unsorted)) (=> (@ (@ tptp.mem V2e1) A_27a) (forall ((V3e2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V3e2) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2e1)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3e2)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0P) V2e1)) V3e2)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s1 $$unsorted)) (=> (@ (@ tptp.mem V1s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epairwise A_27a)) V0R)))) (=> (@ (@ tptp.mem V2s2) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1s1)) V2s2))) (and (@ tptp.p (@ _let_1 V1s1)) (@ tptp.p (@ _let_1 V2s2)) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0R))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 V3x)) V1s1)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 V4y)) V2s2))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3x)) V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4y)) V3x)))))))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Epairwise A_27a)) V0R)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)) V2t))) (@ tptp.p (@ _let_1 V1s))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2y)) (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y))))))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V4y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V3x)) V4y)))))))) (exists ((V5f $$unsorted)) (and (@ (@ tptp.mem V5f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= (@ (@ tptp.ap V5f) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) V3x) (forall ((V6n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6n))) (let ((_let_2 (@ tptp.ap V5f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V0R) (@ _let_2 _let_1))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2y)) (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y))))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Erelation_2EWF A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2Einv A_27a) A_27a)) V0R)))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V4y)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Erelation_2ERTC A_27a)) V0R)) V3x)) V4y))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (= (= V0s1 V1s2) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s1)) V1s2)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s2)) V0s1))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s1)) V1s2)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s1)) V1s2)) (not (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s2)) V0s1)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V0s)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V1t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V2u))) (@ tptp.p (@ _let_1 V2u)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)))) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1t)) V2u))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) V2u)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0a $$unsorted)) (=> (@ (@ tptp.mem V0a) A_27a) (forall ((V1s1 $$unsorted)) (=> (@ (@ tptp.mem V1s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V2s2) (@ (@ tptp.arr A_27b) tptp.bool)) (and (= (@ (@ tptp.ap (@ _let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) V2s2) (@ tptp.c_2Epred__set_2EEMPTY _let_2)) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0a)) V1s1))) V2s2) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) _let_2)) (@ (@ tptp.lam A_27b) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0a)) V3y))))) V2s2))) (@ (@ tptp.ap (@ _let_1 V1s1)) V2s2)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool))) (= (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) _let_1) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND _let_2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) _let_2)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1p $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) V1p)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) V1p)))))) (@ (@ tptp.ap tptp.c_2Eprim__rec_2EPRE) _let_1))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2y)) V1s)) (= V0x V2y))))) (= V1s (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t)) (or (= V1s (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (exists ((V3f_27 $$unsorted)) (and (@ (@ tptp.mem V3f_27) (@ (@ tptp.arr A_27b) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27b) A_27a)) V3f_27)) V2t)) V1s)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ _let_1 V0s))) (not (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Echooser A_27a)) V0s)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s)))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2Echooser A_27a)))) (= (@ (@ tptp.ap (@ _let_2 V1s)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1)) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V1s))) _let_1))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Echooser A_27a)) V0s)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) V0s)))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Epred__set_2Echooser A_27a)))) (= (@ (@ tptp.ap (@ _let_4 V1s)) _let_3) (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V1s))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))))) (forall ((V3s $$unsorted)) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Epred__set_2Echooser A_27a)))) (= (@ (@ tptp.ap (@ _let_3 V3s)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V3s))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) tptp.ty_2Enum_2Enum)) V1f)) V0s)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE tptp.ty_2Enum_2Enum) A_27a)) V0f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s)) (or (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s)))))))))
% 1.89/2.22 (assert (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable tptp.ty_2Enum_2Enum)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1t)) V0s))) (@ tptp.p (@ _let_1 V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0s)) (exists ((V3n tptp.tp__ty_2Enum_2Enum)) (= (@ (@ tptp.ap V1f) (@ tptp.inj__ty_2Enum_2Enum V3n)) V2x)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t)) (@ tptp.p (@ _let_1 V1t))) (@ tptp.p (@ _let_1 V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Epred__set_2Ecount) (@ tptp.inj__ty_2Enum_2Enum V0n))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable tptp.ty_2Enum_2Enum)) V0s)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE tptp.ty_2Enum_2Enum) A_27a)) V0f)) V1s))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2Enum__to__pair) _let_1)) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Enumpair_2Enfst) _let_1))) (@ (@ tptp.ap tptp.c_2Enumpair_2Ensnd) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2Epair__to__num) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_2)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumpair_2Enpair) _let_2)) _let_1)))))))
% 1.89/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2Epair__to__num) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_4)) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) (@ (@ tptp.ap (@ _let_5 _let_6)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2))))) _let_6))) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2))))) _let_1)))))))))))
% 1.89/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2Epair__to__num) (@ (@ tptp.ap tptp.c_2Epred__set_2Enum__to__pair) (@ tptp.inj__ty_2Enum_2Enum V0x)))) V0x)) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.inj__ty_2Enum_2Enum V2y)))) (= (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Epred__set_2Enum__to__pair) (@ (@ tptp.ap tptp.c_2Epred__set_2Epair__to__num) _let_1))) (@ tptp.surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum _let_1))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) V1t))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0s)) V1t)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (or (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) V2t))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable _let_1)) V0s)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1x) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V1x)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V1x))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V0s))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t))) (and (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ A_27a) A_27b)) V0f)) V1s)) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (not (exists ((V1f $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (and (@ (@ tptp.mem V1f) (@ _let_1 _let_2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ESURJ A_27a) _let_2)) V1f)) V0s)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0s) _let_1) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable _let_1)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPOW A_27a)) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Esum_2Esum A_27a) A_27b))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable _let_1)) (@ tptp.c_2Epred__set_2EUNIV _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) (@ tptp.c_2Epred__set_2EUNIV A_27b))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0x)) V1s))) (@ tptp.p (@ _let_1 V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27a) A_27b)) V0s)) V1t))) (or (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (= V1t (@ tptp.c_2Epred__set_2EEMPTY A_27b)) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) V1t))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable _let_1)) (@ tptp.c_2Epred__set_2EUNIV _let_1))) (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) (@ tptp.c_2Epred__set_2EUNIV A_27a))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27b)) (@ tptp.c_2Epred__set_2EUNIV A_27b))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW _let_1)) (@ tptp.c_2Epred__set_2EREST A_27a))) (@ tptp.inj__ty_2Enum_2Enum V0n))) V1s))) V1s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0n tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1s) _let_1) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s))) (not (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW _let_1)) (@ tptp.c_2Epred__set_2EREST A_27a))) (@ tptp.inj__ty_2Enum_2Enum V0n))) V1s) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (not (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EINJ tptp.ty_2Enum_2Enum) A_27a)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V1n $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECHOICE A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW (@ (@ tptp.arr A_27a) tptp.bool))) (@ tptp.c_2Epred__set_2EREST A_27a))) V1n)) V0s)))))) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s)))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eenumerate A_27a)) V0s) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V1f $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eenumerate A_27a)) V0s))) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0s)) (or (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EBIJ tptp.ty_2Enum_2Enum) A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eenumerate A_27a)) V0s))) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))) V0s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0c $$unsorted)) (=> (@ (@ tptp.mem V0c) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Ecountable A_27a)) V0c)) (or (= V0c (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (exists ((V1f $$unsorted)) (and (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) A_27a)) (= V0c (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE tptp.ty_2Enum_2Enum) A_27a)) V1f)) (@ tptp.c_2Epred__set_2EUNIV tptp.ty_2Enum_2Enum))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1M $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V1M) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ (@ tptp.ap _let_1) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) V1M)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_2) (@ (@ tptp.arr A_27b) tptp.bool))) _let_1)) V1M))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s3 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s1)))) (=> (@ (@ tptp.mem V2s3) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V1s2)) V2s3))) (and (@ tptp.p (@ _let_1 V1s2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) V0s1)) V2s3))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0A)) V1B))) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (= _let_2 V0A) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0A)) V1B))) (= (= _let_2 V1B) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1B)) V0A)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) A_27a) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (=> (@ (@ tptp.mem V1x) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EPSUBSET A_27a)) V1x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V0s)) _let_1))) (= V1x _let_1))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1B $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V1B)) V0A))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)))) (let ((_let_4 (@ tptp.ap (@ _let_3 V0A)))) (let ((_let_5 (@ (@ tptp.ap (@ _let_1 V0A)) V1B))) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr A_27a) tptp.bool)) (and (= (@ (@ tptp.ap (@ _let_3 _let_5)) V0A) V0A) (= (@ (@ tptp.ap (@ _let_3 _let_2)) V0A) V0A) (= (@ _let_4 _let_5) V0A) (= (@ _let_4 _let_2) V0A))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0A $$unsorted)) (=> (@ (@ tptp.mem V0A) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1B $$unsorted)) (=> (@ (@ tptp.mem V1B) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_2 V0A)) V1B))) V2x) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V0A)) V2x))) (@ (@ tptp.ap (@ _let_1 V1B)) V2x))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1e $$unsorted)) (=> (@ (@ tptp.mem V1e) A_27a) (forall ((V2s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V2s2) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) V0s)) V1e))) V2s2)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1e)) V2s2))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2P $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)))) (let ((_let_2 (= V0x V1y))) (=> (@ (@ tptp.mem V2P) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1y)) V2P))) (or _let_2 (and (not _let_2) (@ tptp.p (@ _let_1 V2P))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s1 $$unsorted)) (=> (@ (@ tptp.mem V0s1) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1s2) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (or (@ tptp.p (@ _let_1 V0s1)) (@ tptp.p (@ _let_1 V1s2))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V0s1)) V1s2))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)))) (let ((_let_2 (@ (@ tptp.ap (@ _let_1 V2y)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (=> (@ (@ tptp.mem V2y) A_27a) (= (= (@ (@ tptp.ap (@ _let_1 V1x)) V0s) _let_2) (and (= V1x V2y) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) _let_2)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)))) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V0s)) (@ tptp.p (@ _let_2 V1t))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) V1t)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ _let_1 V0s))) (@ _let_1 V1t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2u $$unsorted)) (=> (@ (@ tptp.mem V2u) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V3t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)))) (=> (@ (@ tptp.mem V3t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)) V2u)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V2u))) V3t))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ _let_1 V1s))) V3t))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECARD A_27a)))) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V0s)) (not (= V0s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREST A_27a)) V0s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ _let_1 V0s))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t) (@ tptp.c_2Epred__set_2EEMPTY A_27a)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0s)) V1t))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0r)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V0r)) V1s)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1s)) V2t)) (@ _let_1 V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V0s)) V1t)) V0s))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.ap tptp.c_2Epred__set_2Ecount))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_3))) (= (@ _let_2 (@ (@ tptp.ap _let_4) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION tptp.ty_2Enum_2Enum)) (@ _let_2 _let_3))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) _let_4)) (@ _let_2 _let_1))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27b) A_27a)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2z $$unsorted)) (=> (@ (@ tptp.mem V2z) A_27a) (= (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27b) A_27a)) V0f)) V1s) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V2z)) (@ tptp.c_2Epred__set_2EEMPTY A_27a))) (and (not (= V1s (@ tptp.c_2Epred__set_2EEMPTY A_27b))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V3x)) V1s)) (= (@ (@ tptp.ap V0f) V3x) V2z)))))))))))))
% 1.89/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Epred__set_2Ecount))) (= (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_1)) (@ _let_2 _let_1)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)))) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) V0s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE A_27a)) (@ _let_1 V0s))) V1x))))))))
% 1.89/2.22 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE tptp.ty_2Enum_2Enum)) V0s)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) V0s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) V1s) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V2x))) V1s)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) V1s) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) tptp.bool) A_27b)) V1s)) V0f)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V2x))) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) V1s)) V2x)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) (@ (@ tptp.ap V0f) V2x))) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EEMPTY A_27b)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) (@ tptp.c_2Epred__set_2EUNIV A_27b)) (@ tptp.c_2Epred__set_2EUNIV A_27a)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27b)) V1s)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27a)) (@ _let_1 V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27b)) V1s)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ _let_1 V1s))) (@ _let_1 V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27b)) V1s)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ _let_1 V1s))) (@ _let_1 V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f))) (let ((_let_2 (@ (@ tptp.arr A_27b) tptp.bool))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ (@ tptp.ap _let_1) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27b)) V1s)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_2) (@ (@ tptp.arr A_27a) tptp.bool))) _let_1)) V1s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27b) A_27c)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.c_2Epred__set_2EPREIMAGE A_27a))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27c) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27b) A_27c)) V1g)) V2s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27c) A_27b)) V1g)) V0f))) V2s))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27b)) V1s)) V2t)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) (@ _let_1 V1s))) (@ _let_1 V2t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27a)) (@ tptp.c_2Ecombin_2EI A_27a)) (@ tptp.c_2Ecombin_2EI (@ (@ tptp.arr A_27a) tptp.bool)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27b) A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EK A_27a) A_27b)) V0x))) V1s) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s))) (@ tptp.c_2Epred__set_2EUNIV A_27b))) (@ tptp.c_2Epred__set_2EEMPTY A_27b))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27b)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ _let_1 V1s))) (@ _let_1 V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) V1s)) V2t)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ _let_1 V1s))) (@ _let_1 V2t))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c))) (forall ((V1a $$unsorted)) (=> (@ (@ tptp.mem V1a) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2b $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c))) (let ((_let_2 (@ tptp.c_2Ecombin_2Eo A_27a))) (let ((_let_3 (@ tptp.c_2Epred__set_2EPREIMAGE A_27a))) (=> (@ (@ tptp.mem V2b) (@ (@ tptp.arr A_27c) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 _let_1)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2ECROSS A_27b) A_27c)) V1a)) V2b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_2 A_27b) _let_1)) (@ (@ tptp.c_2Epair_2EFST A_27b) A_27c))) V0f))) V1a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_3 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ _let_2 A_27c) _let_1)) (@ (@ tptp.c_2Epair_2ESND A_27b) A_27c))) V0f))) V2b)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2sp $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)))) (=> (@ (@ tptp.mem V2sp) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ECOMPL A_27b)) V1t)))) V2sp) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDIFF A_27a)) V2sp)) (@ _let_1 V1t)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1s)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V1s)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EPREIMAGE A_27a) A_27b)) V0f)) V1s)))) V1s)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eis__measure__maximal A_27a)) V0m)) V1s)) V2x)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap V0m))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V3y)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 V3y))) (@ _let_1 V2x))))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) V1s)) (not (= V1s (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eis__measure__maximal A_27a)) V0m)) V1s)) V2x))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eis__measure__maximal A_27a)) V0m)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V1x)) (@ tptp.c_2Epred__set_2EEMPTY A_27a)))) V2y)) (= V2y V1x)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2m $$unsorted)) (=> (@ (@ tptp.mem V2m) (@ (@ tptp.arr A_27a) tptp.ty_2Enum_2Enum)) (forall ((V3e $$unsorted)) (=> (@ (@ tptp.mem V3e) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2Eis__measure__maximal A_27a)) V2m)))) (let ((_let_2 (@ tptp.ap V2m))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eprim__rec_2E_3C) (@ _let_2 V3e))) (@ _let_2 V0x)))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT A_27a)) V3e)) V1s))) V4y)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1s)) V4y)))))))))))))))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Eclosed (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2EfixedPoint_2Eclosed A_27a)) (@ (@ tptp.arr (@ _let_2 _let_1)) (@ _let_2 tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Edense (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2EfixedPoint_2Edense A_27a)) (@ (@ tptp.arr (@ _let_2 _let_1)) (@ _let_2 tptp.bool)))))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Eempty (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2EfixedPoint_2Eempty A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool)))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Efnsum (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27a) tptp.bool)))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27a) A_27b)) (@ _let_2 (@ _let_2 _let_1)))))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Egfp (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2EfixedPoint_2Egfp A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr _let_1) _let_1)) _let_1)))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Elfp (tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2EfixedPoint_2Elfp A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr _let_1) _let_1)) _let_1)))))
% 1.89/2.22 (declare-fun tptp.c_2EfixedPoint_2Emonotone (tptp.del tptp.del) $$unsorted)
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr A_27b) tptp.bool))) tptp.bool))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27b)) V0f)) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2Y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V2Y) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)) V2Y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ _let_1 V1X))) (@ _let_1 V2Y)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (= (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGINTER A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V1X $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) V1X)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap V0f) V1X))) V1X)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (= (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V1X $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)) V1X)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)) (@ (@ tptp.ap V0f) V1X))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Eclosed A_27a)) V0f)) V1X)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap V0f) V1X))) V1X)))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Edense A_27a)) V0f)) V1X)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)) (@ (@ tptp.ap V0f) V1X))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Eclosed A_27a)) V0f)) (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Eclosed A_27a)) V0f)) V1X)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) V1X)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Edense A_27a)) V0f)) (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f))) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Edense A_27a)) V0f)) V1X)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)) (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_2) _let_2)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (and (= _let_1 (@ (@ tptp.ap V0f) _let_1)) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (= V1X (@ (@ tptp.ap V0f) V1X)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) V1X))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f))) (let ((_let_2 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_2) _let_2)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (and (= _let_1 (@ (@ tptp.ap V0f) _let_1)) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (= V1X (@ (@ tptp.ap V0f) V1X)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)) (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (forall ((V1X $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap V0f) V1X))) V1X)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) V1X)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (forall ((V1X $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)))) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_1 (@ (@ tptp.ap V0f) V1X))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (forall ((V1X $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1X)) _let_1)))) V1X)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 _let_1)) V1X))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (forall ((V1X $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Egfp A_27a)) V0f))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)))) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_2 (@ (@ tptp.ap V0f) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) V1X)) _let_1)))) (@ tptp.p (@ _let_2 _let_1))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f1 $$unsorted)) (=> (@ (@ tptp.mem V0f1) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V1f2 $$unsorted)) (=> (@ (@ tptp.mem V1f2) (@ (@ tptp.arr A_27b) (@ (@ tptp.arr A_27a) tptp.bool))) (forall ((V2X $$unsorted)) (=> (@ (@ tptp.mem V2X) A_27b) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27a) A_27b)) V0f1)) V1f2)) V2X) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)) (@ (@ tptp.ap V0f1) V2X))) (@ (@ tptp.ap V1f2) V2X))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f1 $$unsorted)) (=> (@ (@ tptp.mem V0f1) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1f2 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27b)))) (=> (@ (@ tptp.mem V1f2) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr A_27b) tptp.bool))) (=> (and (@ tptp.p (@ _let_2 V0f1)) (@ tptp.p (@ _let_2 V1f2))) (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27b) _let_1)) V0f1)) V1f2)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2EfixedPoint_2Eempty A_27a) A_27b) (@ (@ tptp.lam A_27a) (lambda ((V0X $$unsorted)) (@ tptp.c_2Epred__set_2EEMPTY A_27b))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27b)) (@ (@ tptp.c_2EfixedPoint_2Eempty (@ (@ tptp.arr A_27a) tptp.bool)) A_27b)))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.c_2EfixedPoint_2Eempty A_27a) A_27b))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27b) A_27a)))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (and (= (@ (@ tptp.ap (@ _let_2 V0f)) _let_1) V0f) (= (@ (@ tptp.ap (@ _let_2 _let_1)) V0f) V0f)))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2h $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27b) A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0f)))) (=> (@ (@ tptp.mem V2h) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1g)) V2h)) (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1g))) V2h)))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1g $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27b) A_27a)))) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ _let_1 V0f)) V1g) (@ (@ tptp.ap (@ _let_1 V1g)) V0f))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V1g $$unsorted)) (=> (@ (@ tptp.mem V1g) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (forall ((V2X $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27b) A_27a)) V0f)) V1g)) V2X))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)))) (=> (@ (@ tptp.mem V2X) A_27a) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap V0f) V2X))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap V1g) V2X))) _let_1))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f1 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f1) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V1f2 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)))) (let ((_let_3 (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Efnsum A_27a) _let_1)) V0f1)) V1f2)))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (let ((_let_5 (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)))) (=> (@ (@ tptp.mem V1f2) (@ (@ tptp.arr _let_1) _let_1)) (=> (and (@ tptp.p (@ _let_5 V0f1)) (@ tptp.p (@ _let_5 V1f2))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 V0f1))) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_2 V1f2))) _let_3)))))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V1X $$unsorted)) (=> (@ (@ tptp.mem V1X) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2y)))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V1X)) _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap V0f) V1X)))) (@ tptp.p (@ _let_2 _let_1)))))))))))))
% 1.89/2.22 (assert (forall ((A_27a tptp.del) (V0f $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr _let_1) _let_1)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)))) (=> (@ (@ tptp.mem V1x) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2EfixedPoint_2Emonotone A_27a) A_27a)) V0f)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap V0f) (@ tptp.c_2Epred__set_2EEMPTY A_27a))))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2EfixedPoint_2Elfp A_27a)) V0f)))))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral__bit_2EBIT__MODF () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EBIT__MODF) (@ _let_1 (@ (@ tptp.arr (@ _let_1 (@ (@ tptp.arr tptp.bool) tptp.bool))) (@ _let_1 (@ _let_1 (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))))))
% 1.89/2.22 (declare-fun tptp.c_2Enumeral__bit_2EBIT__REV () $$unsorted)
% 1.89/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EBIT__REV) (@ _let_1 (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))
% 2.01/2.22 (declare-fun tptp.fo__c_2Enumeral__bit_2EBIT__REV (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 2.01/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum) (X2 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ (@ tptp.fo__c_2Enumeral__bit_2EBIT__REV X0) X1) X2)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1))) (@ tptp.inj__ty_2Enum_2Enum X2)))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2EFDUB () $$unsorted)
% 2.01/2.22 (assert (let ((_let_1 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EFDUB) (@ (@ tptp.arr _let_1) _let_1))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2ESFUNPOW () $$unsorted)
% 2.01/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ _let_1 tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral__bit_2ESFUNPOW) (@ (@ tptp.arr _let_2) (@ _let_1 _let_2))))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2EiBITWISE () $$unsorted)
% 2.01/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EiBITWISE) (@ _let_1 (@ (@ tptp.arr (@ _let_2 (@ _let_2 tptp.bool))) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum))))))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2EiDIV2 () $$unsorted)
% 2.01/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EiDIV2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 2.01/2.22 (declare-fun tptp.fo__c_2Enumeral__bit_2EiDIV2 (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 2.01/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral__bit_2EiDIV2 X0)) (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiDIV2) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2EiLOG2 () $$unsorted)
% 2.01/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EiLOG2) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 2.01/2.22 (declare-fun tptp.fo__c_2Enumeral__bit_2EiLOG2 (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 2.01/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral__bit_2EiLOG2 X0)) (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2EiMOD__2EXP () $$unsorted)
% 2.01/2.22 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EiMOD__2EXP) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 2.01/2.22 (declare-fun tptp.fo__c_2Enumeral__bit_2EiMOD__2EXP (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 2.01/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Enumeral__bit_2EiMOD__2EXP X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 2.01/2.22 (declare-fun tptp.c_2Enumeral__bit_2EiSUC () $$unsorted)
% 2.01/2.22 (assert (@ (@ tptp.mem tptp.c_2Enumeral__bit_2EiSUC) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))
% 2.01/2.22 (declare-fun tptp.fo__c_2Enumeral__bit_2EiSUC (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 2.01/2.22 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ tptp.fo__c_2Enumeral__bit_2EiSUC X0)) (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiSUC) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 2.01/2.22 (assert (= tptp.c_2Enumeral__bit_2EiMOD__2EXP tptp.c_2Ebit_2EMOD__2EXP))
% 2.01/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0n))) tptp.fo__c_2Earithmetic_2EZERO)) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2n $$unsorted)) (=> (@ (@ tptp.mem V2n) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP) (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) tptp.fo__c_2Earithmetic_2EZERO))) (forall ((V3x tptp.tp__ty_2Enum_2Enum) (V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V3x))))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_4)) (@ _let_2 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_1)))))))))) (forall ((V5x tptp.tp__ty_2Enum_2Enum) (V6n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V5x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_2)))) (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ _let_5 (@ _let_4 (@ _let_3 _let_2)))) _let_1)))))))))) (forall ((V7x tptp.tp__ty_2Enum_2Enum) (V8n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V8n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V7x))))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_5 _let_4)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_4)) (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))) (forall ((V9x tptp.tp__ty_2Enum_2Enum) (V10n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V10n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V9x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_4 (@ _let_3 (@ _let_5 _let_2)))) (@ _let_5 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) (@ (@ tptp.ap (@ _let_4 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2)))) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))))))
% 2.01/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP) _let_2)) (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiMOD__2EXP) _let_2)) _let_1))))))))))
% 2.01/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum) (V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Earithmetic_2EFUNPOW tptp.ty_2Enum_2Enum)) tptp.c_2Earithmetic_2EDIV2)) _let_2)) _let_1)))))))
% 2.01/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) tptp.fo__c_2Enum_2E0) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ _let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0n))))) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_2 _let_1)))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EBIT2))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EMOD) (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))))) (@ _let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) tptp.fo__c_2Enum_2E0))))))
% 2.01/2.22 (assert (forall ((V0i tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0i))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ _let_2 _let_1)))))))))
% 2.01/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y))) V1y)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3x tptp.tp__ty_2Enum_2Enum) (V4y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V4y))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_4))) _let_1)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_1)) _let_3))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_3)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ESBIT) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))))))
% 2.01/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV) _let_2)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))
% 2.01/2.22 (assert (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum) (V3e tptp.tp__ty_2Enum_2Enum) (V4y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0f)) (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.inj__ty_2Enum_2Enum V2b))) (@ tptp.inj__ty_2Enum_2Enum V3e))) (@ tptp.inj__ty_2Enum_2Enum V4y))) V4y)))) (forall ((V5n tptp.tp__ty_2Enum_2Enum) (V6f $$unsorted)) (=> (@ (@ tptp.mem V6f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V7x tptp.tp__ty_2Enum_2Enum) (V8b tptp.tp__ty_2Enum_2Enum) (V9e tptp.tp__ty_2Enum_2Enum) (V10y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V10y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V9e))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V7x))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V8b))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_8 (@ _let_7 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_6)))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum V5n))) (let ((_let_10 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_10 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_9))) V6f)) _let_4)) _let_5)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_10 _let_9)) V6f)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_4)) _let_8))) (@ (@ tptp.ap (@ _let_3 _let_5)) (@ _let_7 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_6))))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2A) _let_8)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V6f) _let_5)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_4)))) (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))) _let_1)))))))))))))))))))
% 2.01/2.22 (assert (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0m))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__MODIFY) _let_3)) V1f)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF) _let_3)) V1f)) _let_2)) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))))
% 2.01/2.22 (assert (= tptp.c_2Enumeral__bit_2EiBITWISE tptp.c_2Ebit_2EBITWISE))
% 2.01/2.22 (assert (and (forall ((V0opr $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V0opr) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1a tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0opr)) (@ tptp.inj__ty_2Enum_2Enum V1a))) (@ tptp.inj__ty_2Enum_2Enum V2b))) tptp.fo__c_2Earithmetic_2EZERO))))) (forall ((V3x tptp.tp__ty_2Enum_2Enum) (V4opr $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V4opr) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V5a tptp.tp__ty_2Enum_2Enum) (V6b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6b))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EDIV2))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V5a))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_6 (@ _let_5 (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum V3x))))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_6)) V4opr)) _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V7w $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V4opr) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V5a)))) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V6b))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) V7w))) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) V7w))))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_6)) (@ _let_5 (@ _let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) V4opr)) (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))))))))) (forall ((V8x tptp.tp__ty_2Enum_2Enum) (V9opr $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V9opr) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V10a tptp.tp__ty_2Enum_2Enum) (V11b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V11b))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EDIV2))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V10a))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V8x))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_6 (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_4)))) V9opr)) _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2ELET tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V12w $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V9opr) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V10a)))) (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V11b))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) V12w))) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) V12w))))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_4)))) V9opr)) (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))))))))))
% 2.01/2.22 (assert (forall ((A_27a tptp.del)) (and (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V1f) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V2a $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (=> (@ (@ tptp.mem V2a) A_27a) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_2)) V1f)) _let_1)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE) _let_2)) V1f)) _let_1)) _let_1))))))))))) (forall ((V3x tptp.tp__ty_2Enum_2Enum) (V4f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V4f) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V5a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V5a)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_4)) V4f)) _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE) _let_4)) V4f)) _let_3)) _let_1)))))))))))) (forall ((V6x tptp.tp__ty_2Enum_2Enum) (V7f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V7f) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V8b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V8b)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V6x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_4)) V7f)) _let_3)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE) _let_4)) V7f)) _let_3)) _let_2)))))))))))) (forall ((V9x tptp.tp__ty_2Enum_2Enum) (V10f $$unsorted)) (let ((_let_1 (@ tptp.arr tptp.bool))) (=> (@ (@ tptp.mem V10f) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V11a tptp.tp__ty_2Enum_2Enum) (V12b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V12b)))) (let ((_let_3 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V11a)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V9x))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBITWISE) _let_4)) V10f)) _let_3)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiBITWISE) _let_4)) V10f)) _let_3)) _let_2)))))))))))))))
% 2.01/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0x))) (@ tptp.inj__ty_2Enum_2Enum V1y))) V1y)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ _let_4 (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum V2n))))) (let ((_let_6 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 _let_5)) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_5)) (@ _let_4 (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) _let_2)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1))))))))))) (forall ((V4n tptp.tp__ty_2Enum_2Enum) (V5y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V5y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_3)))) _let_2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_3)))) _let_2)) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1)))))))))) (forall ((V6n tptp.tp__ty_2Enum_2Enum) (V7x tptp.tp__ty_2Enum_2Enum) (V8y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V8y))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V7x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ _let_4 _let_3))) (let ((_let_6 (@ _let_4 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V6n))))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_6)) _let_5)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_6)) (@ _let_4 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_5))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_3))) (@ _let_2 _let_1))) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1))))))))))))) (forall ((V9n tptp.tp__ty_2Enum_2Enum) (V10x tptp.tp__ty_2Enum_2Enum) (V11y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V11y))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V10x))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ _let_4 _let_3))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V9n))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_6)))) _let_5)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ _let_4 (@ _let_2 _let_6)))) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_5))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_3))) (@ _let_2 _let_1))) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1)))))))))))))))
% 2.01/2.22 (assert (and (forall ((V0m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0m)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE) _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV) _let_3)) _let_1)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2m tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_2 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V1n)))) (let ((_let_3 (@ _let_1 (@ tptp.inj__ty_2Enum_2Enum V2m)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__REVERSE) _let_3)) _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__REV) _let_3)) _let_2)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))))))))
% 2.01/2.22 (assert (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V1x tptp.tp__ty_2Enum_2Enum) (V2b tptp.tp__ty_2Enum_2Enum) (V3e tptp.tp__ty_2Enum_2Enum) (V4y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) V0f)) (@ tptp.inj__ty_2Enum_2Enum V1x))) (@ tptp.inj__ty_2Enum_2Enum V2b))) (@ tptp.inj__ty_2Enum_2Enum V3e))) (@ tptp.inj__ty_2Enum_2Enum V4y))) V4y)))) (forall ((V5n tptp.tp__ty_2Enum_2Enum) (V6f $$unsorted)) (=> (@ (@ tptp.mem V6f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V7b tptp.tp__ty_2Enum_2Enum) (V8e tptp.tp__ty_2Enum_2Enum) (V9y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V9y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V8e))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V7b))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_8 (@ _let_3 (@ _let_7 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_10 (@ _let_3 (@ _let_7 (@ tptp.inj__ty_2Enum_2Enum V5n))))) (let ((_let_11 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_11 _let_10)) V6f)) _let_9)) _let_6)) _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_11 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_10)) _let_8))) V6f)) _let_9)) (@ (@ tptp.ap (@ _let_5 _let_6)) _let_8))) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V6f) _let_6)) tptp.c_2Ebool_2EF))) (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) _let_1)))))))))))))))))) (forall ((V10n tptp.tp__ty_2Enum_2Enum) (V11f $$unsorted)) (=> (@ (@ tptp.mem V11f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V12b tptp.tp__ty_2Enum_2Enum) (V13e tptp.tp__ty_2Enum_2Enum) (V14y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V14y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V13e))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V12b))) (let ((_let_7 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_8 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum V10n))) (let ((_let_10 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_10 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_9)))) V11f)) _let_8)) _let_6)) _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_10 (@ _let_3 (@ _let_7 _let_9)))) V11f)) _let_8)) (@ (@ tptp.ap (@ _let_5 _let_6)) (@ _let_3 (@ _let_7 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V11f) _let_6)) tptp.c_2Ebool_2EF))) (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) _let_1))))))))))))))))) (forall ((V15n tptp.tp__ty_2Enum_2Enum) (V16f $$unsorted)) (=> (@ (@ tptp.mem V16f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V17x tptp.tp__ty_2Enum_2Enum) (V18b tptp.tp__ty_2Enum_2Enum) (V19e tptp.tp__ty_2Enum_2Enum) (V20y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V20y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V19e))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V17x))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum V18b))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_9 (@ _let_3 (@ _let_8 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (let ((_let_10 (@ _let_3 _let_6))) (let ((_let_11 (@ _let_3 (@ _let_8 (@ tptp.inj__ty_2Enum_2Enum V15n))))) (let ((_let_12 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_12 _let_11)) V16f)) _let_10)) _let_7)) _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_12 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_11)) _let_9))) V16f)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_10))) (@ (@ tptp.ap (@ _let_5 _let_7)) _let_9))) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V16f) _let_7)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_6)))) (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) _let_1))))))))))))))))))) (forall ((V21n tptp.tp__ty_2Enum_2Enum) (V22f $$unsorted)) (=> (@ (@ tptp.mem V22f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V23x tptp.tp__ty_2Enum_2Enum) (V24b tptp.tp__ty_2Enum_2Enum) (V25e tptp.tp__ty_2Enum_2Enum) (V26y tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V26y))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V25e))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ _let_3 _let_2))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2E_2B))) (let ((_let_6 (@ tptp.inj__ty_2Enum_2Enum V23x))) (let ((_let_7 (@ tptp.inj__ty_2Enum_2Enum V24b))) (let ((_let_8 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (let ((_let_9 (@ _let_3 _let_6))) (let ((_let_10 (@ tptp.inj__ty_2Enum_2Enum V21n))) (let ((_let_11 (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_11 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_10)))) V22f)) _let_9)) _let_7)) _let_4)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_11 (@ _let_3 (@ _let_8 _let_10)))) V22f)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_9))) (@ (@ tptp.ap (@ _let_5 _let_7)) (@ _let_3 (@ _let_8 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ _let_3 (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap V22f) _let_7)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_6)))) (@ (@ tptp.ap (@ _let_5 _let_4)) _let_1))) _let_1))))))))))))))))))))
% 2.01/2.22 (assert (and (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1f $$unsorted)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V0m)))) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__MODIFY) _let_3)) V1f)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF) _let_3)) V1f)) _let_1)) _let_1)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1)))))))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3f $$unsorted)) (=> (@ (@ tptp.mem V3f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.arr tptp.bool) tptp.bool))) (forall ((V4n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V4n)))) (let ((_let_4 (@ _let_2 (@ tptp.inj__ty_2Enum_2Enum V2m)))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EBIT__MODIFY) _let_4)) V3f)) _let_3)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EBIT__MODF) _let_4)) V3f)) _let_3)) _let_1)) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) _let_1))))))))))))
% 2.01/2.22 (assert (= tptp.c_2Enumeral__bit_2EiSUC tptp.c_2Enum_2ESUC))
% 2.01/2.22 (assert (= tptp.c_2Enumeral__bit_2EiDIV2 tptp.c_2Earithmetic_2EDIV2))
% 2.01/2.22 (assert (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) V0f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V1x))) V1x)))) (forall ((V2f $$unsorted)) (=> (@ (@ tptp.mem V2f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) V2f)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_1)) _let_4))) _let_4)) (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap V2f) _let_1))))))))))))))
% 2.01/2.22 (assert (and (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) V0f)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (forall ((V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ tptp.inj__ty_2Enum_2Enum V2n)))) (let ((_let_2 (@ tptp.ap V1f))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) V1f)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_2 _let_1)))))))))))
% 2.01/2.22 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ETIMES__2EXP) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2ETIMES__2EXP) _let_2)) (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) tptp.c_2Enumeral_2EiDUB)) _let_2)) _let_1))))))))))
% 2.01/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_3 (@ tptp.ap tptp.c_2Enumeral__bit_2EiSUC))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ tptp.surj__ty_2Enum_2Enum _let_4))) (let ((_let_6 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral__bit_2EiDIV2))) (let ((_let_8 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))) (let ((_let_9 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_9)) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 (@ _let_3 _let_9))) tptp.fo__c_2Earithmetic_2EZERO) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_8)) V0n) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 (@ _let_3 _let_8))) _let_5) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 _let_6)) _let_5) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_7 (@ _let_3 _let_6))) _let_5) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_4)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_1))))))))))))))))
% 2.01/2.22 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) (@ tptp.inj__ty_2Enum_2Enum V0n))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EDIV__2EXP) _let_2)) (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) tptp.c_2Enumeral__bit_2EiDIV2)) _let_2)) _let_1))))))))))
% 2.01/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) tptp.c_2Enumeral__bit_2EiDIV2)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0x))) V0x)) (forall ((V1y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) tptp.c_2Enumeral__bit_2EiDIV2)) (@ tptp.inj__ty_2Enum_2Enum V1y))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 tptp.c_2Enumeral__bit_2EiDIV2)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) tptp.c_2Enumeral__bit_2EiDIV2))) (@ _let_3 _let_2))) (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiDIV2) _let_1))))))))) (forall ((V4n tptp.tp__ty_2Enum_2Enum) (V5x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V5x))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EiDIV2))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 tptp.c_2Enumeral__bit_2EiDIV2)) (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_3)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) tptp.c_2Enumeral__bit_2EiDIV2))) (@ _let_4 _let_3))) (@ _let_2 (@ _let_2 _let_1)))))))))))))
% 2.01/2.22 (assert (and (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) tptp.c_2Enumeral_2EiDUB)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0x))) V0x)) (forall ((V1y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) tptp.c_2Enumeral_2EiDUB)) (@ tptp.inj__ty_2Enum_2Enum V1y))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V3x))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 tptp.c_2Enumeral_2EiDUB)) (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_2)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) tptp.c_2Enumeral_2EiDUB))) (@ _let_3 _let_2))) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1))))))))) (forall ((V4n tptp.tp__ty_2Enum_2Enum) (V5x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V5x))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V4n))) (let ((_let_4 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_5 (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 tptp.c_2Enumeral_2EiDUB)) (@ _let_4 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_3)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) tptp.c_2Enumeral_2EiDUB))) (@ _let_4 _let_3))) (@ _let_2 (@ _let_2 _let_1)))))))))))))
% 2.01/2.22 (assert (forall ((V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (and (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) V0f))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V1x))) V1x)) (forall ((V2y tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW) (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) V0f))) (@ tptp.inj__ty_2Enum_2Enum V2y))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) tptp.fo__c_2Enum_2E0)) (forall ((V3n tptp.tp__ty_2Enum_2Enum) (V4x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4x))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB))) (let ((_let_3 (@ _let_2 V0f))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_5 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_6 (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 _let_3)) (@ _let_5 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_4)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ _let_2 _let_3))) (@ _let_5 _let_4))) (@ (@ tptp.ap _let_3) _let_1))))))))))) (forall ((V5n tptp.tp__ty_2Enum_2Enum) (V6x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6x))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB))) (let ((_let_3 (@ _let_2 V0f))) (let ((_let_4 (@ tptp.ap _let_3))) (let ((_let_5 (@ tptp.inj__ty_2Enum_2Enum V5n))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_7 (@ tptp.ap tptp.c_2Enumeral__bit_2ESFUNPOW))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 _let_3)) (@ _let_6 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_5)))) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_7 (@ _let_2 _let_3))) (@ _let_6 _let_5))) (@ _let_4 (@ _let_4 _let_1)))))))))))))))))
% 2.01/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EiDIV2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) tptp.c_2Enumeral__bit_2EiDIV2)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_2 _let_1))))))))
% 2.01/2.22 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral_2EiDUB))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB) tptp.c_2Enumeral_2EiDUB)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_2 _let_1))))))))
% 2.01/2.22 (assert (forall ((V0f $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB))) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)) (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_1 (@ _let_1 V0f))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) tptp.fo__c_2Earithmetic_2EZERO) (forall ((V1x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiSUC) (@ tptp.inj__ty_2Enum_2Enum V1x)))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB))) (let ((_let_3 (@ _let_2 V0f))) (let ((_let_4 (@ tptp.ap _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_4 _let_1))))))))) (forall ((V2x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V2x)))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB))) (let ((_let_3 (@ _let_2 V0f))) (let ((_let_4 (@ tptp.ap _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_4 _let_1))))))))) (forall ((V3x tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum V3x)))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EFDUB))) (let ((_let_3 (@ _let_2 V0f))) (let ((_let_4 (@ tptp.ap _let_3))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ _let_2 _let_3)) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_4 _let_1))))))))))))))
% 2.01/2.22 (assert (forall ((V0base_20_3C_202_20or_20n_20_3D_200 $$unsorted)) (=> (@ (@ tptp.mem V0base_20_3C_202_20or_20n_20_3D_200) tptp.bool) (forall ((V1m tptp.tp__ty_2Enum_2Enum) (V2n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Elogroot_2ELOG) _let_1)))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_5 (@ tptp.ap tptp.c_2Eprim__rec_2E_3C))) (let ((_let_6 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)))) (let ((_let_7 (@ tptp.arr tptp.ty_2Enum_2Enum))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_3 _let_2)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ (@ tptp.ap (@ _let_5 _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.ty_2Enum_2Enum)) _let_2)) _let_4)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Ecombin_2EFAIL (@ _let_7 (@ _let_7 tptp.ty_2Enum_2Enum))) tptp.bool)) tptp.c_2Elogroot_2ELOG)) V0base_20_3C_202_20or_20n_20_3D_200)) _let_1)) _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_6 (@ (@ tptp.ap (@ _let_5 _let_2)) _let_1))) _let_4)) (@ (@ tptp.ap tptp.c_2Enum_2ESUC) (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV) _let_2)) _let_1))))))))))))))))))
% 2.01/2.22 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2) _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_1)) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))))))))
% 2.01/2.22 (assert (and (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))) tptp.fo__c_2Enum_2E0) (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2EBIT1))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_3 _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ _let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ _let_2 _let_1)))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ _let_2 _let_1)))))))))
% 2.01/2.22 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2) (@ (@ tptp.ap tptp.c_2Enumeral_2EiDUB) _let_1)))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOG2) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Enumeral__bit_2EiLOG2) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) _let_1))))))))
% 2.01/2.23 (assert (and (forall ((V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__EQ) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0a))) (@ tptp.inj__ty_2Enum_2Enum V1b))) true)) (forall ((V2n tptp.tp__ty_2Enum_2Enum) (V3a tptp.tp__ty_2Enum_2Enum) (V4b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V4b))) (let ((_let_2 (@ tptp.ap tptp.c_2Earithmetic_2EDIV2))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V3a))) (let ((_let_4 (@ tptp.inj__ty_2Enum_2Enum V2n))) (let ((_let_5 (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__EQ))) (let ((_let_6 (@ tptp.ap tptp.c_2Earithmetic_2EODD))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_4))) _let_3)) _let_1)) (and (= (@ tptp.p (@ _let_6 _let_3)) (@ tptp.p (@ _let_6 _let_1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_5 _let_4)) (@ _let_2 _let_3))) (@ _let_2 _let_1)))))))))))) (forall ((V5n tptp.tp__ty_2Enum_2Enum) (V6a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V6a))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__EQ) (@ tptp.inj__ty_2Enum_2Enum V5n))) _let_1)) _let_1)) true)))))
% 2.01/2.23 (assert (and (forall ((V0a tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__MAX) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ tptp.inj__ty_2Enum_2Enum V0a))) true)) (forall ((V1n tptp.tp__ty_2Enum_2Enum) (V2a tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2a))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_3 (@ tptp.ap tptp.c_2Ebit_2EMOD__2EXP__MAX))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap tptp.c_2Enum_2ESUC) _let_2))) _let_1)) (and (@ tptp.p (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_2)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_1)))))))))))
% 2.01/2.23 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Ebit_2ELOWEST__SET__BIT))) (=> (not (= V0n tptp.fo__c_2Enum_2E0)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 _let_1)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap tptp.c_2Earithmetic_2EODD) _let_1))) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Earithmetic_2EZERO))))) (@ _let_2 (@ (@ tptp.ap tptp.c_2Earithmetic_2EDIV2) _let_1)))))))))))
% 2.01/2.23 (assert (and (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (let ((_let_2 (@ tptp.ap tptp.c_2Enum_2ESUC))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL))) (let ((_let_4 (@ tptp.ap tptp.c_2Ebit_2ELOWEST__SET__BIT))) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_4 (@ _let_3 (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT2) _let_1)))) (@ tptp.surj__ty_2Enum_2Enum (@ _let_2 (@ _let_4 (@ _let_3 (@ _let_2 _let_1))))))))))) (forall ((V1n tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Ebit_2ELOWEST__SET__BIT) (@ (@ tptp.ap tptp.c_2Earithmetic_2ENUMERAL) (@ (@ tptp.ap tptp.c_2Earithmetic_2EBIT1) (@ tptp.inj__ty_2Enum_2Enum V1n))))) tptp.fo__c_2Enum_2E0))))
% 2.01/2.23 (declare-fun tptp.c_2Egcdset_2Egcdset () $$unsorted)
% 2.01/2.23 (assert (@ (@ tptp.mem tptp.c_2Egcdset_2Egcdset) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) tptp.ty_2Enum_2Enum)))
% 2.01/2.23 (assert (forall ((V0s $$unsorted)) (let ((_let_1 (@ tptp.lam tptp.ty_2Enum_2Enum))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC tptp.ty_2Enum_2Enum) tptp.ty_2Enum_2Enum)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))) (let ((_let_4 (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) (let ((_let_5 (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool))) (let ((_let_6 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D _let_5)) V0s)))) (=> (@ (@ tptp.mem V0s) _let_5) (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Egcdset_2Egcdset) V0s)) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND tptp.ty_2Enum_2Enum)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ _let_6 _let_4))) (@ _let_6 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_3)) _let_4))))) _let_3)) (@ (@ tptp.ap tptp.c_2Epred__set_2EMAX__SET) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER tptp.ty_2Enum_2Enum)) (@ _let_2 (@ _let_1 (lambda ((V1n $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.bool)) V1n)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) V1n)) (@ (@ tptp.ap tptp.c_2Epred__set_2EMIN__SET) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDELETE tptp.ty_2Enum_2Enum)) V0s)) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))))))) (@ _let_2 (@ _let_1 (lambda ((V2d $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Enum_2Enum) tptp.bool)) V2d)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.ty_2Enum_2Enum)) (@ (@ tptp.lam tptp.ty_2Enum_2Enum) (lambda ((V3e $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) V3e)) V0s))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) V2d)) V3e)))))))))))))))))))))))
% 2.01/2.23 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1e tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1e))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ (@ tptp.ap tptp.c_2Egcdset_2Egcdset) V0s))) _let_1))))))))
% 2.01/2.23 (assert (forall ((V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (forall ((V1g tptp.tp__ty_2Enum_2Enum)) (=> (forall ((V2e tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2e))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Enum_2Enum)) _let_1)) V0s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V1g))) _let_1))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Edivides_2Edivides) (@ tptp.inj__ty_2Enum_2Enum V1g))) (@ (@ tptp.ap tptp.c_2Egcdset_2Egcdset) V0s))))))))
% 2.01/2.23 (assert (= (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap tptp.c_2Egcdset_2Egcdset) (@ tptp.c_2Epred__set_2EEMPTY tptp.ty_2Enum_2Enum))) tptp.fo__c_2Enum_2E0))
% 2.01/2.23 (assert (forall ((V0x tptp.tp__ty_2Enum_2Enum) (V1s $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Egcdset_2Egcdset))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0x))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.bool)) (= (@ tptp.surj__ty_2Enum_2Enum (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINSERT tptp.ty_2Enum_2Enum)) _let_2)) V1s))) (@ tptp.surj__ty_2Enum_2Enum (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Egcd_2Egcd) _let_2)) (@ _let_1 V1s)))))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2ERREFL__EXP (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (let ((_let_3 (@ _let_1 _let_2))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2ERREFL__EXP A_27a)) (@ (@ tptp.arr _let_3) (@ (@ tptp.arr _let_2) _let_3))))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2ERRUNIV (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2ERRUNIV A_27a)) (@ (@ tptp.arr _let_2) (@ _let_1 _let_2)))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eacyclic (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eacyclic A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) tptp.bool))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eall__choices (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eall__choices A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eantisym (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eantisym A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) tptp.bool))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Echain (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Echain A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Edomain (tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Efchains (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Efchains A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Efinite__prefixes (tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eget__min (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eget__min A_27a)) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod (@ (@ tptp.arr A_27a) tptp.bool)) _let_1)) (@ tptp.ty_2Eoption_2Eoption A_27a)))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eirreflexive (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eirreflexive A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Elinear__order (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Elinear__order A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Emaximal__elements (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Emaximal__elements A_27a)) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) _let_1))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eminimal__elements (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eminimal__elements A_27a)) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) _let_1))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Enth__min (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Enth__min A_27a)) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod (@ (@ tptp.arr A_27a) tptp.bool)) _let_1)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ tptp.ty_2Eoption_2Eoption A_27a))))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Enum__order (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Enum__order A_27a)) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Enum_2Enum)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Epartial__order (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Epartial__order A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eper (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eper A_27a)) (@ _let_1 (@ (@ tptp.arr (@ _let_1 tptp.bool)) tptp.bool))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eper__restrict (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (let ((_let_2 (@ _let_1 tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Eper__restrict A_27a)) (@ (@ tptp.arr _let_2) (@ _let_1 _let_2)))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Erange (tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) tptp.bool)) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Ercomp (tptp.del tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.ty_2Epair_2Eprod A_27a))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Eset__relation_2Ercomp A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr (@ _let_1 A_27c)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27c) A_27b)) tptp.bool)) (@ (@ tptp.arr (@ _let_1 A_27b)) tptp.bool)))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Ereflexive (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Ereflexive A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Erel__to__reln (tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eset__relation_2Erel__to__reln A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Ereln__to__rel (tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eset__relation_2Ereln__to__rel A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Errestrict (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Errestrict A_27a)) (@ (@ tptp.arr _let_1) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) _let_1))))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Estrict (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Estrict A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Estrict__linear__order (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Estrict__linear__order A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Etc (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Etc A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Etransitive (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Etransitive A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) tptp.bool))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Euniv__reln (tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Eset__relation_2Euniv__reln A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)))))
% 2.01/2.23 (declare-fun tptp.c_2Eset__relation_2Eupper__bounds (tptp.del tptp.del) $$unsorted)
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Eset__relation_2Eupper__bounds A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) tptp.bool)) (@ (@ tptp.arr A_27a) tptp.bool))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1t $$unsorted)) (=> (@ (@ tptp.mem V1t) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (= (= V0s V1t) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2x)) V3y))))) (=> (@ (@ tptp.mem V3y) A_27b) (= (@ tptp.p (@ _let_1 V0s)) (@ tptp.p (@ _let_1 V1t))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27b)) V0r) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1x)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))) V0r))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27b)) V0r) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) tptp.bool)) V1y)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27a)) V2x)) V1y))) V0r))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27b)) V1r))) (exists ((V2y $$unsorted)) (and (@ (@ tptp.mem V2y) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V2y))) V1r))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0y $$unsorted)) (=> (@ (@ tptp.mem V0y) A_27a) (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0y)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27b)) V1r))) (exists ((V2x $$unsorted)) (and (@ (@ tptp.mem V2x) A_27b) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27a)) V2x)) V0y))) V1r))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (forall ((V2r $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V2r) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V0x)) V1y))) V2r)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V0x)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27b)) V2r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V1y)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27b) A_27a)) V2r)))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1r_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27b)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V1r_27) (@ (@ tptp.arr _let_2) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_2)) V0r)) V1r_27)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ _let_1 V0r))) (@ _let_1 V1r_27)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1r_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27b) A_27a)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V1r_27) (@ (@ tptp.arr _let_2) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_2)) V0r)) V1r_27)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ _let_1 V0r))) (@ _let_1 V1r_27)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V1s) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27a) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (let ((_let_2 (@ tptp.ap tptp.c_2Ebool_2E_2F_5C))) (let ((_let_3 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) (let ((_let_4 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_4) tptp.bool)) _let_3)) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_4)) _let_3)) V0r))) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2x)) V1s))) (@ (@ tptp.ap (@ _let_1 V3y)) V1s)))))))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (forall ((V2r $$unsorted)) (=> (@ (@ tptp.mem V2r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V3s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V0x)) V1y))))) (=> (@ (@ tptp.mem V3s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V2r)) V3s))) (and (@ tptp.p (@ _let_2 V2r)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0x)) V3s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1y)) V3s)))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) V0x)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V1r)) V2s))) (and (@ tptp.p (@ _let_2 V1r)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27a)) V0x))) V2s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27a)) V0x))) V2s)))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V1s))) V0r)))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1r2 $$unsorted)) (=> (@ (@ tptp.mem V1r2) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_2 V0r1)) V1r2))) V2s) (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V0r1)) V2s))) (@ (@ tptp.ap (@ _let_1 V1r2)) V2s))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0r)))) (=> (@ (@ tptp.mem V2y) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ _let_1 (@ _let_2 V1x))) V2y) (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27a)) V1x)) V2y))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V1s)))) V1s)))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V1s)))) V1s)))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27c)) tptp.bool)) (forall ((V1r2 $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V1r2) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27c) A_27b)) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eset__relation_2Ercomp A_27a) A_27b) A_27c)) V0r1)) V1r2) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V2x)) V3y))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27c)) (@ (@ tptp.lam A_27c) (lambda ((V4z $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27c))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27c)) V2x)) V4z))) V0r1))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27c) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27c) A_27b)) V4z)) V3y))) V1r2)))))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr _let_1) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Estrict A_27a)) V0r) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27a) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C _let_2) tptp.bool)) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_2)) _let_1)) V0r))) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V2y)))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Estrict A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ _let_1 (@ (@ tptp.ap (@ _let_2 V0r)) V1s)) (@ (@ tptp.ap (@ _let_2 (@ _let_1 V0r))) V1s)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0xs $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V0xs) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Euniv__reln A_27a)) V0xs) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27a) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V1x1 $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2x2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x1)) V2x2))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ _let_1 V1x1)) V0xs))) (@ (@ tptp.ap (@ _let_1 V2x2)) V0xs)))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)) V0r)) V1s)) (forall ((V2e $$unsorted)) (=> (@ (@ tptp.mem V2e) A_27b) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27b)) V2e)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EFINITE A_27a)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3e_27 $$unsorted)) (let ((_let_1 (@ tptp.c_2Epair_2E_2C A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 tptp.bool)) V3e_27)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V3e_27)) V2e))) V0r)))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2s_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)) V0r)))) (=> (@ (@ tptp.mem V2s_27) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) V2s_27)) V1s))) (@ tptp.p (@ _let_1 V2s_27)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1r_27 $$unsorted)) (=> (@ (@ tptp.mem V1r_27) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0r)) V2s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) V1r_27)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1r_27)) V2s)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2r_27 $$unsorted)) (=> (@ (@ tptp.mem V2r_27) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V3s_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)))) (=> (@ (@ tptp.mem V3s_27) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0r)) V1s)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) V2r_27)) V0r)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) V3s_27)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2r_27)) V3s_27)))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V0r)))) (=> (@ (@ tptp.mem V2s_27) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ _let_2 V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2s_27)) V1s))) (and (@ tptp.p (@ _let_2 V2s_27)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V2s_27))) V2s_27)))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1r2 $$unsorted)) (=> (@ (@ tptp.mem V1r2) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V2s1 $$unsorted)) (=> (@ (@ tptp.mem V2s1) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V3s2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)))) (=> (@ (@ tptp.mem V3s2) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0r1)) V2s1)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1r2)) V3s2))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) V0r1)) V1r2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EINTER A_27b)) V2s1)) V3s2))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1r2 $$unsorted)) (=> (@ (@ tptp.mem V1r2) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c)) tptp.bool)) (forall ((V2s1 $$unsorted)) (=> (@ (@ tptp.mem V2s1) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V3s2 $$unsorted)) (let ((_let_1 (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a))) (=> (@ (@ tptp.mem V3s2) (@ (@ tptp.arr A_27c) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27b)) V0r1)) V2s1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27b) A_27c)) V1r2)) V3s2)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC A_27b) A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) tptp.bool)) V4x)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27c)) (@ (@ tptp.lam A_27c) (lambda ((V5y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27c)) V5y)) V3s2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27c))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27c)) V4x)) V5y))) V1r2))))))))))) V2s1))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 A_27c)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ (@ tptp.c_2Eset__relation_2Ercomp A_27a) A_27c) A_27b)) V0r1)) V1r2))) V3s2)))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$unsorted)) (=> (@ (@ tptp.mem V0f) (@ (@ tptp.arr A_27a) A_27b)) (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V2s $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27b))) (=> (@ (@ tptp.mem V2s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (= (@ _let_1 V3x) (@ _let_1 V4y)) (= V3x V4y))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27a)) V1r)) V2s))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27b) A_27b)) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27a) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V5x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V6y $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27b) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27b) A_27b)) (@ _let_1 V5x))) (@ _let_1 V6y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V5x)) V6y))) V1r))))))))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE A_27a) A_27b)) V0f)) V2s))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27b) tptp.bool)) (forall ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Efinite__prefixes A_27a) A_27b)) V0r)))) (=> (@ (@ tptp.mem V2t) (@ (@ tptp.arr A_27b) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27b)) V2t)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27b) A_27a)) V0r)))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27b)) V1s)) V2t))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Eset__relation_2Etc A_27a) (@ (@ tptp.lam (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (lambda ((V0r $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) (lambda ((V1a0 $$unsorted)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V2tc_27 $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V3a0 $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) (@ _let_2 (@ _let_1 (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V5y $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V4x)) V5y))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) V3a0)) _let_1))) (@ (@ tptp.ap V0r) _let_1))))))))))) (@ _let_2 (@ _let_1 (lambda ((V6x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V7y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) V3a0)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V6x)) V7y)))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V8z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap V2tc_27))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_2 (@ (@ tptp.ap (@ _let_1 V6x)) V8z)))) (@ _let_2 (@ (@ tptp.ap (@ _let_1 V8z)) V7y)))))))))))))))))) (@ (@ tptp.ap V2tc_27) V3a0))))))))) (@ (@ tptp.ap V2tc_27) V1a0))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (and (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ _let_1 V0r)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))))))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (=> (exists ((V5z $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V5z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_2 V3x)) V5z))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_2 V5z)) V4y))) _let_1))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V3x)) V4y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (or (@ tptp.p (@ _let_1 V0r)) (exists ((V3z $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V3z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_2 V1x)) V3z))) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_2 V3z)) V2y))) _let_1)))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (exists ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V1tc_27))) (and (@ (@ tptp.mem V6z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4x)) V6z)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V6z)) V5y))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V5y)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V7x)) V8y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V7x)) V8y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)))) (let ((_let_2 (@ _let_1 V1s))) (let ((_let_3 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_3)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_3) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_4 V0r)) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ _let_1 V0r))) _let_2))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr _let_1) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_1)) V0r)) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r)))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)))) (let ((_let_2 (@ _let_1 V0r))) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (= (@ _let_1 _let_2) _let_2))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_2)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_2) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ _let_3 V0r)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_1 V0r))) (@ _let_1 V1s))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (exists ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap V1tc_27))) (let ((_let_2 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V6z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_3 V4x)) V6z))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V4x)) V6z)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ _let_3 V6z)) V5y))) _let_2)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V6z)) V5y)))))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V5y)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V7x)) V8y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V7x)) V8y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (or (@ tptp.p (@ _let_1 V0r)) (exists ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V3z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1x)) V3z))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V3z)) V2y))) V0r))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))))) (=> (@ (@ tptp.mem V2y) A_27a) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (or (@ tptp.p (@ _let_1 V0r)) (exists ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V3z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1x)) V3z))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V3z)) V2y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r)))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (exists ((V6z $$unsorted)) (and (@ (@ tptp.mem V6z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V4x)) V6z))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V6z)) V5y)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V5y)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V7x)) V8y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V7x)) V8y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (exists ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V6z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V4x)) V6z))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V6z)) V5y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V6z)) V5y)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V5y)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V7x)) V8y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V7x)) V8y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (exists ((V6z $$unsorted)) (and (@ (@ tptp.mem V6z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V6z)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V6z)) V5y))) V0r)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V5y)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V7x)) V8y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V7x)) V8y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)))) (=> (@ (@ tptp.mem V2x) A_27a) (=> (or (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) V0r))) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) V0r)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V2x)))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (=> (exists ((V5z $$unsorted)) (and (@ (@ tptp.mem V5z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V3x)) V5z)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V5z)) V4y))) V0r)))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V3x)) V4y)))))))) (forall ((V6x $$unsorted)) (=> (@ (@ tptp.mem V6x) A_27a) (forall ((V7y $$unsorted)) (=> (@ (@ tptp.mem V7y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V6x)) V7y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V6x)) V7y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1tc_27 $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V1tc_27) (@ _let_1 (@ _let_1 tptp.bool))) (=> (and (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V2x)) V3y))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (=> (@ (@ tptp.mem V5y) A_27a) (=> (exists ((V6z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (and (@ (@ tptp.mem V6z) A_27a) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V4x)) V6z))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V6z)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V6z)) V5y))) V0r)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V4x)) V5y)))))))) (forall ((V7x $$unsorted)) (=> (@ (@ tptp.mem V7x) A_27a) (forall ((V8y $$unsorted)) (=> (@ (@ tptp.mem V8y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V7x)) V8y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1tc_27) V7x)) V8y))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r1))) (forall ((V3r2 $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V3r2) (@ (@ tptp.arr _let_1) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_1)) V0r1)) V3r2)))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1r2 $$unsorted)) (=> (@ (@ tptp.mem V1r2) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (=> (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (@ tptp.p (@ _let_1 V0r1)) (@ tptp.p (@ _let_1 V1r2)))))))) (forall ((V4x $$unsorted)) (=> (@ (@ tptp.mem V4x) A_27a) (forall ((V5y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V4x)) V5y))))) (=> (@ (@ tptp.mem V5y) A_27a) (=> (@ tptp.p (@ _let_2 (@ _let_1 V0r1))) (@ tptp.p (@ _let_2 (@ _let_1 V1r2))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V1y) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V0x)) V1y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) (@ tptp.c_2Epred__set_2EEMPTY _let_1)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.c_2Epred__set_2EEMPTY (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)))) (= (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) _let_1) _let_1))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V2y))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V1x)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) V0r))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2y)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) V0r)))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2e $$unsorted)) (=> (@ (@ tptp.mem V2e) A_27a) (forall ((V3e_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2e)) V3e_27))))) (=> (@ (@ tptp.mem V3e_27) A_27a) (=> (@ tptp.p (@ _let_2 (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V1x)))) (@ tptp.p (@ _let_2 (@ _let_1 V0r)))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_2) _let_2)) (@ (@ tptp.c_2Epair_2ESWAP A_27a) A_27a))))) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ _let_1 (@ _let_3 V0r)) (@ _let_3 (@ _let_1 V0r)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)) V0r)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V1x))) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r1 $$unsorted)) (=> (@ (@ tptp.mem V0r1) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1r2 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V1r2) (@ (@ tptp.arr _let_2) tptp.bool)) (=> (and (@ tptp.p (@ _let_1 V0r1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_2)) V1r2)) V0r1))) (@ tptp.p (@ _let_1 V1r2))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ _let_1 V0r)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V1s))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)) V0r)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V1x)) V1x))) V0r)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr _let_2) tptp.bool)) (= (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EIMAGE _let_2) _let_2)) (@ (@ tptp.c_2Epair_2ESWAP A_27a) A_27a))) V0r))) (@ tptp.p (@ _let_1 V0r))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0rs $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V0rs) (@ (@ tptp.arr (@ (@ tptp.arr _let_1) tptp.bool)) tptp.bool)) (=> (and (forall ((V1r $$unsorted)) (=> (@ (@ tptp.mem V1r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V2r_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (let ((_let_4 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (let ((_let_5 (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_4)))) (=> (@ (@ tptp.mem V2r_27) _let_4) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 V1r)) V0rs)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 V2r_27)) V0rs)) (not (= V1r V2r_27))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ (@ tptp.ap (@ _let_3 (@ _let_2 V1r))) (@ _let_1 V1r)))) (@ (@ tptp.ap (@ _let_3 (@ _let_2 V2r_27))) (@ _let_1 V2r_27)))))))))))))) (forall ((V3r $$unsorted)) (let ((_let_1 (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool))) (=> (@ (@ tptp.mem V3r) _let_1) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN _let_1)) V3r)) V0rs)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)) V3r))))))) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)) (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EBIGUNION _let_1)) V0rs))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1r_27 $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)))) (let ((_let_4 (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)))) (let ((_let_5 (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION A_27a)))) (=> (@ (@ tptp.mem V1r_27) (@ (@ tptp.arr _let_1) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EDISJOINT A_27a)) (@ (@ tptp.ap (@ _let_5 (@ _let_4 V0r))) (@ _let_3 V0r)))) (@ (@ tptp.ap (@ _let_5 (@ _let_4 V1r_27))) (@ _let_3 V1r_27)))) (@ tptp.p (@ _let_2 V0r)) (@ tptp.p (@ _let_2 V1r_27))) (@ tptp.p (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EUNION _let_1)) V0r)) V1r_27))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Ereflexive A_27a)) V0r)) V1s)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V2x))) V0r)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eirreflexive A_27a)) V0r)) V1s)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V2x))) V0r))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) V0r)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27a) (forall ((V3z $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ _let_1 V1x)))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (=> (@ (@ tptp.mem V3z) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_2 V2y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ (@ tptp.ap (@ _let_1 V2y)) V3z))) V0r))) (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_2 V3z))) V0r))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) V0r)) (= (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r) V0r)))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etc A_27a)) V0r))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eantisym A_27a)) V0r)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (=> (@ (@ tptp.mem V2y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V1x)) V2y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2y)) V1x))) V0r))) (= V1x V2y))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Epartial__order A_27a)) V0r)) V1s)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) V0r))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) V0r))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Ereflexive A_27a)) V0r)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eantisym A_27a)) V0r))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Eantisym A_27a)))) (let ((_let_2 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr _let_2) tptp.bool)) (=> (@ tptp.p (@ _let_1 V0t)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET _let_2)) V1s)) V0t)) (@ tptp.p (@ _let_1 V1s)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Epartial__order A_27a)) V0r)) V1s))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V1s))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Epartial__order A_27a)))) (=> (@ (@ tptp.mem V2s_27) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0r)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2s_27)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V2s_27))) V2s_27)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Estrict A_27a)) V0r))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Epartial__order A_27a)) V0r)) V1s)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) _let_1))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) _let_1))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eantisym A_27a)) _let_1)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Epartial__order A_27a)) V0r)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eacyclic A_27a)) (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Estrict A_27a)) V0r)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Elinear__order A_27a)) V0r)) V1s)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) V0r))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) V0r))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) V0r)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Eantisym A_27a)) V0r)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V3y)) V1s))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V3y)) V2x))) V0r)))))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2s_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Eset__relation_2Elinear__order A_27a)))) (=> (@ (@ tptp.mem V2s_27) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V0r)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)) V2s_27)) V1s))) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Errestrict A_27a)) V0r)) V2s_27))) V2s_27)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Elinear__order A_27a)) V0r)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Epartial__order A_27a)) V0r)) V1s))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Epred__set_2ESUBSET A_27a)))) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Estrict__linear__order A_27a)) V0r)) V1s)) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Edomain A_27a) A_27a)) V0r))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erange A_27a) A_27a)) V0r))) V1s)) (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Etransitive A_27a)) V0r)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V2x))) V0r))))) (forall ((V3x $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (forall ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V4y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_3 V3x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_3 V4y)) V1s)) (not (= V3x V4y))) (or (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V3x)) V4y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ _let_2 (@ (@ tptp.ap (@ _let_1 V4y)) V3x))) V0r)))))))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Estrict__linear__order A_27a)) V0r)) V1s))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V1s))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a)) tptp.bool)) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (=> (@ (@ tptp.mem V3y) A_27a) (=> (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27a)) V2x)) V3y))) V0r)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2Elinear__order A_27a)) V0r)) V1s))) (and (@ tptp.p (@ (@ tptp.ap (@ _let_1 V2x)) V1s)) (@ tptp.p (@ (@ tptp.ap (@ _let_1 V3y)) V1s))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Ereln__to__rel A_27a) A_27b)) V0r) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))) V0r)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erel__to__reln A_27a) A_27b)) V0R) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC _let_1) _let_1)) (@ (@ tptp.ap (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) (@ (@ tptp.ty_2Epair_2Eprod _let_1) tptp.bool))) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.lam A_27b) (lambda ((V2y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))) (@ (@ tptp.ap (@ (@ tptp.ap V0R) V1x)) V2y)))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0s $$unsorted)) (=> (@ (@ tptp.mem V0s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2ERRUNIV A_27a)) V0s) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ _let_1 V1x)) V0s))) (@ (@ tptp.ap (@ _let_1 V2y)) V0s)))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2ERREFL__EXP A_27a)) V0R)) V1s) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERUNION A_27a) A_27a)) V0R)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V3y $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V2x)) V3y))) (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V1s)))))))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (forall ((V1s $$unsorted)) (=> (@ (@ tptp.mem V1s) (@ (@ tptp.arr A_27a) tptp.bool)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Erelation_2ERSUBSET A_27a) A_27a)) V0R)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2ERREFL__EXP A_27a)) V0R)) V1s)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Eset__relation_2ERREFL__EXP A_27a)) V0R)) (@ tptp.c_2Epred__set_2EUNIV A_27a)) V0R)))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (V0R $$unsorted)) (let ((_let_1 (@ tptp.arr A_27a))) (=> (@ (@ tptp.mem V0R) (@ _let_1 (@ _let_1 tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Epred__set_2EREL__RESTRICT A_27a)) V0R)) (@ tptp.c_2Epred__set_2EUNIV A_27a)) V0R)))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0xy $$unsorted)) (=> (@ (@ tptp.mem V0xy) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) (forall ((V1R $$unsorted)) (=> (@ (@ tptp.mem V1R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) V0xy)) (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Erel__to__reln A_27a) A_27b)) V1R))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap V1R) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2EFST A_27a) A_27b)) V0xy))) (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2ESND A_27a) A_27b)) V0xy)))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0r $$unsorted)) (=> (@ (@ tptp.mem V0r) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b)) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (forall ((V2y $$unsorted)) (=> (@ (@ tptp.mem V2y) A_27b) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Ereln__to__rel A_27a) A_27b)) V0r)) V1x)) V2y)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) V1x)) V2y))) V0r))))))))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Eset__relation_2Erel__to__reln A_27a) A_27b) (@ (@ (@ tptp.c_2Epair_2EUNCURRY A_27a) A_27b) tptp.bool))))
% 2.01/2.23 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Eset__relation_2Ereln__to__rel A_27a) A_27b) (@ (@ (@ tptp.c_2Epair_2ECURRY A_27a) A_27b) tptp.bool))))
% 2.01/2.23 (assert (not (forall ((A_27a tptp.del) (A_27b tptp.del) (V0R $$unsorted)) (=> (@ (@ tptp.mem V0R) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) tptp.bool))) (= (@ (@ tptp.ap (@ (@ tptp.c_2Eset__relation_2Ereln__to__rel A_27a) A_27b)) (@ (@ tptp.ap (@ (@ /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 16215 Alarm clock ( read result; case "$result" in
% 299.44/300.21 unsat)
% 299.44/300.21 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.44/300.21 ;;
% 299.44/300.21 sat)
% 299.44/300.21 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.44/300.21 ;;
% 299.44/300.21 esac; exit 1 )
% 299.44/300.22 Alarm clock
% 299.44/300.22 % cvc5---1.0.5 exiting
% 299.44/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------