TSTP Solution File: ITP025^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP025^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 03:17:21 EDT 2023
% Result : Timeout 299.95s 300.18s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : ITP025^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.16 % Command : do_cvc5 %s %d
% 0.15/0.38 % Computer : n003.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sun Aug 27 16:39:40 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.23/0.53 %----Proving TH0
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 % File : ITP025^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.23/0.53 % Domain : Interactive Theorem Proving
% 0.23/0.53 % Problem : HOL4 set theory export of thm_2Elebesgue_2Epos__fn__integral__cmul.p, bushy mode
% 0.23/0.53 % Version : [BG+19] axioms.
% 0.23/0.53 % English :
% 0.23/0.53
% 0.23/0.53 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.23/0.53 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.23/0.53 % Source : [BG+19]
% 0.23/0.53 % Names : thm_2Elebesgue_2Epos__fn__integral__cmul.p [Gau19]
% 0.23/0.53 % : HL412001^2.p [TPAP]
% 0.23/0.53
% 0.23/0.53 % Status : Theorem
% 0.23/0.53 % Rating : 1.00 v7.5.0
% 0.23/0.53 % Syntax : Number of formulae : 197 ( 29 unt; 67 typ; 0 def)
% 0.23/0.53 % Number of atoms : 985 ( 51 equ; 0 cnn)
% 0.23/0.53 % Maximal formula atoms : 36 ( 7 avg)
% 0.23/0.53 % Number of connectives : 1961 ( 48 ~; 32 |; 57 &;1588 @)
% 0.23/0.53 % ( 71 <=>; 165 =>; 0 <=; 0 <~>)
% 0.23/0.53 % Maximal formula depth : 20 ( 8 avg)
% 0.23/0.53 % Number of types : 6 ( 4 usr)
% 0.23/0.54 % Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% 0.23/0.54 % Number of symbols : 72 ( 69 usr; 37 con; 0-3 aty)
% 0.23/0.54 % Number of variables : 245 ( 14 ^; 228 !; 3 ?; 245 :)
% 0.23/0.54 % SPC : TH0_THM_EQU_NAR
% 0.23/0.54
% 0.23/0.54 % Comments :
% 0.23/0.54 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 thf(del_tp,type,
% 0.23/0.54 del: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(bool,type,
% 0.23/0.54 bool: del ).
% 0.23/0.54
% 0.23/0.54 thf(ind,type,
% 0.23/0.54 ind: del ).
% 0.23/0.54
% 0.23/0.54 thf(arr,type,
% 0.23/0.54 arr: del > del > del ).
% 0.23/0.54
% 0.23/0.54 thf(mem,type,
% 0.23/0.54 mem: $i > del > $o ).
% 0.23/0.54
% 0.23/0.54 thf(ap,type,
% 0.23/0.54 ap: $i > $i > $i ).
% 0.23/0.54
% 0.23/0.54 thf(lam,type,
% 0.23/0.54 lam: del > ( $i > $i ) > $i ).
% 0.23/0.54
% 0.23/0.54 thf(p,type,
% 0.23/0.54 p: $i > $o ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_o,type,
% 0.23/0.54 inj__o: $o > $i ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_surj_o,axiom,
% 0.23/0.54 ! [X: $o] :
% 0.23/0.54 ( ( p @ ( inj__o @ X ) )
% 0.23/0.54 = X ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_mem_o,axiom,
% 0.23/0.54 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_iso_mem_o,axiom,
% 0.23/0.54 ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ bool )
% 0.23/0.54 => ( X
% 0.23/0.54 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ap_tp,axiom,
% 0.23/0.54 ! [A: del,B: del,F: $i] :
% 0.23/0.54 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.23/0.54 => ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(lam_tp,axiom,
% 0.23/0.54 ! [A: del,B: del,F: $i > $i] :
% 0.23/0.54 ( ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 => ( mem @ ( F @ X ) @ B ) )
% 0.23/0.54 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(funcext,axiom,
% 0.23/0.54 ! [A: del,B: del,F: $i] :
% 0.23/0.54 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.23/0.54 => ! [G: $i] :
% 0.23/0.54 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.23/0.54 => ( ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 => ( ( ap @ F @ X )
% 0.23/0.54 = ( ap @ G @ X ) ) )
% 0.23/0.54 => ( F = G ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(beta,axiom,
% 0.23/0.54 ! [A: del,F: $i > $i,X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.23/0.54 = ( F @ X ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 thf(tp_ty_2Erealax_2Ereal,type,
% 0.23/0.54 ty_2Erealax_2Ereal: del ).
% 0.23/0.54
% 0.23/0.54 thf(stp_ty_2Erealax_2Ereal,type,
% 0.23/0.54 tp__ty_2Erealax_2Ereal: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_ty_2Erealax_2Ereal,type,
% 0.23/0.54 inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
% 0.23/0.54
% 0.23/0.54 thf(stp_surj_ty_2Erealax_2Ereal,type,
% 0.23/0.54 surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_surj_ty_2Erealax_2Ereal,axiom,
% 0.23/0.54 ! [X: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ X ) )
% 0.23/0.54 = X ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_mem_ty_2Erealax_2Ereal,axiom,
% 0.23/0.54 ! [X: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ X ) @ ty_2Erealax_2Ereal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_iso_mem_ty_2Erealax_2Ereal,axiom,
% 0.23/0.54 ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ ty_2Erealax_2Ereal )
% 0.23/0.54 => ( X
% 0.23/0.54 = ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ X ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_ty_2Epair_2Eprod,type,
% 0.23/0.54 ty_2Epair_2Eprod: del > del > del ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Emeasure_2Em__space,type,
% 0.23/0.54 c_2Emeasure_2Em__space: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Emeasure_2Em__space,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Emeasure_2Em__space @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) @ ( arr @ A_27a @ bool ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2EBOUNDED,type,
% 0.23/0.54 c_2Ebool_2EBOUNDED: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2EBOUNDED,axiom,
% 0.23/0.54 mem @ c_2Ebool_2EBOUNDED @ ( arr @ bool @ bool ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ecombin_2ES,type,
% 0.23/0.54 c_2Ecombin_2ES: del > del > del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ecombin_2ES,axiom,
% 0.23/0.54 ! [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 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ecombin_2EC,type,
% 0.23/0.54 c_2Ecombin_2EC: del > del > del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ecombin_2EC,axiom,
% 0.23/0.54 ! [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 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ecombin_2EI,type,
% 0.23/0.54 c_2Ecombin_2EI: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ecombin_2EI,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Ecombin_2EI @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ecombin_2Eo,type,
% 0.23/0.54 c_2Ecombin_2Eo: del > del > del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ecombin_2Eo,axiom,
% 0.23/0.54 ! [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 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_ty_2Enum_2Enum,type,
% 0.23/0.54 ty_2Enum_2Enum: del ).
% 0.23/0.54
% 0.23/0.54 thf(stp_ty_2Enum_2Enum,type,
% 0.23/0.54 tp__ty_2Enum_2Enum: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_ty_2Enum_2Enum,type,
% 0.23/0.54 inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
% 0.23/0.54
% 0.23/0.54 thf(stp_surj_ty_2Enum_2Enum,type,
% 0.23/0.54 surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_surj_ty_2Enum_2Enum,axiom,
% 0.23/0.54 ! [X: tp__ty_2Enum_2Enum] :
% 0.23/0.54 ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
% 0.23/0.54 = X ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_mem_ty_2Enum_2Enum,axiom,
% 0.23/0.54 ! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_iso_mem_ty_2Enum_2Enum,axiom,
% 0.23/0.54 ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ ty_2Enum_2Enum )
% 0.23/0.54 => ( X
% 0.23/0.54 = ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_ty_2Eextreal_2Eextreal,type,
% 0.23/0.54 ty_2Eextreal_2Eextreal: del ).
% 0.23/0.54
% 0.23/0.54 thf(stp_ty_2Eextreal_2Eextreal,type,
% 0.23/0.54 tp__ty_2Eextreal_2Eextreal: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_ty_2Eextreal_2Eextreal,type,
% 0.23/0.54 inj__ty_2Eextreal_2Eextreal: tp__ty_2Eextreal_2Eextreal > $i ).
% 0.23/0.54
% 0.23/0.54 thf(stp_surj_ty_2Eextreal_2Eextreal,type,
% 0.23/0.54 surj__ty_2Eextreal_2Eextreal: $i > tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_surj_ty_2Eextreal_2Eextreal,axiom,
% 0.23/0.54 ! [X: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( surj__ty_2Eextreal_2Eextreal @ ( inj__ty_2Eextreal_2Eextreal @ X ) )
% 0.23/0.54 = X ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_inj_mem_ty_2Eextreal_2Eextreal,axiom,
% 0.23/0.54 ! [X: tp__ty_2Eextreal_2Eextreal] : ( mem @ ( inj__ty_2Eextreal_2Eextreal @ X ) @ ty_2Eextreal_2Eextreal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_iso_mem_ty_2Eextreal_2Eextreal,axiom,
% 0.23/0.54 ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ ty_2Eextreal_2Eextreal )
% 0.23/0.54 => ( X
% 0.23/0.54 = ( inj__ty_2Eextreal_2Eextreal @ ( surj__ty_2Eextreal_2Eextreal @ X ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2EPosInf,type,
% 0.23/0.54 c_2Eextreal_2EPosInf: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2EPosInf,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2EPosInf @ ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2EPosInf,type,
% 0.23/0.54 fo__c_2Eextreal_2EPosInf: tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2EPosInf,axiom,
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf )
% 0.23/0.54 = c_2Eextreal_2EPosInf ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2ENegInf,type,
% 0.23/0.54 c_2Eextreal_2ENegInf: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2ENegInf,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2ENegInf @ ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2ENegInf,type,
% 0.23/0.54 fo__c_2Eextreal_2ENegInf: tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2ENegInf,axiom,
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf )
% 0.23/0.54 = c_2Eextreal_2ENegInf ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2Eextreal__inv,type,
% 0.23/0.54 c_2Eextreal_2Eextreal__inv: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2Eextreal__inv,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2Eextreal__inv @ ( arr @ ty_2Eextreal_2Eextreal @ ty_2Eextreal_2Eextreal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2Eextreal__inv,type,
% 0.23/0.54 fo__c_2Eextreal_2Eextreal__inv: tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2Eextreal__inv,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__inv @ X0 ) )
% 0.23/0.54 = ( ap @ c_2Eextreal_2Eextreal__inv @ ( inj__ty_2Eextreal_2Eextreal @ X0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2Eextreal__div,type,
% 0.23/0.54 c_2Eextreal_2Eextreal__div: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2Eextreal__div,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2Eextreal__div @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ ty_2Eextreal_2Eextreal ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2Eextreal__div,type,
% 0.23/0.54 fo__c_2Eextreal_2Eextreal__div: tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2Eextreal__div,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Eextreal_2Eextreal,X1: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__div @ X0 @ X1 ) )
% 0.23/0.54 = ( ap @ ( ap @ c_2Eextreal_2Eextreal__div @ ( inj__ty_2Eextreal_2Eextreal @ X0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X1 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2Eextreal__le,type,
% 0.23/0.54 c_2Eextreal_2Eextreal__le: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2Eextreal__le,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2Eextreal__le @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2Eextreal__sup,type,
% 0.23/0.54 c_2Eextreal_2Eextreal__sup: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2Eextreal__sup,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2Eextreal__sup @ ( arr @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) @ ty_2Eextreal_2Eextreal ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2ENormal,type,
% 0.23/0.54 c_2Eextreal_2ENormal: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2ENormal,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2ENormal @ ( arr @ ty_2Erealax_2Ereal @ ty_2Eextreal_2Eextreal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2ENormal,type,
% 0.23/0.54 fo__c_2Eextreal_2ENormal: tp__ty_2Erealax_2Ereal > tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2ENormal,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2ENormal @ X0 ) )
% 0.23/0.54 = ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2Eextreal__mul,type,
% 0.23/0.54 c_2Eextreal_2Eextreal__mul: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2Eextreal__mul,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2Eextreal__mul @ ( arr @ ty_2Eextreal_2Eextreal @ ( arr @ ty_2Eextreal_2Eextreal @ ty_2Eextreal_2Eextreal ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2Eextreal__mul,type,
% 0.23/0.54 fo__c_2Eextreal_2Eextreal__mul: tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal > tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2Eextreal__mul,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Eextreal_2Eextreal,X1: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__mul @ X0 @ X1 ) )
% 0.23/0.54 = ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ X0 ) ) @ ( inj__ty_2Eextreal_2Eextreal @ X1 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Elebesgue_2Epsfis,type,
% 0.23/0.54 c_2Elebesgue_2Epsfis: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Elebesgue_2Epsfis,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Elebesgue_2Epsfis @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) @ ( arr @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal ) @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Eextreal_2Eextreal__of__num,type,
% 0.23/0.54 c_2Eextreal_2Eextreal__of__num: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Eextreal_2Eextreal__of__num,axiom,
% 0.23/0.54 mem @ c_2Eextreal_2Eextreal__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Eextreal_2Eextreal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Eextreal_2Eextreal__of__num,type,
% 0.23/0.54 fo__c_2Eextreal_2Eextreal__of__num: tp__ty_2Enum_2Enum > tp__ty_2Eextreal_2Eextreal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Eextreal_2Eextreal__of__num,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Enum_2Enum] :
% 0.23/0.54 ( ( inj__ty_2Eextreal_2Eextreal @ ( fo__c_2Eextreal_2Eextreal__of__num @ X0 ) )
% 0.23/0.54 = ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Elebesgue_2Epos__fn__integral,type,
% 0.23/0.54 c_2Elebesgue_2Epos__fn__integral: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Elebesgue_2Epos__fn__integral,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Elebesgue_2Epos__fn__integral @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) @ ( arr @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal ) @ ty_2Eextreal_2Eextreal ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Emeasure_2Emeasure__space,type,
% 0.23/0.54 c_2Emeasure_2Emeasure__space: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Emeasure_2Emeasure__space,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Emeasure_2Emeasure__space @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2ET,type,
% 0.23/0.54 c_2Ebool_2ET: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2ET,axiom,
% 0.23/0.54 mem @ c_2Ebool_2ET @ bool ).
% 0.23/0.54
% 0.23/0.54 thf(ax_true_p,axiom,
% 0.23/0.54 p @ c_2Ebool_2ET ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Epair_2E_2C,type,
% 0.23/0.54 c_2Epair_2E_2C: del > del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Epair_2E_2C,axiom,
% 0.23/0.54 ! [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 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2E_3F,type,
% 0.23/0.54 c_2Ebool_2E_3F: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2E_3F,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_ex_p,axiom,
% 0.23/0.54 ! [A: del,Q: $i] :
% 0.23/0.54 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.23/0.54 => ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
% 0.23/0.54 <=> ? [X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 & ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Epred__set_2EGSPEC,type,
% 0.23/0.54 c_2Epred__set_2EGSPEC: del > del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Epred__set_2EGSPEC,axiom,
% 0.23/0.54 ! [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 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2EIN,type,
% 0.23/0.54 c_2Ebool_2EIN: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2EIN,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Erealax_2Ereal__lt,type,
% 0.23/0.54 c_2Erealax_2Ereal__lt: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Erealax_2Ereal__lt,axiom,
% 0.23/0.54 mem @ c_2Erealax_2Ereal__lt @ ( arr @ ty_2Erealax_2Ereal @ ( arr @ ty_2Erealax_2Ereal @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Erealax_2Einv,type,
% 0.23/0.54 c_2Erealax_2Einv: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Erealax_2Einv,axiom,
% 0.23/0.54 mem @ c_2Erealax_2Einv @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Erealax_2Einv,type,
% 0.23/0.54 fo__c_2Erealax_2Einv: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Erealax_2Einv,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Einv @ X0 ) )
% 0.23/0.54 = ( ap @ c_2Erealax_2Einv @ ( inj__ty_2Erealax_2Ereal @ X0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Enum_2E0,type,
% 0.23/0.54 c_2Enum_2E0: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Enum_2E0,axiom,
% 0.23/0.54 mem @ c_2Enum_2E0 @ ty_2Enum_2Enum ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Enum_2E0,type,
% 0.23/0.54 fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Enum_2E0,axiom,
% 0.23/0.54 ( ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 )
% 0.23/0.54 = c_2Enum_2E0 ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ereal_2Ereal__of__num,type,
% 0.23/0.54 c_2Ereal_2Ereal__of__num: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ereal_2Ereal__of__num,axiom,
% 0.23/0.54 mem @ c_2Ereal_2Ereal__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Erealax_2Ereal ) ).
% 0.23/0.54
% 0.23/0.54 thf(stp_fo_c_2Ereal_2Ereal__of__num,type,
% 0.23/0.54 fo__c_2Ereal_2Ereal__of__num: tp__ty_2Enum_2Enum > tp__ty_2Erealax_2Ereal ).
% 0.23/0.54
% 0.23/0.54 thf(stp_eq_fo_c_2Ereal_2Ereal__of__num,axiom,
% 0.23/0.54 ! [X0: tp__ty_2Enum_2Enum] :
% 0.23/0.54 ( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Ereal_2Ereal__of__num @ X0 ) )
% 0.23/0.54 = ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ X0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ereal_2Ereal__lte,type,
% 0.23/0.54 c_2Ereal_2Ereal__lte: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ereal_2Ereal__lte,axiom,
% 0.23/0.54 mem @ c_2Ereal_2Ereal__lte @ ( arr @ ty_2Erealax_2Ereal @ ( arr @ ty_2Erealax_2Ereal @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2EF,type,
% 0.23/0.54 c_2Ebool_2EF: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2EF,axiom,
% 0.23/0.54 mem @ c_2Ebool_2EF @ bool ).
% 0.23/0.54
% 0.23/0.54 thf(ax_false_p,axiom,
% 0.23/0.54 ~ ( p @ c_2Ebool_2EF ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.23/0.54 c_2Ebool_2E_2F_5C: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.23/0.54 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_and_p,axiom,
% 0.23/0.54 ! [Q: $i] :
% 0.23/0.54 ( ( mem @ Q @ bool )
% 0.23/0.54 => ! [R: $i] :
% 0.23/0.54 ( ( mem @ R @ bool )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.23/0.54 <=> ( ( p @ Q )
% 0.23/0.54 & ( p @ R ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Emin_2E_3D,type,
% 0.23/0.54 c_2Emin_2E_3D: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Emin_2E_3D,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_eq_p,axiom,
% 0.23/0.54 ! [A: del,X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 => ! [Y: $i] :
% 0.23/0.54 ( ( mem @ Y @ A )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.23/0.54 <=> ( X = Y ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.23/0.54 c_2Ebool_2E_5C_2F: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.23/0.54 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_or_p,axiom,
% 0.23/0.54 ! [Q: $i] :
% 0.23/0.54 ( ( mem @ Q @ bool )
% 0.23/0.54 => ! [R: $i] :
% 0.23/0.54 ( ( mem @ R @ bool )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.23/0.54 <=> ( ( p @ Q )
% 0.23/0.54 | ( p @ R ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2E_7E,type,
% 0.23/0.54 c_2Ebool_2E_7E: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.23/0.54 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_neg_p,axiom,
% 0.23/0.54 ! [Q: $i] :
% 0.23/0.54 ( ( mem @ Q @ bool )
% 0.23/0.54 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.23/0.54 <=> ~ ( p @ Q ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.23/0.54 c_2Emin_2E_3D_3D_3E: $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.23/0.54 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_imp_p,axiom,
% 0.23/0.54 ! [Q: $i] :
% 0.23/0.54 ( ( mem @ Q @ bool )
% 0.23/0.54 => ! [R: $i] :
% 0.23/0.54 ( ( mem @ R @ bool )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.23/0.54 <=> ( ( p @ Q )
% 0.23/0.54 => ( p @ R ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(tp_c_2Ebool_2E_21,type,
% 0.23/0.54 c_2Ebool_2E_21: del > $i ).
% 0.23/0.54
% 0.23/0.54 thf(mem_c_2Ebool_2E_21,axiom,
% 0.23/0.54 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_all_p,axiom,
% 0.23/0.54 ! [A: del,Q: $i] :
% 0.23/0.54 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.23/0.54 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.23/0.54 <=> ! [X: $i] :
% 0.23/0.54 ( ( mem @ X @ A )
% 0.23/0.54 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Ebool_2EETA__AX,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
% 0.23/0.54 => ( ( lam @ A_27a
% 0.23/0.54 @ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
% 0.23/0.54 = V0t ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.23/0.54 $true ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.23/0.54 ! [V0t1: $i] :
% 0.23/0.54 ( ( mem @ V0t1 @ bool )
% 0.23/0.54 => ! [V1t2: $i] :
% 0.23/0.54 ( ( mem @ V1t2 @ bool )
% 0.23/0.54 => ( ( ( p @ V0t1 )
% 0.23/0.54 => ( p @ V1t2 ) )
% 0.23/0.54 => ( ( ( p @ V1t2 )
% 0.23/0.54 => ( p @ V0t1 ) )
% 0.23/0.54 => ( ( p @ V0t1 )
% 0.23/0.54 <=> ( p @ V1t2 ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EFALSITY,axiom,
% 0.23/0.54 ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( $false
% 0.23/0.54 => ( p @ V0t ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
% 0.23/0.54 ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ( p @ V0t )
% 0.23/0.54 | ~ ( p @ V0t ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.23/0.54 ! [A_27a: del,V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ! [V1x: $i] :
% 0.23/0.54 ( ( mem @ V1x @ A_27a )
% 0.23/0.54 => ( p @ V0t ) )
% 0.23/0.54 <=> ( p @ V0t ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
% 0.23/0.54 ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ( ( $true
% 0.23/0.54 & ( p @ V0t ) )
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 & $true )
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 & ( ( $false
% 0.23/0.54 & ( p @ V0t ) )
% 0.23/0.54 <=> $false )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 & $false )
% 0.23/0.54 <=> $false )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 & ( p @ V0t ) )
% 0.23/0.54 <=> ( p @ V0t ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.23/0.54 ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ( ( $true
% 0.23/0.54 => ( p @ V0t ) )
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 => $true )
% 0.23/0.54 <=> $true )
% 0.23/0.54 & ( ( $false
% 0.23/0.54 => ( p @ V0t ) )
% 0.23/0.54 <=> $true )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 => ( p @ V0t ) )
% 0.23/0.54 <=> $true )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 => $false )
% 0.23/0.54 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.23/0.54 ( ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ~ ~ ( p @ V0t )
% 0.23/0.54 <=> ( p @ V0t ) ) )
% 0.23/0.54 & ( ~ $true
% 0.23/0.54 <=> $false )
% 0.23/0.54 & ( ~ $false
% 0.23/0.54 <=> $true ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.23/0.54 ! [A_27a: del,V0x: $i] :
% 0.23/0.54 ( ( mem @ V0x @ A_27a )
% 0.23/0.54 => ( ( V0x = V0x )
% 0.23/0.54 <=> $true ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.23/0.54 ! [A_27a: del,V0x: $i] :
% 0.23/0.54 ( ( mem @ V0x @ A_27a )
% 0.23/0.54 => ! [V1y: $i] :
% 0.23/0.54 ( ( mem @ V1y @ A_27a )
% 0.23/0.54 => ( ( V0x = V1y )
% 0.23/0.54 <=> ( V1y = V0x ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EFUN__EQ__THM,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.23/0.54 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.23/0.54 => ! [V1g: $i] :
% 0.23/0.54 ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
% 0.23/0.54 => ( ( V0f = V1g )
% 0.23/0.54 <=> ! [V2x: $i] :
% 0.23/0.54 ( ( mem @ V2x @ A_27a )
% 0.23/0.54 => ( ( ap @ V0f @ V2x )
% 0.23/0.54 = ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.23/0.54 ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ( ( $true
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 <=> $true )
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 & ( ( $false
% 0.23/0.54 <=> ( p @ V0t ) )
% 0.23/0.54 <=> ~ ( p @ V0t ) )
% 0.23/0.54 & ( ( ( p @ V0t )
% 0.23/0.54 <=> $false )
% 0.23/0.54 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,axiom,
% 0.23/0.54 ! [A_27a: del,V0P: $i] :
% 0.23/0.54 ( ( mem @ V0P @ bool )
% 0.23/0.54 => ! [V1Q: $i] :
% 0.23/0.54 ( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
% 0.23/0.54 => ( ( ( p @ V0P )
% 0.23/0.54 & ! [V2x: $i] :
% 0.23/0.54 ( ( mem @ V2x @ A_27a )
% 0.23/0.54 => ( p @ ( ap @ V1Q @ V2x ) ) ) )
% 0.23/0.54 <=> ! [V3x: $i] :
% 0.23/0.54 ( ( mem @ V3x @ A_27a )
% 0.23/0.54 => ( ( p @ V0P )
% 0.23/0.54 & ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,axiom,
% 0.23/0.54 ! [V0A: $i] :
% 0.23/0.54 ( ( mem @ V0A @ bool )
% 0.23/0.54 => ! [V1B: $i] :
% 0.23/0.54 ( ( mem @ V1B @ bool )
% 0.23/0.54 => ! [V2C: $i] :
% 0.23/0.54 ( ( mem @ V2C @ bool )
% 0.23/0.54 => ( ( ( ( p @ V1B )
% 0.23/0.54 & ( p @ V2C ) )
% 0.23/0.54 | ( p @ V0A ) )
% 0.23/0.54 <=> ( ( ( p @ V1B )
% 0.23/0.54 | ( p @ V0A ) )
% 0.23/0.54 & ( ( p @ V2C )
% 0.23/0.54 | ( p @ V0A ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 0.23/0.54 ! [V0t1: $i] :
% 0.23/0.54 ( ( mem @ V0t1 @ bool )
% 0.23/0.54 => ! [V1t2: $i] :
% 0.23/0.54 ( ( mem @ V1t2 @ bool )
% 0.23/0.54 => ! [V2t3: $i] :
% 0.23/0.54 ( ( mem @ V2t3 @ bool )
% 0.23/0.54 => ( ( ( p @ V0t1 )
% 0.23/0.54 => ( ( p @ V1t2 )
% 0.23/0.54 => ( p @ V2t3 ) ) )
% 0.23/0.54 <=> ( ( ( p @ V0t1 )
% 0.23/0.54 & ( p @ V1t2 ) )
% 0.23/0.54 => ( p @ V2t3 ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EIMP__CONG,axiom,
% 0.23/0.54 ! [V0x: $i] :
% 0.23/0.54 ( ( mem @ V0x @ bool )
% 0.23/0.54 => ! [V1x_27: $i] :
% 0.23/0.54 ( ( mem @ V1x_27 @ bool )
% 0.23/0.54 => ! [V2y: $i] :
% 0.23/0.54 ( ( mem @ V2y @ bool )
% 0.23/0.54 => ! [V3y_27: $i] :
% 0.23/0.54 ( ( mem @ V3y_27 @ bool )
% 0.23/0.54 => ( ( ( ( p @ V0x )
% 0.23/0.54 <=> ( p @ V1x_27 ) )
% 0.23/0.54 & ( ( p @ V1x_27 )
% 0.23/0.54 => ( ( p @ V2y )
% 0.23/0.54 <=> ( p @ V3y_27 ) ) ) )
% 0.23/0.54 => ( ( ( p @ V0x )
% 0.23/0.54 => ( p @ V2y ) )
% 0.23/0.54 <=> ( ( p @ V1x_27 )
% 0.23/0.54 => ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EUNWIND__THM2,axiom,
% 0.23/0.54 ! [A_27a: del,V0P: $i] :
% 0.23/0.54 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.23/0.54 => ! [V1a: $i] :
% 0.23/0.54 ( ( mem @ V1a @ A_27a )
% 0.23/0.54 => ( ? [V2x: $i] :
% 0.23/0.54 ( ( mem @ V2x @ A_27a )
% 0.23/0.54 & ( V2x = V1a )
% 0.23/0.54 & ( p @ ( ap @ V0P @ V2x ) ) )
% 0.23/0.54 <=> ( p @ ( ap @ V0P @ V1a ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ebool_2EBOUNDED__THM,axiom,
% 0.23/0.54 ! [V0v: $i] :
% 0.23/0.54 ( ( mem @ V0v @ bool )
% 0.23/0.54 => ( ( p @ ( ap @ c_2Ebool_2EBOUNDED @ V0v ) )
% 0.23/0.54 <=> $true ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Ecombin_2ES__DEF,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,A_27c: del] :
% 0.23/0.54 ( ( c_2Ecombin_2ES @ A_27a @ A_27b @ A_27c )
% 0.23/0.54 = ( lam @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) )
% 0.23/0.54 @ ^ [V0f: $i] :
% 0.23/0.54 ( lam @ ( arr @ A_27a @ A_27b )
% 0.23/0.54 @ ^ [V1g: $i] :
% 0.23/0.54 ( lam @ A_27a
% 0.23/0.54 @ ^ [V2x: $i] : ( ap @ ( ap @ V0f @ V2x ) @ ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Ecombin_2EC__DEF,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,A_27c: del] :
% 0.23/0.54 ( ( c_2Ecombin_2EC @ A_27a @ A_27b @ A_27c )
% 0.23/0.54 = ( lam @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) )
% 0.23/0.54 @ ^ [V0f: $i] :
% 0.23/0.54 ( lam @ A_27b
% 0.23/0.54 @ ^ [V1x: $i] :
% 0.23/0.54 ( lam @ A_27a
% 0.23/0.54 @ ^ [V2y: $i] : ( ap @ ( ap @ V0f @ V2y ) @ V1x ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Ecombin_2Eo__DEF,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
% 0.23/0.54 ( ( mem @ V0f @ ( arr @ A_27c @ A_27b ) )
% 0.23/0.54 => ! [V1g: $i] :
% 0.23/0.54 ( ( mem @ V1g @ ( arr @ A_27a @ A_27c ) )
% 0.23/0.54 => ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1g )
% 0.23/0.54 = ( lam @ A_27a
% 0.23/0.54 @ ^ [V2x: $i] : ( ap @ V0f @ ( ap @ V1g @ V2x ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ecombin_2EI__THM,axiom,
% 0.23/0.54 ! [A_27a: del,V0x: $i] :
% 0.23/0.54 ( ( mem @ V0x @ A_27a )
% 0.23/0.54 => ( ( ap @ ( c_2Ecombin_2EI @ A_27a ) @ V0x )
% 0.23/0.54 = V0x ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ecombin_2EI__o__ID,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.23/0.54 ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
% 0.23/0.54 => ( ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27b ) @ ( c_2Ecombin_2EI @ A_27b ) ) @ V0f )
% 0.23/0.54 = V0f )
% 0.23/0.54 & ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ A_27b @ A_27a ) @ V0f ) @ ( c_2Ecombin_2EI @ A_27a ) )
% 0.23/0.54 = V0f ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Eextreal_2Eextreal__of__num__def,axiom,
% 0.23/0.54 ! [V0n: tp__ty_2Enum_2Enum] :
% 0.23/0.54 ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2ENormal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Eextreal__le__def,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal,V2a: tp__ty_2Eextreal_2Eextreal,V3v2: tp__ty_2Erealax_2Ereal,V4v3: tp__ty_2Erealax_2Ereal,V5v5: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) )
% 0.23/0.54 <=> ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) ) )
% 0.23/0.54 & ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2a ) ) )
% 0.23/0.54 <=> $true )
% 0.23/0.54 & ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf ) ) @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf ) ) )
% 0.23/0.54 <=> $true )
% 0.23/0.54 & ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V3v2 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf ) ) )
% 0.23/0.54 <=> $true )
% 0.23/0.54 & ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf ) ) @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf ) ) )
% 0.23/0.54 <=> $false )
% 0.23/0.54 & ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V4v3 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf ) ) )
% 0.23/0.54 <=> $false )
% 0.23/0.54 & ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf ) ) @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V5v5 ) ) ) )
% 0.23/0.54 <=> $false ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Eextreal_2Eextreal__inv__def,axiom,
% 0.23/0.54 ( ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__inv @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2ENegInf ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2ENormal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
% 0.23/0.54 & ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__inv @ ( inj__ty_2Eextreal_2Eextreal @ fo__c_2Eextreal_2EPosInf ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2ENormal @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
% 0.23/0.54 & ! [V0x: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__inv @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2ENormal @ ( ap @ c_2Erealax_2Einv @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Eextreal_2Eextreal__div__def,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Eextreal_2Eextreal,V1y: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__div @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( ap @ c_2Eextreal_2Eextreal__inv @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Emul__lzero,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Ele__lmul__imp,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Eextreal_2Eextreal,V1y: tp__ty_2Eextreal_2Eextreal,V2z: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) )
% 0.23/0.54 & ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Emul__comm,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Eextreal_2Eextreal,V1y: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V0x ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Ele__rdiv,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Eextreal_2Eextreal,V2z: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) )
% 0.23/0.54 <=> ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__div @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Ele__ldiv,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Eextreal_2Eextreal,V2z: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) )
% 0.23/0.54 <=> ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__div @ ( inj__ty_2Eextreal_2Eextreal @ V1y ) ) @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2z ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Esup__le,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) )
% 0.23/0.54 => ! [V1x: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ c_2Eextreal_2Eextreal__sup @ V0p ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) )
% 0.23/0.54 <=> ! [V2y: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ V0p @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Ele__sup,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) )
% 0.23/0.54 => ! [V1x: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) @ ( ap @ c_2Eextreal_2Eextreal__sup @ V0p ) ) )
% 0.23/0.54 <=> ! [V2y: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ! [V3z: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ V0p @ ( inj__ty_2Eextreal_2Eextreal @ V3z ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V3z ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Eextreal_2Esup__eq,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ ( arr @ ty_2Eextreal_2Eextreal @ bool ) )
% 0.23/0.54 => ! [V1x: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__sup @ V0p ) )
% 0.23/0.54 = V1x )
% 0.23/0.54 <=> ( ! [V2y: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ V0p @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V2y ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) ) )
% 0.23/0.54 & ! [V3y: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ! [V4z: tp__ty_2Eextreal_2Eextreal] :
% 0.23/0.54 ( ( p @ ( ap @ V0p @ ( inj__ty_2Eextreal_2Eextreal @ V4z ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V4z ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V3y ) ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( inj__ty_2Eextreal_2Eextreal @ V1x ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V3y ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Elebesgue_2Epos__fn__integral__def,axiom,
% 0.23/0.54 ! [A_27a: del,V0m: $i] :
% 0.23/0.54 ( ( mem @ V0m @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) )
% 0.23/0.54 => ! [V1f: $i] :
% 0.23/0.54 ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal ) )
% 0.23/0.54 => ( ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ ( c_2Elebesgue_2Epos__fn__integral @ A_27a ) @ V0m ) @ V1f ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal
% 0.23/0.54 @ ( ap @ c_2Eextreal_2Eextreal__sup
% 0.23/0.54 @ ( ap @ ( c_2Epred__set_2EGSPEC @ ty_2Eextreal_2Eextreal @ ty_2Eextreal_2Eextreal )
% 0.23/0.54 @ ( lam @ ty_2Eextreal_2Eextreal
% 0.23/0.54 @ ^ [V2r: $i] :
% 0.23/0.54 ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Eextreal_2Eextreal @ bool ) @ V2r )
% 0.23/0.54 @ ( ap @ ( c_2Ebool_2E_3F @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal ) )
% 0.23/0.54 @ ( lam @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal )
% 0.23/0.54 @ ^ [V3g: $i] :
% 0.23/0.54 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Eextreal_2Eextreal ) @ V2r ) @ ( ap @ ( ap @ ( c_2Elebesgue_2Epsfis @ A_27a ) @ V0m ) @ V3g ) ) )
% 0.23/0.54 @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.23/0.54 @ ( lam @ A_27a
% 0.23/0.54 @ ^ [V4x: $i] : ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ V3g @ V4x ) ) @ ( ap @ V1f @ V4x ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Elebesgue_2Epsfis__cmul,axiom,
% 0.23/0.54 ! [A_27a: del,V0m: $i] :
% 0.23/0.54 ( ( mem @ V0m @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) )
% 0.23/0.54 => ! [V1f: $i] :
% 0.23/0.54 ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal ) )
% 0.23/0.54 => ! [V2a: tp__ty_2Eextreal_2Eextreal,V3z: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( ( p @ ( ap @ ( c_2Emeasure_2Emeasure__space @ A_27a ) @ V0m ) )
% 0.23/0.54 & ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Eextreal_2Eextreal ) @ ( inj__ty_2Eextreal_2Eextreal @ V2a ) ) @ ( ap @ ( ap @ ( c_2Elebesgue_2Epsfis @ A_27a ) @ V0m ) @ V1f ) ) )
% 0.23/0.54 & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) )
% 0.23/0.54 => ( p
% 0.23/0.54 @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Eextreal_2Eextreal ) @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) @ ( inj__ty_2Eextreal_2Eextreal @ V2a ) ) )
% 0.23/0.54 @ ( ap @ ( ap @ ( c_2Elebesgue_2Epsfis @ A_27a ) @ V0m )
% 0.23/0.54 @ ( lam @ A_27a
% 0.23/0.54 @ ^ [V4x: $i] : ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V3z ) ) ) @ ( ap @ V1f @ V4x ) ) ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Elebesgue_2Epos__fn__integral__zero,axiom,
% 0.23/0.54 ! [A_27a: del,V0m: $i] :
% 0.23/0.54 ( ( mem @ V0m @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) )
% 0.23/0.54 => ( ( p @ ( ap @ ( c_2Emeasure_2Emeasure__space @ A_27a ) @ V0m ) )
% 0.23/0.54 => ( ( surj__ty_2Eextreal_2Eextreal
% 0.23/0.54 @ ( ap @ ( ap @ ( c_2Elebesgue_2Epos__fn__integral @ A_27a ) @ V0m )
% 0.23/0.54 @ ( lam @ A_27a
% 0.23/0.54 @ ^ [V1x: $i] : ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Epair_2ECLOSED__PAIR__EQ,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,V0x: $i] :
% 0.23/0.54 ( ( mem @ V0x @ A_27a )
% 0.23/0.54 => ! [V1y: $i] :
% 0.23/0.54 ( ( mem @ V1y @ A_27b )
% 0.23/0.54 => ! [V2a: $i] :
% 0.23/0.54 ( ( mem @ V2a @ A_27a )
% 0.23/0.54 => ! [V3b: $i] :
% 0.23/0.54 ( ( mem @ V3b @ A_27b )
% 0.23/0.54 => ( ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y )
% 0.23/0.54 = ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2a ) @ V3b ) )
% 0.23/0.54 <=> ( ( V0x = V2a )
% 0.23/0.54 & ( V1y = V3b ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Epred__set_2ESPECIFICATION,axiom,
% 0.23/0.54 ! [A_27a: del,V0P: $i] :
% 0.23/0.54 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.23/0.54 => ! [V1x: $i] :
% 0.23/0.54 ( ( mem @ V1x @ A_27a )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ V0P ) )
% 0.23/0.54 <=> ( p @ ( ap @ V0P @ V1x ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,
% 0.23/0.54 ! [A_27a: del,A_27b: del,V0f: $i] :
% 0.23/0.54 ( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Epair_2Eprod @ A_27a @ bool ) ) )
% 0.23/0.54 => ! [V1v: $i] :
% 0.23/0.54 ( ( mem @ V1v @ A_27a )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1v ) @ ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27b ) @ V0f ) ) )
% 0.23/0.54 <=> ? [V2x: $i] :
% 0.23/0.54 ( ( mem @ V2x @ A_27b )
% 0.23/0.54 & ( ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V1v ) @ c_2Ebool_2ET )
% 0.23/0.54 = ( ap @ V0f @ V2x ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ereal_2EREAL__LT__LE,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Erealax_2Ereal,V1y: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( p @ ( ap @ ( ap @ c_2Erealax_2Ereal__lt @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
% 0.23/0.54 <=> ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) @ ( inj__ty_2Erealax_2Ereal @ V1y ) ) )
% 0.23/0.54 & ( V0x != V1y ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Ereal_2EREAL__LE__INV,axiom,
% 0.23/0.54 ! [V0x: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Erealax_2Einv @ ( inj__ty_2Erealax_2Ereal @ V0x ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2ENOT__NOT,axiom,
% 0.23/0.54 ! [V0t: $i] :
% 0.23/0.54 ( ( mem @ V0t @ bool )
% 0.23/0.54 => ( ~ ~ ( p @ V0t )
% 0.23/0.54 <=> ( p @ V0t ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2EAND__INV__IMP,axiom,
% 0.23/0.54 ! [V0A: $i] :
% 0.23/0.54 ( ( mem @ V0A @ bool )
% 0.23/0.54 => ( ( p @ V0A )
% 0.23/0.54 => ( ~ ( p @ V0A )
% 0.23/0.54 => $false ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2EOR__DUAL2,axiom,
% 0.23/0.54 ! [V0A: $i] :
% 0.23/0.54 ( ( mem @ V0A @ bool )
% 0.23/0.54 => ! [V1B: $i] :
% 0.23/0.54 ( ( mem @ V1B @ bool )
% 0.23/0.54 => ( ( ~ ( ( p @ V0A )
% 0.23/0.54 | ( p @ V1B ) )
% 0.23/0.54 => $false )
% 0.23/0.54 <=> ( ( ( p @ V0A )
% 0.23/0.54 => $false )
% 0.23/0.54 => ( ~ ( p @ V1B )
% 0.23/0.54 => $false ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2EOR__DUAL3,axiom,
% 0.23/0.54 ! [V0A: $i] :
% 0.23/0.54 ( ( mem @ V0A @ bool )
% 0.23/0.54 => ! [V1B: $i] :
% 0.23/0.54 ( ( mem @ V1B @ bool )
% 0.23/0.54 => ( ( ~ ( ~ ( p @ V0A )
% 0.23/0.54 | ( p @ V1B ) )
% 0.23/0.54 => $false )
% 0.23/0.54 <=> ( ( p @ V0A )
% 0.23/0.54 => ( ~ ( p @ V1B )
% 0.23/0.54 => $false ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2EAND__INV2,axiom,
% 0.23/0.54 ! [V0A: $i] :
% 0.23/0.54 ( ( mem @ V0A @ bool )
% 0.23/0.54 => ( ( ~ ( p @ V0A )
% 0.23/0.54 => $false )
% 0.23/0.54 => ( ( ( p @ V0A )
% 0.23/0.54 => $false )
% 0.23/0.54 => $false ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Edc__eq,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ! [V2r: $i] :
% 0.23/0.54 ( ( mem @ V2r @ bool )
% 0.23/0.54 => ( ( ( p @ V0p )
% 0.23/0.54 <=> ( ( p @ V1q )
% 0.23/0.54 <=> ( p @ V2r ) ) )
% 0.23/0.54 <=> ( ( ( p @ V0p )
% 0.23/0.54 | ( p @ V1q )
% 0.23/0.54 | ( p @ V2r ) )
% 0.23/0.54 & ( ( p @ V0p )
% 0.23/0.54 | ~ ( p @ V2r )
% 0.23/0.54 | ~ ( p @ V1q ) )
% 0.23/0.54 & ( ( p @ V1q )
% 0.23/0.54 | ~ ( p @ V2r )
% 0.23/0.54 | ~ ( p @ V0p ) )
% 0.23/0.54 & ( ( p @ V2r )
% 0.23/0.54 | ~ ( p @ V1q )
% 0.23/0.54 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Edc__conj,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ! [V2r: $i] :
% 0.23/0.54 ( ( mem @ V2r @ bool )
% 0.23/0.54 => ( ( ( p @ V0p )
% 0.23/0.54 <=> ( ( p @ V1q )
% 0.23/0.54 & ( p @ V2r ) ) )
% 0.23/0.54 <=> ( ( ( p @ V0p )
% 0.23/0.54 | ~ ( p @ V1q )
% 0.23/0.54 | ~ ( p @ V2r ) )
% 0.23/0.54 & ( ( p @ V1q )
% 0.23/0.54 | ~ ( p @ V0p ) )
% 0.23/0.54 & ( ( p @ V2r )
% 0.23/0.54 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Edc__disj,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ! [V2r: $i] :
% 0.23/0.54 ( ( mem @ V2r @ bool )
% 0.23/0.54 => ( ( ( p @ V0p )
% 0.23/0.54 <=> ( ( p @ V1q )
% 0.23/0.54 | ( p @ V2r ) ) )
% 0.23/0.54 <=> ( ( ( p @ V0p )
% 0.23/0.54 | ~ ( p @ V1q ) )
% 0.23/0.54 & ( ( p @ V0p )
% 0.23/0.54 | ~ ( p @ V2r ) )
% 0.23/0.54 & ( ( p @ V1q )
% 0.23/0.54 | ( p @ V2r )
% 0.23/0.54 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Edc__imp,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ! [V2r: $i] :
% 0.23/0.54 ( ( mem @ V2r @ bool )
% 0.23/0.54 => ( ( ( p @ V0p )
% 0.23/0.54 <=> ( ( p @ V1q )
% 0.23/0.54 => ( p @ V2r ) ) )
% 0.23/0.54 <=> ( ( ( p @ V0p )
% 0.23/0.54 | ( p @ V1q ) )
% 0.23/0.54 & ( ( p @ V0p )
% 0.23/0.54 | ~ ( p @ V2r ) )
% 0.23/0.54 & ( ~ ( p @ V1q )
% 0.23/0.54 | ( p @ V2r )
% 0.23/0.54 | ~ ( p @ V0p ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Edc__neg,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ( ( ( p @ V0p )
% 0.23/0.54 <=> ~ ( p @ V1q ) )
% 0.23/0.54 <=> ( ( ( p @ V0p )
% 0.23/0.54 | ( p @ V1q ) )
% 0.23/0.54 & ( ~ ( p @ V1q )
% 0.23/0.54 | ~ ( p @ V0p ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Epth__ni1,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ( ~ ( ( p @ V0p )
% 0.23/0.54 => ( p @ V1q ) )
% 0.23/0.54 => ( p @ V0p ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Epth__ni2,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ( ~ ( ( p @ V0p )
% 0.23/0.54 => ( p @ V1q ) )
% 0.23/0.54 => ~ ( p @ V1q ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Epth__no1,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ( ~ ( ( p @ V0p )
% 0.23/0.54 | ( p @ V1q ) )
% 0.23/0.54 => ~ ( p @ V0p ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Epth__no2,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ! [V1q: $i] :
% 0.23/0.54 ( ( mem @ V1q @ bool )
% 0.23/0.54 => ( ~ ( ( p @ V0p )
% 0.23/0.54 | ( p @ V1q ) )
% 0.23/0.54 => ~ ( p @ V1q ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Esat_2Epth__nn,axiom,
% 0.23/0.54 ! [V0p: $i] :
% 0.23/0.54 ( ( mem @ V0p @ bool )
% 0.23/0.54 => ( ~ ~ ( p @ V0p )
% 0.23/0.54 => ( p @ V0p ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(conj_thm_2Elebesgue_2Epos__fn__integral__cmul,conjecture,
% 0.23/0.54 ! [A_27a: del,V0m: $i] :
% 0.23/0.54 ( ( mem @ V0m @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ bool ) @ ( ty_2Epair_2Eprod @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ ty_2Erealax_2Ereal ) ) ) )
% 0.23/0.54 => ! [V1f: $i] :
% 0.23/0.54 ( ( mem @ V1f @ ( arr @ A_27a @ ty_2Eextreal_2Eextreal ) )
% 0.23/0.54 => ! [V2c: tp__ty_2Erealax_2Ereal] :
% 0.23/0.54 ( ( ( p @ ( ap @ ( c_2Emeasure_2Emeasure__space @ A_27a ) @ V0m ) )
% 0.23/0.54 & ! [V3x: $i] :
% 0.23/0.54 ( ( mem @ V3x @ A_27a )
% 0.23/0.54 => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( c_2Emeasure_2Em__space @ A_27a ) @ V0m ) ) )
% 0.23/0.54 => ( p @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__le @ ( ap @ c_2Eextreal_2Eextreal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ V1f @ V3x ) ) ) ) )
% 0.23/0.54 & ( p @ ( ap @ ( ap @ c_2Ereal_2Ereal__lte @ ( ap @ c_2Ereal_2Ereal__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Erealax_2Ereal @ V2c ) ) ) )
% 0.23/0.54 => ( ( surj__ty_2Eextreal_2Eextreal
% 0.23/0.54 @ ( ap @ ( ap @ ( c_2Elebesgue_2Epos__fn__integral @ A_27a ) @ V0m )
% 0.23/0.54 @ ( lam @ A_27a
% 0.23/0.54 @ ^ [V4x: $i] : ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V2c ) ) ) @ ( ap @ V1f @ V4x ) ) ) ) )
% 0.23/0.54 = ( surj__ty_2Eextreal_2Eextreal @ ( ap @ ( ap @ c_2Eextreal_2Eextreal__mul @ ( ap @ c_2Eextreal_2ENormal @ ( inj__ty_2Erealax_2Ereal @ V2c ) ) ) @ ( ap @ ( ap @ ( c_2Elebesgue_2Epos__fn__integral @ A_27a ) @ V0m ) @ V1f ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.58 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.cVVGufSnlR/cvc5---1.0.5_17260.p...
% 0.23/0.58 (declare-sort $$unsorted 0)
% 0.23/0.58 (declare-sort tptp.del 0)
% 0.23/0.58 (declare-fun tptp.bool () tptp.del)
% 0.23/0.58 (declare-fun tptp.ind () tptp.del)
% 0.23/0.58 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.23/0.58 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.23/0.58 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.23/0.58 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.23/0.58 (declare-fun tptp.p ($$unsorted) Bool)
% 0.23/0.58 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.23/0.58 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.23/0.58 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.23/0.58 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.23/0.58 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.23/0.58 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.23/0.58 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.23/0.58 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.23/0.58 (declare-fun tptp.ty_2Erealax_2Ereal () tptp.del)
% 0.23/0.58 (declare-sort tptp.tp__ty_2Erealax_2Ereal 0)
% 0.23/0.58 (declare-fun tptp.inj__ty_2Erealax_2Ereal (tptp.tp__ty_2Erealax_2Ereal) $$unsorted)
% 0.23/0.58 (declare-fun tptp.surj__ty_2Erealax_2Ereal ($$unsorted) tptp.tp__ty_2Erealax_2Ereal)
% 0.23/0.58 (assert (forall ((X tptp.tp__ty_2Erealax_2Ereal)) (= (@ tptp.surj__ty_2Erealax_2Ereal (@ tptp.inj__ty_2Erealax_2Ereal X)) X)))
% 0.23/0.58 (assert (forall ((X tptp.tp__ty_2Erealax_2Ereal)) (@ (@ tptp.mem (@ tptp.inj__ty_2Erealax_2Ereal X)) tptp.ty_2Erealax_2Ereal)))
% 0.23/0.58 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Erealax_2Ereal) (= X (@ tptp.inj__ty_2Erealax_2Ereal (@ tptp.surj__ty_2Erealax_2Ereal X))))))
% 0.23/0.58 (declare-fun tptp.ty_2Epair_2Eprod (tptp.del tptp.del) tptp.del)
% 0.23/0.58 (declare-fun tptp.c_2Emeasure_2Em__space (tptp.del) $$unsorted)
% 0.23/0.58 (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_2Emeasure_2Em__space A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_1) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_2 tptp.bool)) (@ _let_2 tptp.ty_2Erealax_2Ereal)))) _let_1))))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2EBOUNDED () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EBOUNDED) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.23/0.58 (declare-fun tptp.c_2Ecombin_2ES (tptp.del tptp.del tptp.del) $$unsorted)
% 0.23/0.58 (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)))))))
% 0.23/0.58 (declare-fun tptp.c_2Ecombin_2EC (tptp.del tptp.del tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ tptp.arr A_27b))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Ecombin_2EC A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ _let_1 (@ _let_2 A_27c))) (@ _let_2 (@ _let_1 A_27c))))))))
% 0.23/0.58 (declare-fun tptp.c_2Ecombin_2EI (tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ecombin_2EI A_27a)) (@ (@ tptp.arr A_27a) A_27a))))
% 0.23/0.58 (declare-fun tptp.c_2Ecombin_2Eo (tptp.del tptp.del tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ (@ (@ tptp.c_2Ecombin_2Eo A_27a) A_27b) A_27c)) (@ (@ tptp.arr (@ (@ tptp.arr A_27c) A_27b)) (@ (@ tptp.arr (@ _let_1 A_27c)) (@ _let_1 A_27b)))))))
% 0.23/0.58 (declare-fun tptp.ty_2Enum_2Enum () tptp.del)
% 0.23/0.58 (declare-sort tptp.tp__ty_2Enum_2Enum 0)
% 0.23/0.58 (declare-fun tptp.inj__ty_2Enum_2Enum (tptp.tp__ty_2Enum_2Enum) $$unsorted)
% 0.23/0.58 (declare-fun tptp.surj__ty_2Enum_2Enum ($$unsorted) tptp.tp__ty_2Enum_2Enum)
% 0.23/0.58 (assert (forall ((X tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ tptp.inj__ty_2Enum_2Enum X)) X)))
% 0.23/0.58 (assert (forall ((X tptp.tp__ty_2Enum_2Enum)) (@ (@ tptp.mem (@ tptp.inj__ty_2Enum_2Enum X)) tptp.ty_2Enum_2Enum)))
% 0.23/0.58 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Enum_2Enum) (= X (@ tptp.inj__ty_2Enum_2Enum (@ tptp.surj__ty_2Enum_2Enum X))))))
% 0.23/0.58 (declare-fun tptp.ty_2Eextreal_2Eextreal () tptp.del)
% 0.23/0.58 (declare-sort tptp.tp__ty_2Eextreal_2Eextreal 0)
% 0.23/0.58 (declare-fun tptp.inj__ty_2Eextreal_2Eextreal (tptp.tp__ty_2Eextreal_2Eextreal) $$unsorted)
% 0.23/0.58 (declare-fun tptp.surj__ty_2Eextreal_2Eextreal ($$unsorted) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ tptp.inj__ty_2Eextreal_2Eextreal X)) X)))
% 0.23/0.58 (assert (forall ((X tptp.tp__ty_2Eextreal_2Eextreal)) (@ (@ tptp.mem (@ tptp.inj__ty_2Eextreal_2Eextreal X)) tptp.ty_2Eextreal_2Eextreal)))
% 0.23/0.58 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Eextreal_2Eextreal) (= X (@ tptp.inj__ty_2Eextreal_2Eextreal (@ tptp.surj__ty_2Eextreal_2Eextreal X))))))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2EPosInf () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Eextreal_2EPosInf) tptp.ty_2Eextreal_2Eextreal))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2EPosInf () tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (= (@ tptp.inj__ty_2Eextreal_2Eextreal tptp.fo__c_2Eextreal_2EPosInf) tptp.c_2Eextreal_2EPosInf))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2ENegInf () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Eextreal_2ENegInf) tptp.ty_2Eextreal_2Eextreal))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2ENegInf () tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (= (@ tptp.inj__ty_2Eextreal_2Eextreal tptp.fo__c_2Eextreal_2ENegInf) tptp.c_2Eextreal_2ENegInf))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2Eextreal__inv () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__inv) (@ (@ tptp.arr tptp.ty_2Eextreal_2Eextreal) tptp.ty_2Eextreal_2Eextreal)))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2Eextreal__inv (tptp.tp__ty_2Eextreal_2Eextreal) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ tptp.fo__c_2Eextreal_2Eextreal__inv X0)) (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__inv) (@ tptp.inj__ty_2Eextreal_2Eextreal X0)))))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2Eextreal__div () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Eextreal_2Eextreal))) (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__div) (@ _let_1 (@ _let_1 tptp.ty_2Eextreal_2Eextreal)))))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2Eextreal__div (tptp.tp__ty_2Eextreal_2Eextreal tptp.tp__ty_2Eextreal_2Eextreal) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal) (X1 tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ (@ tptp.fo__c_2Eextreal_2Eextreal__div X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__div) (@ tptp.inj__ty_2Eextreal_2Eextreal X0))) (@ tptp.inj__ty_2Eextreal_2Eextreal X1)))))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2Eextreal__le () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Eextreal_2Eextreal))) (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__le) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2Eextreal__sup () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__sup) (@ (@ tptp.arr (@ (@ tptp.arr tptp.ty_2Eextreal_2Eextreal) tptp.bool)) tptp.ty_2Eextreal_2Eextreal)))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2ENormal () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Eextreal_2ENormal) (@ (@ tptp.arr tptp.ty_2Erealax_2Ereal) tptp.ty_2Eextreal_2Eextreal)))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2ENormal (tptp.tp__ty_2Erealax_2Ereal) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Erealax_2Ereal)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ tptp.fo__c_2Eextreal_2ENormal X0)) (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) (@ tptp.inj__ty_2Erealax_2Ereal X0)))))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2Eextreal__mul () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Eextreal_2Eextreal))) (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__mul) (@ _let_1 (@ _let_1 tptp.ty_2Eextreal_2Eextreal)))))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2Eextreal__mul (tptp.tp__ty_2Eextreal_2Eextreal tptp.tp__ty_2Eextreal_2Eextreal) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Eextreal_2Eextreal) (X1 tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ (@ tptp.fo__c_2Eextreal_2Eextreal__mul X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) (@ tptp.inj__ty_2Eextreal_2Eextreal X0))) (@ tptp.inj__ty_2Eextreal_2Eextreal X1)))))
% 0.23/0.58 (declare-fun tptp.c_2Elebesgue_2Epsfis (tptp.del) $$unsorted)
% 0.23/0.58 (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_2Elebesgue_2Epsfis A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_3 tptp.bool)) (@ _let_3 tptp.ty_2Erealax_2Ereal)))) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Eextreal_2Eextreal)) (@ (@ tptp.arr tptp.ty_2Eextreal_2Eextreal) tptp.bool)))))))))
% 0.23/0.58 (declare-fun tptp.c_2Eextreal_2Eextreal__of__num () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Eextreal_2Eextreal__of__num) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Eextreal_2Eextreal)))
% 0.23/0.58 (declare-fun tptp.fo__c_2Eextreal_2Eextreal__of__num (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Eextreal_2Eextreal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Eextreal_2Eextreal (@ tptp.fo__c_2Eextreal_2Eextreal__of__num X0)) (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__of__num) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 0.23/0.58 (declare-fun tptp.c_2Elebesgue_2Epos__fn__integral (tptp.del) $$unsorted)
% 0.23/0.58 (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_2Elebesgue_2Epos__fn__integral A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_2) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_3 tptp.bool)) (@ _let_3 tptp.ty_2Erealax_2Ereal)))) (@ (@ tptp.arr (@ _let_1 tptp.ty_2Eextreal_2Eextreal)) tptp.ty_2Eextreal_2Eextreal))))))))
% 0.23/0.58 (declare-fun tptp.c_2Emeasure_2Emeasure__space (tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Emeasure_2Emeasure__space A_27a)) (@ (@ tptp.arr (@ (@ tptp.ty_2Epair_2Eprod _let_1) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_2 tptp.bool)) (@ _let_2 tptp.ty_2Erealax_2Ereal)))) tptp.bool))))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.23/0.58 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.23/0.58 (declare-fun tptp.c_2Epair_2E_2C (tptp.del tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)) (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) A_27b))))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2E_3F (tptp.del) $$unsorted)
% 0.23/0.58 (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))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (declare-fun tptp.c_2Epred__set_2EGSPEC (tptp.del tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Epred__set_2EGSPEC A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) (@ (@ tptp.ty_2Epair_2Eprod A_27a) tptp.bool))) (@ (@ tptp.arr A_27a) tptp.bool)))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2EIN (tptp.del) $$unsorted)
% 0.23/0.58 (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))))))
% 0.23/0.58 (declare-fun tptp.c_2Erealax_2Ereal__lt () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Erealax_2Ereal))) (@ (@ tptp.mem tptp.c_2Erealax_2Ereal__lt) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.23/0.58 (declare-fun tptp.c_2Erealax_2Einv () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Erealax_2Einv) (@ (@ tptp.arr tptp.ty_2Erealax_2Ereal) tptp.ty_2Erealax_2Ereal)))
% 0.23/0.58 (declare-fun tptp.fo__c_2Erealax_2Einv (tptp.tp__ty_2Erealax_2Ereal) tptp.tp__ty_2Erealax_2Ereal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Erealax_2Ereal)) (= (@ tptp.inj__ty_2Erealax_2Ereal (@ tptp.fo__c_2Erealax_2Einv X0)) (@ (@ tptp.ap tptp.c_2Erealax_2Einv) (@ tptp.inj__ty_2Erealax_2Ereal X0)))))
% 0.23/0.58 (declare-fun tptp.c_2Enum_2E0 () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Enum_2E0) tptp.ty_2Enum_2Enum))
% 0.23/0.58 (declare-fun tptp.fo__c_2Enum_2E0 () tptp.tp__ty_2Enum_2Enum)
% 0.23/0.58 (assert (= (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0) tptp.c_2Enum_2E0))
% 0.23/0.58 (declare-fun tptp.c_2Ereal_2Ereal__of__num () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Ereal_2Ereal__of__num) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) tptp.ty_2Erealax_2Ereal)))
% 0.23/0.58 (declare-fun tptp.fo__c_2Ereal_2Ereal__of__num (tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Erealax_2Ereal)
% 0.23/0.58 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Erealax_2Ereal (@ tptp.fo__c_2Ereal_2Ereal__of__num X0)) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) (@ tptp.inj__ty_2Enum_2Enum X0)))))
% 0.23/0.58 (declare-fun tptp.c_2Ereal_2Ereal__lte () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Erealax_2Ereal))) (@ (@ tptp.mem tptp.c_2Ereal_2Ereal__lte) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.23/0.58 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.23/0.58 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 0.23/0.58 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.23/0.58 (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))))))
% 0.23/0.58 (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)))))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.23/0.58 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_5C_2F) Q)) R)) (or (@ tptp.p Q) (@ tptp.p R))))))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.23/0.58 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.23/0.58 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.23/0.58 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.23/0.58 (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))))))))
% 0.23/0.58 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.23/0.58 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.23/0.58 (assert (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) (@ (@ tptp.arr A_27a) A_27b)) (= (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0t) V1x))) V0t))))
% 0.23/0.58 (assert true)
% 0.23/0.58 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (let ((_let_1 (@ tptp.p V1t2))) (let ((_let_2 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V1t2) tptp.bool) (=> (=> _let_2 _let_1) (=> (=> _let_1 _let_2) (= _let_2 _let_1))))))))))
% 0.23/0.58 (assert (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (=> false (@ tptp.p V0t)))))
% 0.23/0.58 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or _let_1 (not _let_1))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (@ tptp.p V0t))) (@ tptp.p V0t)))))
% 0.23/0.58 (assert (forall ((V0t $$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))))))
% 0.23/0.58 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (=> true _let_1) _let_1) (= (=> _let_1 true) true) (= (=> false _let_1) true) (= (=> _let_1 _let_1) true) (= (=> _let_1 false) (not _let_1)))))))
% 0.23/0.58 (assert (and (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))) (= (not true) false) (= (not false) true)))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= V0x V1y) (= V1y V0x)))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$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))))))))))
% 0.23/0.58 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (let ((_let_2 (not _let_1))) (=> (@ (@ tptp.mem V0t) tptp.bool) (and (= (= true _let_1) _let_1) (= (= _let_1 true) _let_1) (= (= false _let_1) _let_2) (= (= _let_1 false) _let_2)))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0P $$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 $$unsorted)) (=> (@ (@ tptp.mem V3x) A_27a) (and (@ tptp.p V0P) (@ tptp.p (@ (@ tptp.ap V1Q) V3x)))))))))))
% 0.23/0.58 (assert (forall ((V0A $$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)))))))))))))
% 0.23/0.58 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) tptp.bool) (forall ((V2t3 $$unsorted)) (let ((_let_1 (@ tptp.p V2t3))) (let ((_let_2 (@ tptp.p V1t2))) (let ((_let_3 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V2t3) tptp.bool) (= (=> _let_3 (=> _let_2 _let_1)) (=> (and _let_3 _let_2) _let_1))))))))))))
% 0.23/0.58 (assert (forall ((V0x $$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 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (= _let_4 _let_2) (=> _let_2 (= _let_3 _let_1))) (= (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0P $$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))))))))
% 0.23/0.58 (assert (forall ((V0v $$unsorted)) (=> (@ (@ tptp.mem V0v) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2EBOUNDED) V0v)) true))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del)) (= (@ (@ (@ tptp.c_2Ecombin_2ES A_27a) A_27b) A_27c) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) (@ (@ tptp.arr A_27b) A_27c))) (lambda ((V0f $$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)))))))))))
% 0.23/0.58 (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 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap V0f) V2y)) V1x))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (A_27c tptp.del) (V0f $$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))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (@ (@ tptp.ap (@ tptp.c_2Ecombin_2EI A_27a)) V0x) V0x))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$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))))))
% 0.23/0.58 (assert (forall ((V0n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V0n))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__of__num) _let_1)) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) _let_1)))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Erealax_2Ereal) (V1y tptp.tp__ty_2Erealax_2Ereal) (V2a tptp.tp__ty_2Eextreal_2Eextreal) (V3v2 tptp.tp__ty_2Erealax_2Ereal) (V4v3 tptp.tp__ty_2Erealax_2Ereal) (V5v5 tptp.tp__ty_2Erealax_2Ereal)) (let ((_let_1 (@ tptp.ap tptp.c_2Eextreal_2ENormal))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal tptp.fo__c_2Eextreal_2EPosInf))) (let ((_let_3 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (let ((_let_4 (@ tptp.ap (@ _let_3 _let_2)))) (let ((_let_5 (@ tptp.inj__ty_2Eextreal_2Eextreal tptp.fo__c_2Eextreal_2ENegInf))) (let ((_let_6 (@ tptp.inj__ty_2Erealax_2Ereal V1y))) (let ((_let_7 (@ tptp.inj__ty_2Erealax_2Ereal V0x))) (and (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_1 _let_7))) (@ _let_1 _let_6))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__lte) _let_7)) _let_6))) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 _let_5)) (@ tptp.inj__ty_2Eextreal_2Eextreal V2a))) true) (= (@ tptp.p (@ _let_4 _let_2)) true) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_1 (@ tptp.inj__ty_2Erealax_2Ereal V3v2)))) _let_2)) true) (= (@ tptp.p (@ _let_4 _let_5)) false) (= (@ tptp.p (@ (@ tptp.ap (@ _let_3 (@ _let_1 (@ tptp.inj__ty_2Erealax_2Ereal V4v3)))) _let_5)) false) (= (@ tptp.p (@ _let_4 (@ _let_1 (@ tptp.inj__ty_2Erealax_2Ereal V5v5)))) false)))))))))))
% 0.23/0.58 (assert (let ((_let_1 (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))) (let ((_let_2 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__inv))) (and (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ _let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal tptp.fo__c_2Eextreal_2ENegInf))) _let_1) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ _let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal tptp.fo__c_2Eextreal_2EPosInf))) _let_1) (forall ((V0x tptp.tp__ty_2Erealax_2Ereal)) (let ((_let_1 (@ tptp.inj__ty_2Erealax_2Ereal V0x))) (let ((_let_2 (@ tptp.ap tptp.c_2Eextreal_2ENormal))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__inv) (@ _let_2 _let_1))) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ _let_2 (@ (@ tptp.ap tptp.c_2Erealax_2Einv) _let_1)))))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__div) _let_2)) _let_1)) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) _let_2)) (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__inv) _let_1))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) _let_1)) (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (@ tptp.surj__ty_2Eextreal_2Eextreal _let_1)))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal) (V2z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V2z))) (let ((_let_3 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) _let_2)))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_5 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__of__num) (@ 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)))))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Eextreal_2Eextreal) (V1y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V0x))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_3 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul))) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Erealax_2Ereal) (V1y tptp.tp__ty_2Eextreal_2Eextreal) (V2z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Erealax_2Ereal V0x))) (let ((_let_2 (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) _let_1))) (let ((_let_3 (@ tptp.inj__ty_2Eextreal_2Eextreal V2z))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_5 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Erealax_2Ereal__lt) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) _let_1)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) _let_4)) _let_2))) _let_3)) (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__div) _let_3)) _let_2))))))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Erealax_2Ereal) (V1y tptp.tp__ty_2Eextreal_2Eextreal) (V2z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V2z))) (let ((_let_2 (@ tptp.inj__ty_2Erealax_2Ereal V0x))) (let ((_let_3 (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) _let_2))) (let ((_let_4 (@ tptp.inj__ty_2Eextreal_2Eextreal V1y))) (let ((_let_5 (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Erealax_2Ereal__lt) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) _let_2)) (= (@ tptp.p (@ (@ tptp.ap (@ _let_5 _let_4)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) _let_1)) _let_3))) (@ tptp.p (@ (@ tptp.ap (@ _let_5 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__div) _let_4)) _let_3))) _let_1)))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr tptp.ty_2Eextreal_2Eextreal) tptp.bool)) (forall ((V1x tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__sup) V0p))) (@ tptp.inj__ty_2Eextreal_2Eextreal V1x))) (forall ((V2y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V2y))) (=> (@ tptp.p (@ (@ tptp.ap V0p) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) _let_1)) (@ tptp.inj__ty_2Eextreal_2Eextreal V1x)))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr tptp.ty_2Eextreal_2Eextreal) tptp.bool)) (forall ((V1x tptp.tp__ty_2Eextreal_2Eextreal)) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) (@ tptp.inj__ty_2Eextreal_2Eextreal V1x))) (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__sup) V0p))) (forall ((V2y tptp.tp__ty_2Eextreal_2Eextreal)) (=> (forall ((V3z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V3z))) (=> (@ tptp.p (@ (@ tptp.ap V0p) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) _let_1)) (@ tptp.inj__ty_2Eextreal_2Eextreal V2y)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) (@ tptp.inj__ty_2Eextreal_2Eextreal V1x))) (@ tptp.inj__ty_2Eextreal_2Eextreal V2y))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) (@ (@ tptp.arr tptp.ty_2Eextreal_2Eextreal) tptp.bool)) (forall ((V1x tptp.tp__ty_2Eextreal_2Eextreal)) (= (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__sup) V0p)) V1x) (and (forall ((V2y tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V2y))) (=> (@ tptp.p (@ (@ tptp.ap V0p) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) _let_1)) (@ tptp.inj__ty_2Eextreal_2Eextreal V1x)))))) (forall ((V3y tptp.tp__ty_2Eextreal_2Eextreal)) (=> (forall ((V4z tptp.tp__ty_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.inj__ty_2Eextreal_2Eextreal V4z))) (=> (@ tptp.p (@ (@ tptp.ap V0p) _let_1)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) _let_1)) (@ tptp.inj__ty_2Eextreal_2Eextreal V3y)))))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) (@ tptp.inj__ty_2Eextreal_2Eextreal V1x))) (@ tptp.inj__ty_2Eextreal_2Eextreal V3y)))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.ty_2Epair_2Eprod _let_1) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_2 tptp.bool)) (@ _let_2 tptp.ty_2Erealax_2Ereal)))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.ty_2Eextreal_2Eextreal)) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Elebesgue_2Epos__fn__integral A_27a)) V0m)) V1f)) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__sup) (@ (@ tptp.ap (@ (@ tptp.c_2Epred__set_2EGSPEC tptp.ty_2Eextreal_2Eextreal) tptp.ty_2Eextreal_2Eextreal)) (@ (@ tptp.lam tptp.ty_2Eextreal_2Eextreal) (lambda ((V2r $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.ty_2Eextreal_2Eextreal))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C tptp.ty_2Eextreal_2Eextreal) tptp.bool)) V2r)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F _let_1)) (@ (@ tptp.lam _let_1) (lambda ((V3g $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Eextreal_2Eextreal)) V2r)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Elebesgue_2Epsfis A_27a)) V0m)) V3g)))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__le) (@ (@ tptp.ap V3g) V4x))) (@ (@ tptp.ap V1f) V4x))))))))))))))))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.ty_2Epair_2Eprod _let_1) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_2 tptp.bool)) (@ _let_2 tptp.ty_2Erealax_2Ereal)))) (forall ((V1f $$unsorted)) (=> (@ (@ tptp.mem V1f) (@ (@ tptp.arr A_27a) tptp.ty_2Eextreal_2Eextreal)) (forall ((V2a tptp.tp__ty_2Eextreal_2Eextreal) (V3z tptp.tp__ty_2Erealax_2Ereal)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Elebesgue_2Epsfis A_27a)) V0m)))) (let ((_let_2 (@ tptp.inj__ty_2Eextreal_2Eextreal V2a))) (let ((_let_3 (@ tptp.inj__ty_2Erealax_2Ereal V3z))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ebool_2EIN tptp.ty_2Eextreal_2Eextreal)))) (=> (and (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Emeasure_2Emeasure__space A_27a)) V0m)) (@ tptp.p (@ (@ tptp.ap (@ _let_4 _let_2)) (@ _let_1 V1f))) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__lte) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))) _let_3))) (@ tptp.p (@ (@ tptp.ap (@ _let_4 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) _let_3))) _let_2))) (@ _let_1 (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__mul) (@ (@ tptp.ap tptp.c_2Eextreal_2ENormal) (@ tptp.inj__ty_2Erealax_2Ereal V3z)))) (@ (@ tptp.ap V1f) V4x))))))))))))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0m $$unsorted)) (let ((_let_1 (@ (@ tptp.arr A_27a) tptp.bool))) (let ((_let_2 (@ tptp.arr _let_1))) (=> (@ (@ tptp.mem V0m) (@ (@ tptp.ty_2Epair_2Eprod _let_1) (@ (@ tptp.ty_2Epair_2Eprod (@ _let_2 tptp.bool)) (@ _let_2 tptp.ty_2Erealax_2Ereal)))) (=> (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Emeasure_2Emeasure__space A_27a)) V0m)) (= (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Elebesgue_2Epos__fn__integral A_27a)) V0m)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))) (@ tptp.surj__ty_2Eextreal_2Eextreal (@ (@ tptp.ap tptp.c_2Eextreal_2Eextreal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27b) (forall ((V2a $$unsorted)) (=> (@ (@ tptp.mem V2a) A_27a) (forall ((V3b $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.c_2Epair_2E_2C A_27a) A_27b)))) (=> (@ (@ tptp.mem V3b) A_27b) (= (= (@ (@ tptp.ap (@ _let_1 V0x)) V1y) (@ (@ tptp.ap (@ _let_1 V2a)) V3b)) (and (= V0x V2a) (= V1y V3b)))))))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (=> (@ (@ tptp.mem V1x) A_27a) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V1x)) V0P)) (@ tptp.p (@ (@ tptp.ap V0P) V1x))))))))
% 0.23/0.58 (assert (forall ((A_27a tptp.del) (A_27b tptp.del) (V0f $$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))))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Erealax_2Ereal) (V1y tptp.tp__ty_2Erealax_2Ereal)) (let ((_let_1 (@ tptp.inj__ty_2Erealax_2Ereal V1y))) (let ((_let_2 (@ tptp.inj__ty_2Erealax_2Ereal V0x))) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Erealax_2Ereal__lt) _let_2)) _let_1)) (and (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__lte) _let_2)) _let_1)) (not (= V0x V1y))))))))
% 0.23/0.58 (assert (forall ((V0x tptp.tp__ty_2Erealax_2Ereal)) (let ((_let_1 (@ tptp.inj__ty_2Erealax_2Ereal V0x))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__lte) (@ (@ tptp.ap tptp.c_2Ereal_2Ereal__of__num) (@ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)))))) (=> (@ tptp.p (@ _let_2 _let_1)) (@ tptp.p (@ _let_2 (@ (@ tptp.ap tptp.c_2Erealax_2Einv) _let_1))))))))
% 0.23/0.58 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (= (not (not _let_1)) _let_1)))))
% 0.23/0.58 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> _let_1 (=> (not _let_1) false))))))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (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))))))))))
% 0.23/0.58 (assert (forall ((V0A $$unsorted)) (let ((_let_1 (@ tptp.p V0A))) (=> (@ (@ tptp.mem V0A) tptp.bool) (=> (=> (not _let_1) false) (=> (=> _let_1 false) false))))))
% 0.23/0.58 (assert (forall ((V0p $$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))))))))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.p V2r))) (let ((_let_4 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (and _let_4 _let_3)) (and (or _let_1 (not _let_4) (not _let_3)) (or _let_4 _let_2) (or _let_3 _let_2))))))))))))))
% 0.23/0.58 (assert (forall ((V0p $$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))))))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (=> (@ (@ tptp.mem V1q) tptp.bool) (forall ((V2r $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V2r))) (let ((_let_3 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V2r) tptp.bool) (= (= _let_1 (=> _let_3 _let_2)) (and (or _let_1 _let_3) (or _let_1 (not _let_2)) (or (not _let_3) _let_2 (not _let_1))))))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (let ((_let_2 (@ tptp.p V1q))) (let ((_let_3 (not _let_2))) (=> (@ (@ tptp.mem V1q) tptp.bool) (= (= _let_1 _let_3) (and (or _let_1 _let_2) (or _let_3 (not _let_1))))))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V0p))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (not (=> _let_1 (@ tptp.p V1q))) _let_1)))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsorted)) (let ((_let_1 (@ tptp.p V1q))) (=> (@ (@ tptp.mem V1q) tptp.bool) (=> (not (=> (@ tptp.p V0p) _let_1)) (not _let_1))))))))
% 0.23/0.58 (assert (forall ((V0p $$unsorted)) (=> (@ (@ tptp.mem V0p) tptp.bool) (forall ((V1q $$unsor/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 17387 Alarm clock ( read result; case "$result" in
% 299.95/300.18 unsat)
% 299.95/300.18 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.95/300.18 ;;
% 299.95/300.18 sat)
% 299.95/300.18 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.95/300.18 ;;
% 299.95/300.18 esac; exit 1 )
% 299.95/300.19 Alarm clock
% 299.95/300.19 % cvc5---1.0.5 exiting
% 299.95/300.19 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------