TSTP Solution File: ITP001^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP001^5 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 03:13:50 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ITP001^5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 15:55:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : ITP001^5 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.21/0.52 % Domain : Interactive Theorem Proving
% 0.21/0.52 % Problem : HOL4 set theory export of thm_2Ebool_2ETRUTH.p, chainy mode
% 0.21/0.52 % Version : [BG+19] axioms.
% 0.21/0.52 % English :
% 0.21/0.52
% 0.21/0.52 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.21/0.52 % : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% 0.21/0.52 % Source : [BG+19]
% 0.21/0.52 % Names : thm_2Ebool_2ETRUTH.p [Gau20]
% 0.21/0.52 % : HL400001^5.p [TPAP]
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % Rating : 0.08 v8.1.0, 0.09 v7.5.0
% 0.21/0.52 % Syntax : Number of formulae : 114 ( 26 unt; 41 typ; 0 def)
% 0.21/0.52 % Number of atoms : 547 ( 29 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 12 ( 7 avg)
% 0.21/0.52 % Number of connectives : 889 ( 3 ~; 2 |; 4 &; 839 @)
% 0.21/0.52 % ( 11 <=>; 30 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 13 ( 6 avg)
% 0.21/0.52 % Number of types : 4 ( 2 usr)
% 0.21/0.52 % Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 52 ( 49 usr; 21 con; 0-2 aty)
% 0.21/0.52 % Number of variables : 149 ( 54 ^; 93 !; 2 ?; 149 :)
% 0.21/0.52 % SPC : TH0_THM_EQU_NAR
% 0.21/0.52
% 0.21/0.52 % Comments :
% 0.21/0.52 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(del_tp,type,
% 0.21/0.52 del: $tType ).
% 0.21/0.52
% 0.21/0.52 thf(bool,type,
% 0.21/0.52 bool: del ).
% 0.21/0.52
% 0.21/0.52 thf(ind,type,
% 0.21/0.52 ind: del ).
% 0.21/0.52
% 0.21/0.52 thf(arr,type,
% 0.21/0.52 arr: del > del > del ).
% 0.21/0.52
% 0.21/0.52 thf(mem,type,
% 0.21/0.52 mem: $i > del > $o ).
% 0.21/0.52
% 0.21/0.52 thf(ap,type,
% 0.21/0.52 ap: $i > $i > $i ).
% 0.21/0.52
% 0.21/0.52 thf(lam,type,
% 0.21/0.52 lam: del > ( $i > $i ) > $i ).
% 0.21/0.52
% 0.21/0.52 thf(p,type,
% 0.21/0.52 p: $i > $o ).
% 0.21/0.52
% 0.21/0.52 thf(stp_inj_o,type,
% 0.21/0.52 inj__o: $o > $i ).
% 0.21/0.52
% 0.21/0.52 thf(stp_inj_surj_o,axiom,
% 0.21/0.52 ! [X: $o] :
% 0.21/0.52 ( ( p @ ( inj__o @ X ) )
% 0.21/0.52 = X ) ).
% 0.21/0.52
% 0.21/0.52 thf(stp_inj_mem_o,axiom,
% 0.21/0.52 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.21/0.52
% 0.21/0.52 thf(stp_iso_mem_o,axiom,
% 0.21/0.52 ! [X: $i] :
% 0.21/0.52 ( ( mem @ X @ bool )
% 0.21/0.52 => ( X
% 0.21/0.52 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ap_tp,axiom,
% 0.21/0.52 ! [A: del,B: del,F: $i] :
% 0.21/0.52 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.52 => ! [X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(lam_tp,axiom,
% 0.21/0.52 ! [A: del,B: del,F: $i > $i] :
% 0.21/0.52 ( ! [X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 => ( mem @ ( F @ X ) @ B ) )
% 0.21/0.52 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(funcext,axiom,
% 0.21/0.52 ! [A: del,B: del,F: $i] :
% 0.21/0.52 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.52 => ! [G: $i] :
% 0.21/0.52 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.21/0.52 => ( ! [X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 => ( ( ap @ F @ X )
% 0.21/0.52 = ( ap @ G @ X ) ) )
% 0.21/0.52 => ( F = G ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(beta,axiom,
% 0.21/0.52 ! [A: del,F: $i > $i,X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.21/0.52 = ( F @ X ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(tp_c_2Emin_2E_3D,type,
% 0.21/0.52 c_2Emin_2E_3D: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Emin_2E_3D,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_eq_p,axiom,
% 0.21/0.52 ! [A: del,X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 => ! [Y: $i] :
% 0.21/0.52 ( ( mem @ Y @ A )
% 0.21/0.52 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.21/0.52 <=> ( X = Y ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.21/0.52 c_2Emin_2E_3D_3D_3E: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.21/0.52 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_imp_p,axiom,
% 0.21/0.52 ! [Q: $i] :
% 0.21/0.52 ( ( mem @ Q @ bool )
% 0.21/0.52 => ! [R: $i] :
% 0.21/0.52 ( ( mem @ R @ bool )
% 0.21/0.52 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.21/0.52 <=> ( ( p @ Q )
% 0.21/0.52 => ( p @ R ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Emin_2E_40,type,
% 0.21/0.52 c_2Emin_2E_40: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Emin_2E_40,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_40 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(tp_ty_2Ebool_2Eitself,type,
% 0.21/0.52 ty_2Ebool_2Eitself: del > del ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2E_21,type,
% 0.21/0.52 c_2Ebool_2E_21: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2E_21,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_all_p,axiom,
% 0.21/0.52 ! [A: del,Q: $i] :
% 0.21/0.52 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.21/0.52 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.21/0.52 <=> ! [X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.21/0.52 c_2Ebool_2E_2F_5C: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.21/0.52 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_and_p,axiom,
% 0.21/0.52 ! [Q: $i] :
% 0.21/0.52 ( ( mem @ Q @ bool )
% 0.21/0.52 => ! [R: $i] :
% 0.21/0.52 ( ( mem @ R @ bool )
% 0.21/0.52 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.21/0.52 <=> ( ( p @ Q )
% 0.21/0.52 & ( p @ R ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2E_3F,type,
% 0.21/0.52 c_2Ebool_2E_3F: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2E_3F,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_ex_p,axiom,
% 0.21/0.52 ! [A: del,Q: $i] :
% 0.21/0.52 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.21/0.52 => ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
% 0.21/0.52 <=> ? [X: $i] :
% 0.21/0.52 ( ( mem @ X @ A )
% 0.21/0.52 & ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2E_3F_21,type,
% 0.21/0.52 c_2Ebool_2E_3F_21: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2E_3F_21,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EARB,type,
% 0.21/0.52 c_2Ebool_2EARB: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EARB,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EARB @ A_27a ) @ A_27a ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EBOUNDED,type,
% 0.21/0.52 c_2Ebool_2EBOUNDED: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EBOUNDED,axiom,
% 0.21/0.52 mem @ c_2Ebool_2EBOUNDED @ ( arr @ bool @ bool ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ECOND,type,
% 0.21/0.52 c_2Ebool_2ECOND: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ECOND,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EDATATYPE,type,
% 0.21/0.52 c_2Ebool_2EDATATYPE: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EDATATYPE,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EDATATYPE @ A_27a ) @ ( arr @ A_27a @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EF,type,
% 0.21/0.52 c_2Ebool_2EF: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EF,axiom,
% 0.21/0.52 mem @ c_2Ebool_2EF @ bool ).
% 0.21/0.52
% 0.21/0.52 thf(ax_false_p,axiom,
% 0.21/0.52 ~ ( p @ c_2Ebool_2EF ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EIN,type,
% 0.21/0.52 c_2Ebool_2EIN: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EIN,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2EIN @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ELET,type,
% 0.21/0.52 c_2Ebool_2ELET: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ELET,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ELET @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EONE__ONE,type,
% 0.21/0.52 c_2Ebool_2EONE__ONE: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EONE__ONE,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2EONTO,type,
% 0.21/0.52 c_2Ebool_2EONTO: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2EONTO,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2EONTO @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ERES__ABSTRACT,type,
% 0.21/0.52 c_2Ebool_2ERES__ABSTRACT: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ERES__ABSTRACT,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ERES__ABSTRACT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ERES__EXISTS,type,
% 0.21/0.52 c_2Ebool_2ERES__EXISTS: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ERES__EXISTS,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ERES__EXISTS__UNIQUE,type,
% 0.21/0.52 c_2Ebool_2ERES__EXISTS__UNIQUE: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ERES__EXISTS__UNIQUE,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ERES__FORALL,type,
% 0.21/0.52 c_2Ebool_2ERES__FORALL: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ERES__FORALL,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ERES__SELECT,type,
% 0.21/0.52 c_2Ebool_2ERES__SELECT: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ERES__SELECT,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ERES__SELECT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ET,type,
% 0.21/0.52 c_2Ebool_2ET: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ET,axiom,
% 0.21/0.52 mem @ c_2Ebool_2ET @ bool ).
% 0.21/0.52
% 0.21/0.52 thf(ax_true_p,axiom,
% 0.21/0.52 p @ c_2Ebool_2ET ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2ETYPE__DEFINITION,type,
% 0.21/0.52 c_2Ebool_2ETYPE__DEFINITION: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2ETYPE__DEFINITION,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ A_27a ) @ bool ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2E_5C_2F,type,
% 0.21/0.52 c_2Ebool_2E_5C_2F: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.21/0.52 mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_or_p,axiom,
% 0.21/0.52 ! [Q: $i] :
% 0.21/0.52 ( ( mem @ Q @ bool )
% 0.21/0.52 => ! [R: $i] :
% 0.21/0.52 ( ( mem @ R @ bool )
% 0.21/0.52 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
% 0.21/0.52 <=> ( ( p @ Q )
% 0.21/0.52 | ( p @ R ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2Eitself__case,type,
% 0.21/0.52 c_2Ebool_2Eitself__case: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2Eitself__case,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eitself__case @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ( arr @ A_27b @ A_27b ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2Eliteral__case,type,
% 0.21/0.52 c_2Ebool_2Eliteral__case: del > del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2Eliteral__case,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27b ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2Ethe__value,type,
% 0.21/0.52 c_2Ebool_2Ethe__value: del > $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2Ethe__value,axiom,
% 0.21/0.52 ! [A_27a: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A_27a ) @ ( ty_2Ebool_2Eitself @ A_27a ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(tp_c_2Ebool_2E_7E,type,
% 0.21/0.52 c_2Ebool_2E_7E: $i ).
% 0.21/0.52
% 0.21/0.52 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.21/0.52 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_neg_p,axiom,
% 0.21/0.52 ! [Q: $i] :
% 0.21/0.52 ( ( mem @ Q @ bool )
% 0.21/0.52 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.21/0.52 <=> ~ ( p @ Q ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ET__DEF,axiom,
% 0.21/0.52 ( $true
% 0.21/0.52 <=> ( ( lam @ bool
% 0.21/0.52 @ ^ [V0x: $i] : V0x )
% 0.21/0.52 = ( lam @ bool
% 0.21/0.52 @ ^ [V1x: $i] : V1x ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EFORALL__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0P: $i] :
% 0.21/0.52 ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V0P )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V1x: $i] : c_2Ebool_2ET ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EEXISTS__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2E_3F @ A_27a )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0P: $i] : ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EAND__DEF,axiom,
% 0.21/0.52 ( c_2Ebool_2E_2F_5C
% 0.21/0.52 = ( lam @ bool
% 0.21/0.52 @ ^ [V0t1: $i] :
% 0.21/0.52 ( lam @ bool
% 0.21/0.52 @ ^ [V1t2: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ bool )
% 0.21/0.52 @ ( lam @ bool
% 0.21/0.52 @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) ) @ V2t ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EOR__DEF,axiom,
% 0.21/0.52 ( c_2Ebool_2E_5C_2F
% 0.21/0.52 = ( lam @ bool
% 0.21/0.52 @ ^ [V0t1: $i] :
% 0.21/0.52 ( lam @ bool
% 0.21/0.52 @ ^ [V1t2: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ bool )
% 0.21/0.52 @ ( lam @ bool
% 0.21/0.52 @ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t1 ) @ V2t ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V1t2 ) @ V2t ) ) @ V2t ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EF__DEF,axiom,
% 0.21/0.52 ( $false
% 0.21/0.52 <=> ! [V0t: $i] :
% 0.21/0.52 ( ( mem @ V0t @ bool )
% 0.21/0.52 => ( p @ V0t ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ENOT__DEF,axiom,
% 0.21/0.52 ( c_2Ebool_2E_7E
% 0.21/0.52 = ( lam @ bool
% 0.21/0.52 @ ^ [V0t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ V0t ) @ c_2Ebool_2EF ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2E_3F_21 @ A_27a )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0P: $i] :
% 0.21/0.52 ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ebool_2E_3F @ A_27a ) @ V0P ) )
% 0.21/0.52 @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V1x: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V2y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V1x ) ) @ ( ap @ V0P @ V2y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x ) @ V2y ) ) ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ELET__DEF,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] :
% 0.21/0.52 ( ( c_2Ebool_2ELET @ A_27a @ A_27b )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.21/0.52 @ ^ [V0f: $i] :
% 0.21/0.52 ( lam @ A_27a
% 0.21/0.52 @ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ECOND__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2ECOND @ A_27a )
% 0.21/0.52 = ( lam @ bool
% 0.21/0.52 @ ^ [V0t: $i] :
% 0.21/0.52 ( lam @ A_27a
% 0.21/0.52 @ ^ [V1t1: $i] :
% 0.21/0.52 ( lam @ A_27a
% 0.21/0.52 @ ^ [V2t2: $i] :
% 0.21/0.52 ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V1t1 ) ) ) @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0t ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V2t2 ) ) ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EONE__ONE__DEF,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] :
% 0.21/0.52 ( ( c_2Ebool_2EONE__ONE @ A_27a @ A_27b )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.21/0.52 @ ^ [V0f: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V1x1: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V2x2: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ ( ap @ V0f @ V1x1 ) ) @ ( ap @ V0f @ V2x2 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V1x1 ) @ V2x2 ) ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EONTO__DEF,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] :
% 0.21/0.52 ( ( c_2Ebool_2EONTO @ A_27a @ A_27b )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.21/0.52 @ ^ [V0f: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ A_27b )
% 0.21/0.52 @ ( lam @ A_27b
% 0.21/0.52 @ ^ [V1y: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1y ) @ ( ap @ V0f @ V2x ) ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ETYPE__DEFINITION,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] :
% 0.21/0.52 ( ( c_2Ebool_2ETYPE__DEFINITION @ A_27a @ A_27b )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0P: $i] :
% 0.21/0.52 ( lam @ ( arr @ A_27b @ A_27a )
% 0.21/0.52 @ ^ [V1rep: $i] :
% 0.21/0.52 ( ap
% 0.21/0.52 @ ( ap @ c_2Ebool_2E_2F_5C
% 0.21/0.52 @ ( ap @ ( c_2Ebool_2E_21 @ A_27b )
% 0.21/0.52 @ ( lam @ A_27b
% 0.21/0.52 @ ^ [V2x_27: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ A_27b )
% 0.21/0.52 @ ( lam @ A_27b
% 0.21/0.52 @ ^ [V3x_27_27: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ ( ap @ V1rep @ V2x_27 ) ) @ ( ap @ V1rep @ V3x_27_27 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V2x_27 ) @ V3x_27_27 ) ) ) ) ) ) )
% 0.21/0.52 @ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V4x: $i] :
% 0.21/0.52 ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V0P @ V4x ) )
% 0.21/0.52 @ ( ap @ ( c_2Ebool_2E_3F @ A_27b )
% 0.21/0.52 @ ( lam @ A_27b
% 0.21/0.52 @ ^ [V5x_27: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V4x ) @ ( ap @ V1rep @ V5x_27 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom,
% 0.21/0.52 ! [V0t: $i] :
% 0.21/0.52 ( ( mem @ V0t @ bool )
% 0.21/0.52 => ( ( ( p @ V0t )
% 0.21/0.52 <=> $true )
% 0.21/0.52 | ( ( p @ V0t )
% 0.21/0.52 <=> $false ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EETA__AX,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del,V0t: $i] :
% 0.21/0.52 ( ( mem @ V0t @ ( arr @ A_27a @ A_27b ) )
% 0.21/0.52 => ( ( lam @ A_27a
% 0.21/0.52 @ ^ [V1x: $i] : ( ap @ V0t @ V1x ) )
% 0.21/0.52 = V0t ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ESELECT__AX,axiom,
% 0.21/0.52 ! [A_27a: del,V0P: $i] :
% 0.21/0.52 ( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
% 0.21/0.52 => ! [V1x: $i] :
% 0.21/0.52 ( ( mem @ V1x @ A_27a )
% 0.21/0.52 => ( ( p @ ( ap @ V0P @ V1x ) )
% 0.21/0.52 => ( p @ ( ap @ V0P @ ( ap @ ( c_2Emin_2E_40 @ A_27a ) @ V0P ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(stp_i,type,
% 0.21/0.52 tp__i: $tType ).
% 0.21/0.52
% 0.21/0.52 thf(stp_inj_i,type,
% 0.21/0.52 inj__i: tp__i > $i ).
% 0.21/0.52
% 0.21/0.52 thf(stp_surj_i,type,
% 0.21/0.52 surj__i: $i > tp__i ).
% 0.21/0.52
% 0.21/0.52 thf(stp_inj_surj_i,axiom,
% 0.21/0.52 ! [X: tp__i] :
% 0.21/0.52 ( ( surj__i @ ( inj__i @ X ) )
% 0.21/0.52 = X ) ).
% 0.21/0.52
% 0.21/0.52 thf(stp_inj_mem_i,axiom,
% 0.21/0.52 ! [X: tp__i] : ( mem @ ( inj__i @ X ) @ ind ) ).
% 0.21/0.52
% 0.21/0.52 thf(stp_iso_mem_i,axiom,
% 0.21/0.52 ! [X: $i] :
% 0.21/0.52 ( ( mem @ X @ ind )
% 0.21/0.52 => ( X
% 0.21/0.52 = ( inj__i @ ( surj__i @ X ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EINFINITY__AX,axiom,
% 0.21/0.52 ? [V0f: $i] :
% 0.21/0.52 ( ( mem @ V0f @ ( arr @ ind @ ind ) )
% 0.21/0.52 & ( p @ ( ap @ ( c_2Ebool_2EONE__ONE @ ind @ ind ) @ V0f ) )
% 0.21/0.52 & ~ ( p @ ( ap @ ( c_2Ebool_2EONTO @ ind @ ind ) @ V0f ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2Eliteral__case__DEF,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] :
% 0.21/0.52 ( ( c_2Ebool_2Eliteral__case @ A_27a @ A_27b )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ A_27b )
% 0.21/0.52 @ ^ [V0f: $i] :
% 0.21/0.52 ( lam @ A_27a
% 0.21/0.52 @ ^ [V1x: $i] : ( ap @ V0f @ V1x ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2EIN__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2EIN @ A_27a )
% 0.21/0.52 = ( lam @ A_27a
% 0.21/0.52 @ ^ [V0x: $i] :
% 0.21/0.52 ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V1f: $i] : ( ap @ V1f @ V0x ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ERES__FORALL__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2ERES__FORALL @ A_27a )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0p: $i] :
% 0.21/0.52 ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V1m: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_21 @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ERES__EXISTS__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2ERES__EXISTS @ A_27a )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0p: $i] :
% 0.21/0.52 ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V1m: $i] :
% 0.21/0.52 ( ap @ ( c_2Ebool_2E_3F @ A_27a )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ( c_2Ebool_2ERES__EXISTS__UNIQUE @ A_27a )
% 0.21/0.52 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V0p: $i] :
% 0.21/0.52 ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.52 @ ^ [V1m: $i] :
% 0.21/0.52 ( ap
% 0.21/0.52 @ ( ap @ c_2Ebool_2E_2F_5C
% 0.21/0.52 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__EXISTS @ A_27a ) @ V0p )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.52 @ ^ [V2x: $i] : ( ap @ V1m @ V2x ) ) ) )
% 0.21/0.52 @ ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
% 0.21/0.52 @ ( lam @ A_27a
% 0.21/0.54 @ ^ [V3x: $i] :
% 0.21/0.54 ( ap @ ( ap @ ( c_2Ebool_2ERES__FORALL @ A_27a ) @ V0p )
% 0.21/0.54 @ ( lam @ A_27a
% 0.21/0.54 @ ^ [V4y: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1m @ V3x ) ) @ ( ap @ V1m @ V4y ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3x ) @ V4y ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(ax_thm_2Ebool_2ERES__SELECT__DEF,axiom,
% 0.21/0.54 ! [A_27a: del] :
% 0.21/0.54 ( ( c_2Ebool_2ERES__SELECT @ A_27a )
% 0.21/0.54 = ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.54 @ ^ [V0p: $i] :
% 0.21/0.54 ( lam @ ( arr @ A_27a @ bool )
% 0.21/0.54 @ ^ [V1m: $i] :
% 0.21/0.54 ( ap @ ( c_2Emin_2E_40 @ A_27a )
% 0.21/0.54 @ ( lam @ A_27a
% 0.21/0.54 @ ^ [V2x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ V0p ) ) @ ( ap @ V1m @ V2x ) ) ) ) ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(ax_thm_2Ebool_2EBOUNDED__DEF,axiom,
% 0.21/0.54 ( c_2Ebool_2EBOUNDED
% 0.21/0.54 = ( lam @ bool
% 0.21/0.54 @ ^ [V0v: $i] : c_2Ebool_2ET ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(ax_thm_2Ebool_2EDATATYPE__TAG__DEF,axiom,
% 0.21/0.54 ! [A_27a: del] :
% 0.21/0.54 ( ( c_2Ebool_2EDATATYPE @ A_27a )
% 0.21/0.54 = ( lam @ A_27a
% 0.21/0.54 @ ^ [V0x: $i] : c_2Ebool_2ET ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(conj_thm_2Ebool_2ETRUTH,conjecture,
% 0.21/0.54 $true ).
% 0.21/0.54
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.VC9ernlWIV/cvc5---1.0.5_16059.p...
% 0.21/0.54 (declare-sort $$unsorted 0)
% 0.21/0.54 (declare-sort tptp.del 0)
% 0.21/0.54 (declare-fun tptp.bool () tptp.del)
% 0.21/0.54 (declare-fun tptp.ind () tptp.del)
% 0.21/0.54 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.21/0.54 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.21/0.54 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.21/0.54 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.21/0.54 (declare-fun tptp.p ($$unsorted) Bool)
% 0.21/0.54 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.21/0.54 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.21/0.54 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.21/0.54 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.21/0.54 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.21/0.54 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.21/0.54 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.21/0.54 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.21/0.54 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.21/0.54 (assert (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))))
% 0.21/0.54 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.21/0.54 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.54 (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))))))))
% 0.21/0.54 (declare-fun tptp.c_2Emin_2E_40 (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a))))
% 0.21/0.54 (declare-fun tptp.ty_2Ebool_2Eitself (tptp.del) tptp.del)
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.21/0.54 (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))))
% 0.21/0.54 (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))))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.21/0.54 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.54 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2E_3F (tptp.del) $$unsorted)
% 0.21/0.54 (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))))
% 0.21/0.54 (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))))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2E_3F_21 (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EARB (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EARB A_27a)) A_27a)))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EBOUNDED () $$unsorted)
% 0.21/0.54 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EBOUNDED) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ECOND (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 A_27a)))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EDATATYPE (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EDATATYPE A_27a)) (@ (@ tptp.arr A_27a) tptp.bool))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.21/0.54 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.21/0.54 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EIN (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EIN A_27a)) (@ _let_1 (@ (@ tptp.arr (@ _let_1 tptp.bool)) tptp.bool))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ELET (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EONE__ONE (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) tptp.bool))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2EONTO (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) tptp.bool))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ERES__ABSTRACT (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr _let_2) _let_2)))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ERES__EXISTS (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ERES__EXISTS__UNIQUE (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ERES__FORALL (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ERES__SELECT (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__SELECT A_27a)) (@ _let_1 (@ _let_1 A_27a))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.21/0.54 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.21/0.54 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2ETYPE__DEFINITION (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27a)) tptp.bool)))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2E_5C_2F () $$unsorted)
% 0.21/0.54 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.54 (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))))))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2Eitself__case (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eitself__case A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) (@ (@ tptp.arr A_27b) A_27b)))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2Eliteral__case (tptp.del tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2Ethe__value (tptp.del) $$unsorted)
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2Ethe__value A_27a)) (@ tptp.ty_2Ebool_2Eitself A_27a))))
% 0.21/0.54 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.21/0.54 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.21/0.54 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.21/0.54 (assert (let ((_let_1 (@ tptp.lam tptp.bool))) (= true (= (@ _let_1 (lambda ((V0x $$unsorted)) V0x)) (@ _let_1 (lambda ((V1x $$unsorted)) V1x))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2ET))))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P)))))))
% 0.21/0.54 (assert (= tptp.c_2Ebool_2E_2F_5C (@ (@ tptp.lam tptp.bool) (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V0t1)) (@ (@ tptp.ap (@ _let_1 V1t2)) V2t)))) V2t)))))))))))
% 0.21/0.54 (assert (= tptp.c_2Ebool_2E_5C_2F (@ (@ tptp.lam tptp.bool) (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V0t1)) V2t))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V1t2)) V2t))) V2t))))))))))))
% 0.21/0.54 (assert (= false (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (@ tptp.p V0t)))))
% 0.21/0.54 (assert (= tptp.c_2Ebool_2E_7E (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V0t)) tptp.c_2Ebool_2EF)))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) V0P))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V1x))) (@ _let_1 V2y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V2y)))))))))))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ECOND A_27a) (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1t1 $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) V0t)))) (let ((_let_3 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ _let_3 (@ _let_2 tptp.c_2Ebool_2ET))) (@ _let_1 V1t1)))) (@ (@ tptp.ap (@ _let_3 (@ _let_2 tptp.c_2Ebool_2EF))) (@ _let_1 V2t2))))))))))))))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x1 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x2 $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) (@ _let_1 V1x1))) (@ _let_1 V2x2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x1)) V2x2))))))))))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V1y)) (@ (@ tptp.ap V0f) V2x)))))))))))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27b) A_27a)) (lambda ((V1rep $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V2x_27 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V3x_27_27 $$unsorted)) (let ((_let_1 (@ tptp.ap V1rep))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 V2x_27))) (@ _let_1 V3x_27_27)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27))))))))))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) (@ (@ tptp.ap V0P) V4x))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V5x_27 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4x)) (@ (@ tptp.ap V1rep) V5x_27)))))))))))))))))
% 0.21/0.54 (assert (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or (= _let_1 true) (= _let_1 false))))))
% 0.21/0.54 (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))))
% 0.21/0.54 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V1x) A_27a) (=> (@ tptp.p (@ _let_1 V1x)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P))))))))))
% 0.21/0.54 (declare-sort tptp.tp__i 0)
% 0.21/0.54 (declare-fun tptp.inj__i (tptp.tp__i) $$unsorted)
% 0.21/0.54 (declare-fun tptp.surj__i ($$unsorted) tptp.tp__i)
% 0.21/0.54 (assert (forall ((X tptp.tp__i)) (= (@ tptp.surj__i (@ tptp.inj__i X)) X)))
% 0.21/0.54 (assert (forall ((X tptp.tp__i)) (@ (@ tptp.mem (@ tptp.inj__i X)) tptp.ind)))
% 0.21/0.54 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ind) (= X (@ tptp.inj__i (@ tptp.surj__i X))))))
% 0.21/0.54 (assert (exists ((V0f $$unsorted)) (and (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ind) tptp.ind)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ind) tptp.ind)) V0f)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONTO tptp.ind) tptp.ind)) V0f))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EIN A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1f $$unsorted)) (@ (@ tptp.ap V1f) V0x))))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__FORALL A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0p)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1m) V2x)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1m))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V3x))) (@ _let_1 V4y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))))))
% 0.21/0.55 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__SELECT A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))))
% 0.21/0.55 (assert (= tptp.c_2Ebool_2EBOUNDED (@ (@ tptp.lam tptp.bool) (lambda ((V0v $$unsorted)) tptp.c_2Ebool_2ET))))
% 0.21/0.58 (assert (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EDATATYPE A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET)))))
% 0.21/0.58 (assert (not true))
% 0.21/0.58 (set-info :filename cvc5---1.0.5_16059)
% 0.21/0.58 (check-sat-assuming ( true ))
% 0.21/0.58 ------- get file name : TPTP file name is ITP001^5
% 0.21/0.58 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16059.smt2...
% 0.21/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.58 % SZS status Theorem for ITP001^5
% 0.21/0.58 % SZS output start Proof for ITP001^5
% 0.21/0.58 (
% 0.21/0.58 (let ((_let_1 (not true))) (let ((_let_2 (@ tptp.lam tptp.bool))) (let ((_let_3 (@ tptp.arr tptp.bool))) (let ((_let_4 (@ _let_3 tptp.bool))) (let ((_let_5 (@ _let_3 _let_4))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args ((forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)) (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))) (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))) (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))) (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))) (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))) (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))))) (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)))))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) _let_5) (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))))))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) A_27a))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))) (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))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) _let_5) (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))))))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))) (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))))))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_3F_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EARB A_27a)) A_27a)) (@ (@ tptp.mem tptp.c_2Ebool_2EBOUNDED) _let_4) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 A_27a)))))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2EDATATYPE A_27a)) (@ (@ tptp.arr A_27a) tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool) (not (@ tptp.p tptp.c_2Ebool_2EF)) (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))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) tptp.bool))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) A_27b)) tptp.bool))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (let ((_let_2 (@ _let_1 A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ERES__ABSTRACT A_27a) A_27b)) (@ (@ tptp.arr (@ _let_1 tptp.bool)) (@ (@ tptp.arr _let_2) _let_2)))))) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ERES__SELECT A_27a)) (@ _let_1 (@ _let_1 A_27a))))) (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool) (@ tptp.p tptp.c_2Ebool_2ET) (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) (@ (@ tptp.arr (@ (@ tptp.arr A_27b) A_27a)) tptp.bool)))) (@ (@ tptp.mem tptp.c_2Ebool_2E_5C_2F) _let_5) (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))))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eitself__case A_27a) A_27b)) (@ (@ tptp.arr (@ tptp.ty_2Ebool_2Eitself A_27a)) (@ (@ tptp.arr A_27b) A_27b)))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (let ((_let_1 (@ (@ tptp.arr A_27a) A_27b))) (@ (@ tptp.mem (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b)) (@ (@ tptp.arr _let_1) _let_1)))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2Ethe__value A_27a)) (@ tptp.ty_2Ebool_2Eitself A_27a))) (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) _let_4) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))) (= true (= (@ _let_2 (lambda ((V0x $$unsorted)) V0x)) (@ _let_2 (lambda ((V1x $$unsorted)) V1x)))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D (@ (@ tptp.arr A_27a) tptp.bool))) V0P)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) tptp.c_2Ebool_2ET))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap V0P) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P)))))) (= tptp.c_2Ebool_2E_2F_5C (@ _let_2 (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V0t1)) (@ (@ tptp.ap (@ _let_1 V1t2)) V2t)))) V2t)))))))))) (= tptp.c_2Ebool_2E_5C_2F (@ _let_2 (lambda ((V0t1 $$unsorted)) (@ (@ tptp.lam tptp.bool) (lambda ((V1t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 tptp.bool)) (@ (@ tptp.lam tptp.bool) (lambda ((V2t $$unsorted)) (let ((_let_1 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V0t1)) V2t))) (@ (@ tptp.ap (@ _let_1 (@ (@ tptp.ap (@ _let_1 V1t2)) V2t))) V2t))))))))))) (= false (forall ((V0t $$unsorted)) (=> (@ (@ tptp.mem V0t) tptp.bool) (@ tptp.p V0t)))) (= tptp.c_2Ebool_2E_7E (@ _let_2 (lambda ((V0t $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) V0t)) tptp.c_2Ebool_2EF)))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2E_3F_21 A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) V0P))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2y $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V1x))) (@ _let_1 V2y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x)) V2y)))))))))))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ELET A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ECOND A_27a) (@ (@ tptp.lam tptp.bool) (lambda ((V0t $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1t1 $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V2t2 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V3x $$unsorted)) (let ((_let_1 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)))) (let ((_let_2 (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) V0t)))) (let ((_let_3 (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ _let_3 (@ _let_2 tptp.c_2Ebool_2ET))) (@ _let_1 V1t1)))) (@ (@ tptp.ap (@ _let_3 (@ _let_2 tptp.c_2Ebool_2EF))) (@ _let_1 V2t2))))))))))))))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONE__ONE A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V1x1 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x2 $$unsorted)) (let ((_let_1 (@ tptp.ap V0f))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) (@ _let_1 V1x1))) (@ _let_1 V2x2)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V1x1)) V2x2))))))))))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2EONTO A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V1y $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V1y)) (@ (@ tptp.ap V0f) V2x)))))))))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2ETYPE__DEFINITION A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0P $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27b) A_27a)) (lambda ((V1rep $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V2x_27 $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V3x_27_27 $$unsorted)) (let ((_let_1 (@ tptp.ap V1rep))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 V2x_27))) (@ _let_1 V3x_27_27)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27b)) V2x_27)) V3x_27_27))))))))))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V4x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D tptp.bool)) (@ (@ tptp.ap V0P) V4x))) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27b)) (@ (@ tptp.lam A_27b) (lambda ((V5x_27 $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V4x)) (@ (@ tptp.ap V1rep) V5x_27)))))))))))))))) (forall ((V0t $$unsorted)) (let ((_let_1 (@ tptp.p V0t))) (=> (@ (@ tptp.mem V0t) tptp.bool) (or (= _let_1 true) (= _let_1 false))))) (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))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) (@ (@ tptp.arr A_27a) tptp.bool)) (forall ((V1x $$unsorted)) (let ((_let_1 (@ tptp.ap V0P))) (=> (@ (@ tptp.mem V1x) A_27a) (=> (@ tptp.p (@ _let_1 V1x)) (@ tptp.p (@ _let_1 (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) V0P))))))))) (forall ((X tptp.tp__i)) (= (@ tptp.surj__i (@ tptp.inj__i X)) X)) (forall ((X tptp.tp__i)) (@ (@ tptp.mem (@ tptp.inj__i X)) tptp.ind)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ind) (= X (@ tptp.inj__i (@ tptp.surj__i X))))) (exists ((V0f $$unsorted)) (and (@ (@ tptp.mem V0f) (@ (@ tptp.arr tptp.ind) tptp.ind)) (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONE__ONE tptp.ind) tptp.ind)) V0f)) (not (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.c_2Ebool_2EONTO tptp.ind) tptp.ind)) V0f))))) (forall ((A_27a tptp.del) (A_27b tptp.del)) (= (@ (@ tptp.c_2Ebool_2Eliteral__case A_27a) A_27b) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) A_27b)) (lambda ((V0f $$unsorted)) (@ (@ tptp.lam A_27a) (lambda ((V1x $$unsorted)) (@ (@ tptp.ap V0f) V1x))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EIN A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1f $$unsorted)) (@ (@ tptp.ap V1f) V0x))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__FORALL A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_3F A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (let ((_let_1 (@ tptp.lam A_27a))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__EXISTS A_27a)) V0p)) (@ _let_1 (lambda ((V2x $$unsorted)) (@ (@ tptp.ap V1m) V2x)))))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ _let_1 (lambda ((V3x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ERES__FORALL A_27a)) V0p)) (@ (@ tptp.lam A_27a) (lambda ((V4y $$unsorted)) (let ((_let_1 (@ tptp.ap V1m))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ _let_1 V3x))) (@ _let_1 V4y)))) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A_27a)) V3x)) V4y))))))))))))))))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2ERES__SELECT A_27a) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V0p $$unsorted)) (@ (@ tptp.lam (@ (@ tptp.arr A_27a) tptp.bool)) (lambda ((V1m $$unsorted)) (@ (@ tptp.ap (@ tptp.c_2Emin_2E_40 A_27a)) (@ (@ tptp.lam A_27a) (lambda ((V2x $$unsorted)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2EIN A_27a)) V2x)) V0p))) (@ (@ tptp.ap V1m) V2x))))))))))) (= tptp.c_2Ebool_2EBOUNDED (@ _let_2 (lambda ((V0v $$unsorted)) tptp.c_2Ebool_2ET))) (forall ((A_27a tptp.del)) (= (@ tptp.c_2Ebool_2EDATATYPE A_27a) (@ (@ tptp.lam A_27a) (lambda ((V0x $$unsorted)) tptp.c_2Ebool_2ET)))) _let_1 true))))))))
% 0.21/0.59 )
% 0.21/0.59 % SZS output end Proof for ITP001^5
% 0.21/0.59 % cvc5---1.0.5 exiting
% 0.21/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------