TSTP Solution File: ITP013^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP013^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:14:58 EDT 2023
% Result : Theorem 197.47s 198.42s
% Output : Proof 197.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP013^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.18/0.35 % Computer : n014.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Sun Aug 27 10:16:01 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : ITP013^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.21/0.50 % Domain : Interactive Theorem Proving
% 0.21/0.50 % Problem : HOL4 set theory export of thm_2Ewords_2En2w__sub.p, bushy mode
% 0.21/0.50 % Version : [BG+19] axioms.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.21/0.50 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [BG+19]
% 0.21/0.50 % Names : thm_2Ewords_2En2w__sub.p [Gau19]
% 0.21/0.50 % : HL406001^2.p [TPAP]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 1.00 v7.5.0
% 0.21/0.50 % Syntax : Number of formulae : 77 ( 8 unt; 31 typ; 0 def)
% 0.21/0.50 % Number of atoms : 293 ( 22 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 17 ( 6 avg)
% 0.21/0.50 % Number of connectives : 580 ( 6 ~; 0 |; 14 &; 474 @)
% 0.21/0.50 % ( 25 <=>; 61 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 20 ( 7 avg)
% 0.21/0.50 % Number of types : 4 ( 2 usr)
% 0.21/0.50 % Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 37 ( 34 usr; 18 con; 0-2 aty)
% 0.21/0.50 % Number of variables : 82 ( 0 ^; 82 !; 0 ?; 82 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments :
% 0.21/0.50 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(del_tp,type,
% 0.21/0.50 del: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(bool,type,
% 0.21/0.50 bool: del ).
% 0.21/0.50
% 0.21/0.50 thf(ind,type,
% 0.21/0.50 ind: del ).
% 0.21/0.50
% 0.21/0.50 thf(arr,type,
% 0.21/0.50 arr: del > del > del ).
% 0.21/0.50
% 0.21/0.50 thf(mem,type,
% 0.21/0.50 mem: $i > del > $o ).
% 0.21/0.50
% 0.21/0.50 thf(ap,type,
% 0.21/0.50 ap: $i > $i > $i ).
% 0.21/0.50
% 0.21/0.50 thf(lam,type,
% 0.21/0.50 lam: del > ( $i > $i ) > $i ).
% 0.21/0.50
% 0.21/0.50 thf(p,type,
% 0.21/0.50 p: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_o,type,
% 0.21/0.50 inj__o: $o > $i ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_surj_o,axiom,
% 0.21/0.50 ! [X: $o] :
% 0.21/0.50 ( ( p @ ( inj__o @ X ) )
% 0.21/0.50 = X ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_mem_o,axiom,
% 0.21/0.50 ! [X: $o] : ( mem @ ( inj__o @ X ) @ bool ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_iso_mem_o,axiom,
% 0.21/0.50 ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ bool )
% 0.21/0.50 => ( X
% 0.21/0.50 = ( inj__o @ ( p @ X ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ap_tp,axiom,
% 0.21/0.50 ! [A: del,B: del,F: $i] :
% 0.21/0.50 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.50 => ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( mem @ ( ap @ F @ X ) @ B ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(lam_tp,axiom,
% 0.21/0.50 ! [A: del,B: del,F: $i > $i] :
% 0.21/0.50 ( ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( mem @ ( F @ X ) @ B ) )
% 0.21/0.50 => ( mem @ ( lam @ A @ F ) @ ( arr @ A @ B ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(funcext,axiom,
% 0.21/0.50 ! [A: del,B: del,F: $i] :
% 0.21/0.50 ( ( mem @ F @ ( arr @ A @ B ) )
% 0.21/0.50 => ! [G: $i] :
% 0.21/0.50 ( ( mem @ G @ ( arr @ A @ B ) )
% 0.21/0.50 => ( ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( ( ap @ F @ X )
% 0.21/0.50 = ( ap @ G @ X ) ) )
% 0.21/0.50 => ( F = G ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(beta,axiom,
% 0.21/0.50 ! [A: del,F: $i > $i,X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( ( ap @ ( lam @ A @ F ) @ X )
% 0.21/0.50 = ( F @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(tp_c_2Ebool_2E_7E,type,
% 0.21/0.50 c_2Ebool_2E_7E: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_7E,axiom,
% 0.21/0.50 mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_neg_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
% 0.21/0.50 <=> ~ ( p @ Q ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Emin_2E_3D_3D_3E,type,
% 0.21/0.50 c_2Emin_2E_3D_3D_3E: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.21/0.50 mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_imp_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ! [R: $i] :
% 0.21/0.50 ( ( mem @ R @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
% 0.21/0.50 <=> ( ( p @ Q )
% 0.21/0.50 => ( p @ R ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2EF,type,
% 0.21/0.50 c_2Ebool_2EF: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2EF,axiom,
% 0.21/0.50 mem @ c_2Ebool_2EF @ bool ).
% 0.21/0.50
% 0.21/0.50 thf(ax_false_p,axiom,
% 0.21/0.50 ~ ( p @ c_2Ebool_2EF ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2ET,type,
% 0.21/0.50 c_2Ebool_2ET: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2ET,axiom,
% 0.21/0.50 mem @ c_2Ebool_2ET @ bool ).
% 0.21/0.50
% 0.21/0.50 thf(ax_true_p,axiom,
% 0.21/0.50 p @ c_2Ebool_2ET ).
% 0.21/0.50
% 0.21/0.50 thf(tp_ty_2Efcp_2Ecart,type,
% 0.21/0.50 ty_2Efcp_2Ecart: del > del > del ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ewords_2Eword__sub,type,
% 0.21/0.50 c_2Ewords_2Eword__sub: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ewords_2Eword__sub,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_ty_2Enum_2Enum,type,
% 0.21/0.50 ty_2Enum_2Enum: del ).
% 0.21/0.50
% 0.21/0.50 thf(stp_ty_2Enum_2Enum,type,
% 0.21/0.50 tp__ty_2Enum_2Enum: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_ty_2Enum_2Enum,type,
% 0.21/0.50 inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
% 0.21/0.50
% 0.21/0.50 thf(stp_surj_ty_2Enum_2Enum,type,
% 0.21/0.50 surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_surj_ty_2Enum_2Enum,axiom,
% 0.21/0.50 ! [X: tp__ty_2Enum_2Enum] :
% 0.21/0.50 ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
% 0.21/0.50 = X ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_inj_mem_ty_2Enum_2Enum,axiom,
% 0.21/0.50 ! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_iso_mem_ty_2Enum_2Enum,axiom,
% 0.21/0.50 ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ ty_2Enum_2Enum )
% 0.21/0.50 => ( X
% 0.21/0.50 = ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Earithmetic_2E_2D,type,
% 0.21/0.50 c_2Earithmetic_2E_2D: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Earithmetic_2E_2D,axiom,
% 0.21/0.50 mem @ c_2Earithmetic_2E_2D @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_fo_c_2Earithmetic_2E_2D,type,
% 0.21/0.50 fo__c_2Earithmetic_2E_2D: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 0.21/0.50
% 0.21/0.50 thf(stp_eq_fo_c_2Earithmetic_2E_2D,axiom,
% 0.21/0.50 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 0.21/0.50 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2E_2D @ X0 @ X1 ) )
% 0.21/0.50 = ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Earithmetic_2E_3C_3D,type,
% 0.21/0.50 c_2Earithmetic_2E_3C_3D: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Earithmetic_2E_3C_3D,axiom,
% 0.21/0.50 mem @ c_2Earithmetic_2E_3C_3D @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2ECOND,type,
% 0.21/0.50 c_2Ebool_2ECOND: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2ECOND,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Earithmetic_2E_2B,type,
% 0.21/0.50 c_2Earithmetic_2E_2B: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Earithmetic_2E_2B,axiom,
% 0.21/0.50 mem @ c_2Earithmetic_2E_2B @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(stp_fo_c_2Earithmetic_2E_2B,type,
% 0.21/0.50 fo__c_2Earithmetic_2E_2B: tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).
% 0.21/0.50
% 0.21/0.50 thf(stp_eq_fo_c_2Earithmetic_2E_2B,axiom,
% 0.21/0.50 ! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
% 0.21/0.50 ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Earithmetic_2E_2B @ X0 @ X1 ) )
% 0.21/0.50 = ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__ty_2Enum_2Enum @ X1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ewords_2En2w,type,
% 0.21/0.50 c_2Ewords_2En2w: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ewords_2En2w,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ewords_2Eword__2comp,type,
% 0.21/0.50 c_2Ewords_2Eword__2comp: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ewords_2Eword__2comp,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ewords_2Eword__add,type,
% 0.21/0.50 c_2Ewords_2Eword__add: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ewords_2Eword__add,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Emin_2E_3D,type,
% 0.21/0.50 c_2Emin_2E_3D: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Emin_2E_3D,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_eq_p,axiom,
% 0.21/0.50 ! [A: del,X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ! [Y: $i] :
% 0.21/0.50 ( ( mem @ Y @ A )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
% 0.21/0.50 <=> ( X = Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2E_21,type,
% 0.21/0.50 c_2Ebool_2E_21: del > $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_21,axiom,
% 0.21/0.50 ! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_all_p,axiom,
% 0.21/0.50 ! [A: del,Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ ( arr @ A @ bool ) )
% 0.21/0.50 => ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
% 0.21/0.50 <=> ! [X: $i] :
% 0.21/0.50 ( ( mem @ X @ A )
% 0.21/0.50 => ( p @ ( ap @ Q @ X ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(tp_c_2Ebool_2E_2F_5C,type,
% 0.21/0.50 c_2Ebool_2E_2F_5C: $i ).
% 0.21/0.50
% 0.21/0.50 thf(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.21/0.50 mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(ax_and_p,axiom,
% 0.21/0.50 ! [Q: $i] :
% 0.21/0.50 ( ( mem @ Q @ bool )
% 0.21/0.50 => ! [R: $i] :
% 0.21/0.50 ( ( mem @ R @ bool )
% 0.21/0.50 => ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
% 0.21/0.50 <=> ( ( p @ Q )
% 0.21/0.50 & ( p @ R ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.21/0.50 $true ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ( ( $true
% 0.21/0.50 => ( p @ V0t ) )
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 => $true )
% 0.21/0.50 <=> $true )
% 0.21/0.50 & ( ( $false
% 0.21/0.50 => ( p @ V0t ) )
% 0.21/0.50 <=> $true )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 => ( p @ V0t ) )
% 0.21/0.50 <=> $true )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 => $false )
% 0.21/0.50 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.21/0.50 ! [A_27a: del,V0x: $i] :
% 0.21/0.50 ( ( mem @ V0x @ A_27a )
% 0.21/0.50 => ( ( V0x = V0x )
% 0.21/0.50 <=> $true ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.21/0.50 ! [A_27a: del,V0x: $i] :
% 0.21/0.50 ( ( mem @ V0x @ A_27a )
% 0.21/0.50 => ! [V1y: $i] :
% 0.21/0.50 ( ( mem @ V1y @ A_27a )
% 0.21/0.50 => ( ( V0x = V1y )
% 0.21/0.50 <=> ( V1y = V0x ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.21/0.50 ! [V0t: $i] :
% 0.21/0.50 ( ( mem @ V0t @ bool )
% 0.21/0.50 => ( ( ( $true
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 <=> $true )
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 & ( ( $false
% 0.21/0.50 <=> ( p @ V0t ) )
% 0.21/0.50 <=> ~ ( p @ V0t ) )
% 0.21/0.50 & ( ( ( p @ V0t )
% 0.21/0.50 <=> $false )
% 0.21/0.50 <=> ~ ( p @ V0t ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 0.21/0.50 ! [V0t1: $i] :
% 0.21/0.50 ( ( mem @ V0t1 @ bool )
% 0.21/0.50 => ! [V1t2: $i] :
% 0.21/0.50 ( ( mem @ V1t2 @ bool )
% 0.21/0.50 => ! [V2t3: $i] :
% 0.21/0.50 ( ( mem @ V2t3 @ bool )
% 0.21/0.50 => ( ( ( p @ V0t1 )
% 0.21/0.50 => ( ( p @ V1t2 )
% 0.21/0.50 => ( p @ V2t3 ) ) )
% 0.21/0.50 <=> ( ( ( p @ V0t1 )
% 0.21/0.50 & ( p @ V1t2 ) )
% 0.21/0.50 => ( p @ V2t3 ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2EIMP__CONG,axiom,
% 0.21/0.50 ! [V0x: $i] :
% 0.21/0.50 ( ( mem @ V0x @ bool )
% 0.21/0.50 => ! [V1x_27: $i] :
% 0.21/0.50 ( ( mem @ V1x_27 @ bool )
% 0.21/0.50 => ! [V2y: $i] :
% 0.21/0.50 ( ( mem @ V2y @ bool )
% 0.21/0.50 => ! [V3y_27: $i] :
% 0.21/0.50 ( ( mem @ V3y_27 @ bool )
% 0.21/0.50 => ( ( ( ( p @ V0x )
% 0.21/0.50 <=> ( p @ V1x_27 ) )
% 0.21/0.50 & ( ( p @ V1x_27 )
% 0.21/0.50 => ( ( p @ V2y )
% 0.21/0.50 <=> ( p @ V3y_27 ) ) ) )
% 0.21/0.50 => ( ( ( p @ V0x )
% 0.21/0.50 => ( p @ V2y ) )
% 0.21/0.50 <=> ( ( p @ V1x_27 )
% 0.21/0.50 => ( p @ V3y_27 ) ) ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(conj_thm_2Ebool_2ECOND__CONG,axiom,
% 0.21/0.50 ! [A_27a: del,V0P: $i] :
% 0.21/0.50 ( ( mem @ V0P @ bool )
% 0.21/0.50 => ! [V1Q: $i] :
% 0.21/0.50 ( ( mem @ V1Q @ bool )
% 0.21/0.50 => ! [V2x: $i] :
% 0.21/0.50 ( ( mem @ V2x @ A_27a )
% 0.21/0.50 => ! [V3x_27: $i] :
% 0.21/0.50 ( ( mem @ V3x_27 @ A_27a )
% 0.21/0.50 => ! [V4y: $i] :
% 0.21/0.50 ( ( mem @ V4y @ A_27a )
% 0.21/0.50 => ! [V5y_27: $i] :
% 0.21/0.50 ( ( mem @ V5y_27 @ A_27a )
% 0.21/0.50 => ( ( ( ( p @ V0P )
% 0.21/0.50 <=> ( p @ V1Q ) )
% 0.21/0.50 & ( ( p @ V1Q )
% 0.21/0.50 => ( V2x = V3x_27 ) )
% 0.21/0.50 & ( ~ ( p @ V1Q )
% 0.21/0.50 => ( V4y = V5y_27 ) ) )
% 0.21/0.50 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ V2x ) @ V4y )
% 0.21/0.52 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ V3x_27 ) @ V5y_27 ) ) ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj_thm_2Ebool_2Ebool__case__thm,axiom,
% 0.21/0.52 ! [A_27a: del] :
% 0.21/0.52 ( ! [V0t1: $i] :
% 0.21/0.52 ( ( mem @ V0t1 @ A_27a )
% 0.21/0.52 => ! [V1t2: $i] :
% 0.21/0.52 ( ( mem @ V1t2 @ A_27a )
% 0.21/0.52 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
% 0.21/0.52 = V0t1 ) ) )
% 0.21/0.52 & ! [V2t1: $i] :
% 0.21/0.52 ( ( mem @ V2t1 @ A_27a )
% 0.21/0.52 => ! [V3t2: $i] :
% 0.21/0.52 ( ( mem @ V3t2 @ A_27a )
% 0.21/0.52 => ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ V3t2 )
% 0.21/0.52 = V3t2 ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax_thm_2Ewords_2Eword__sub__def,axiom,
% 0.21/0.52 ! [A_27a: del,V0v: $i] :
% 0.21/0.52 ( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
% 0.21/0.52 => ! [V1w: $i] :
% 0.21/0.52 ( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
% 0.21/0.52 => ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w )
% 0.21/0.52 = ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj_thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
% 0.21/0.52 ! [A_27a: del,A_27b: del] :
% 0.21/0.52 ( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
% 0.21/0.52 ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
% 0.21/0.52 = ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
% 0.21/0.52 & ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
% 0.21/0.52 ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
% 0.21/0.52 = ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(conj_thm_2Ewords_2En2w__sub,conjecture,
% 0.21/0.52 ! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
% 0.21/0.52 ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
% 0.21/0.52 => ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
% 0.21/0.52 = ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.QJDgkI5ktx/cvc5---1.0.5_31814.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.del 0)
% 0.21/0.52 (declare-fun tptp.bool () tptp.del)
% 0.21/0.52 (declare-fun tptp.ind () tptp.del)
% 0.21/0.52 (declare-fun tptp.arr (tptp.del tptp.del) tptp.del)
% 0.21/0.52 (declare-fun tptp.mem ($$unsorted tptp.del) Bool)
% 0.21/0.52 (declare-fun tptp.ap ($$unsorted $$unsorted) $$unsorted)
% 0.21/0.52 (declare-fun tptp.lam (tptp.del (-> $$unsorted $$unsorted)) $$unsorted)
% 0.21/0.52 (declare-fun tptp.p ($$unsorted) Bool)
% 0.21/0.52 (declare-fun tptp.inj__o (Bool) $$unsorted)
% 0.21/0.52 (assert (forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)))
% 0.21/0.52 (assert (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)))
% 0.21/0.52 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (B tptp.del) (F (-> $$unsorted $$unsorted))) (=> (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ F X)) B))) (@ (@ tptp.mem (@ (@ tptp.lam A) F)) (@ (@ tptp.arr A) B)))))
% 0.21/0.52 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap F) X) (@ (@ tptp.ap G) X)))) (= F G)))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (F (-> $$unsorted $$unsorted)) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_7E () $$unsorted)
% 0.21/0.52 (assert (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) (@ (@ tptp.arr tptp.bool) tptp.bool)))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))))
% 0.21/0.52 (declare-fun tptp.c_2Emin_2E_3D_3D_3E () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) Q)) R)) (=> (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2EF () $$unsorted)
% 0.21/0.52 (assert (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool))
% 0.21/0.52 (assert (not (@ tptp.p tptp.c_2Ebool_2EF)))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2ET () $$unsorted)
% 0.21/0.52 (assert (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))
% 0.21/0.52 (assert (@ tptp.p tptp.c_2Ebool_2ET))
% 0.21/0.52 (declare-fun tptp.ty_2Efcp_2Ecart (tptp.del tptp.del) tptp.del)
% 0.21/0.52 (declare-fun tptp.c_2Ewords_2Eword__sub (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Ewords_2Eword__sub A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 0.21/0.52 (declare-fun tptp.ty_2Enum_2Enum () tptp.del)
% 0.21/0.52 (declare-sort tptp.tp__ty_2Enum_2Enum 0)
% 0.21/0.52 (declare-fun tptp.inj__ty_2Enum_2Enum (tptp.tp__ty_2Enum_2Enum) $$unsorted)
% 0.21/0.52 (declare-fun tptp.surj__ty_2Enum_2Enum ($$unsorted) tptp.tp__ty_2Enum_2Enum)
% 0.21/0.52 (assert (forall ((X tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ tptp.inj__ty_2Enum_2Enum X)) X)))
% 0.21/0.52 (assert (forall ((X tptp.tp__ty_2Enum_2Enum)) (@ (@ tptp.mem (@ tptp.inj__ty_2Enum_2Enum X)) tptp.ty_2Enum_2Enum)))
% 0.21/0.52 (assert (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Enum_2Enum) (= X (@ tptp.inj__ty_2Enum_2Enum (@ tptp.surj__ty_2Enum_2Enum X))))))
% 0.21/0.52 (declare-fun tptp.c_2Earithmetic_2E_2D () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2D) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 0.21/0.52 (declare-fun tptp.fo__c_2Earithmetic_2E_2D (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 0.21/0.52 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2D X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 0.21/0.52 (declare-fun tptp.c_2Earithmetic_2E_3C_3D () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_3C_3D) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2ECOND (tptp.del) $$unsorted)
% 0.21/0.52 (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)))))))
% 0.21/0.52 (declare-fun tptp.c_2Earithmetic_2E_2B () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.ty_2Enum_2Enum))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2B) (@ _let_1 (@ _let_1 tptp.ty_2Enum_2Enum)))))
% 0.21/0.52 (declare-fun tptp.fo__c_2Earithmetic_2E_2B (tptp.tp__ty_2Enum_2Enum tptp.tp__ty_2Enum_2Enum) tptp.tp__ty_2Enum_2Enum)
% 0.21/0.52 (assert (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2B X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))
% 0.21/0.52 (declare-fun tptp.c_2Ewords_2En2w (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ewords_2En2w A_27a)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a)))))
% 0.21/0.52 (declare-fun tptp.c_2Ewords_2Eword__2comp (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ewords_2Eword__2comp A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))
% 0.21/0.52 (declare-fun tptp.c_2Ewords_2Eword__add (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Ewords_2Eword__add A_27a)) (@ _let_2 (@ _let_2 _let_1)))))))
% 0.21/0.52 (declare-fun tptp.c_2Emin_2E_3D (tptp.del) $$unsorted)
% 0.21/0.52 (assert (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))))
% 0.21/0.52 (assert (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_21 (tptp.del) $$unsorted)
% 0.21/0.52 (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))))
% 0.21/0.52 (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))))))))
% 0.21/0.52 (declare-fun tptp.c_2Ebool_2E_2F_5C () $$unsorted)
% 0.21/0.52 (assert (let ((_let_1 (@ tptp.arr tptp.bool))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) (@ _let_1 (@ _let_1 tptp.bool)))))
% 0.21/0.52 (assert (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))))
% 0.21/0.52 (assert true)
% 0.21/0.52 (assert (forall ((V0t $$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)))))))
% 0.21/0.52 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))))
% 0.21/0.52 (assert (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= V0x V1y) (= V1y V0x)))))))
% 0.21/0.52 (assert (forall ((V0t $$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)))))))
% 0.21/0.52 (assert (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) tptp.bool) (forall ((V2t3 $$unsorted)) (let ((_let_1 (@ tptp.p V2t3))) (let ((_let_2 (@ tptp.p V1t2))) (let ((_let_3 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V2t3) tptp.bool) (= (=> _let_3 (=> _let_2 _let_1)) (=> (and _let_3 _let_2) _let_1))))))))))))
% 0.21/0.52 (assert (forall ((V0x $$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 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (= _let_4 _let_2) (=> _let_2 (= _let_3 _let_1))) (= (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))))
% 0.21/0.52 (assert (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3x_27 $$unsorted)) (=> (@ (@ tptp.mem V3x_27) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5y_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (let ((_let_2 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V5y_27) A_27a) (=> (and (= (@ tptp.p V0P) _let_2) (=> _let_2 (= V2x V3x_27)) (=> (not _let_2) (= V4y V5y_27))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2x)) V4y) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V3x_27)) V5y_27))))))))))))))))))
% 40.78/41.16 (assert (forall ((A_27a tptp.del)) (and (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1))))) (forall ((V2t1 $$unsorted)) (=> (@ (@ tptp.mem V2t1) A_27a) (forall ((V3t2 $$unsorted)) (=> (@ (@ tptp.mem V3t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2EF)) V2t1)) V3t2) V3t2))))))))
% 40.78/41.16 (assert (forall ((A_27a tptp.del) (V0v $$unsorted)) (=> (@ (@ tptp.mem V0v) (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a)) (forall ((V1w $$unsorted)) (=> (@ (@ tptp.mem V1w) (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__sub A_27a)) V0v)) V1w) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add A_27a)) V0v)) (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp A_27a)) V1w))))))))
% 40.78/41.16 (assert (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ewords_2En2w A_27a)))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp A_27a)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add A_27a)) (@ _let_4 (@ _let_3 _let_2)))) (@ _let_4 (@ _let_3 _let_1))) (@ _let_4 (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ewords_2En2w A_27b)))) (let ((_let_5 (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp A_27b)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add A_27b)) (@ _let_4 _let_1))) (@ _let_5 (@ _let_4 _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (@ _let_5 (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))))
% 40.78/41.16 (assert (not (forall ((A_27a tptp.del) (V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ewords_2En2w A_27a)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_3)) (= (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__sub A_27a)) (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))
% 40.78/41.16 (set-info :filename cvc5---1.0.5_31814)
% 40.78/41.16 (check-sat-assuming ( true ))
% 40.78/41.16 ------- get file name : TPTP file name is ITP013^2
% 40.78/41.16 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31814.smt2...
% 40.78/41.16 --- Run --ho-elim --full-saturate-quant at 10...
% 40.78/41.16 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 40.78/41.16 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 40.78/41.16 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 40.78/41.16 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.78/41.16 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 197.47/198.42 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 197.47/198.42 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 197.47/198.42 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 197.47/198.42 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 197.47/198.42 % SZS status Theorem for ITP013^2
% 197.47/198.42 % SZS output start Proof for ITP013^2
% 197.47/198.42 (
% 197.47/198.42 (let ((_let_1 (not (forall ((A_27a tptp.del) (V0a tptp.tp__ty_2Enum_2Enum) (V1b tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1b))) (let ((_let_2 (@ tptp.ap (@ tptp.c_2Ewords_2En2w A_27a)))) (let ((_let_3 (@ tptp.inj__ty_2Enum_2Enum V0a))) (=> (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_1)) _let_3)) (= (@ _let_2 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) _let_3)) _let_1)) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__sub A_27a)) (@ _let_2 _let_3))) (@ _let_2 _let_1))))))))))) (let ((_let_2 (forall ((A_27a tptp.del) (A_27b tptp.del)) (and (forall ((V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ewords_2En2w A_27a)))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp A_27a)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add A_27a)) (@ _let_4 (@ _let_3 _let_2)))) (@ _let_4 (@ _let_3 _let_1))) (@ _let_4 (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))) (forall ((V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ewords_2En2w A_27b)))) (let ((_let_5 (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp A_27b)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add A_27b)) (@ _let_4 _let_1))) (@ _let_5 (@ _let_4 _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27b))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (@ _let_5 (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1))))))))))))))) (let ((_let_3 (forall ((A_27a tptp.del) (V0v $$unsorted)) (=> (@ (@ tptp.mem V0v) (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a)) (forall ((V1w $$unsorted)) (=> (@ (@ tptp.mem V1w) (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a)) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__sub A_27a)) V0v)) V1w) (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add A_27a)) V0v)) (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp A_27a)) V1w))))))))) (let ((_let_4 (forall ((A_27a tptp.del)) (and (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) A_27a) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2ET)) V0t1)) V1t2) V0t1))))) (forall ((V2t1 $$unsorted)) (=> (@ (@ tptp.mem V2t1) A_27a) (forall ((V3t2 $$unsorted)) (=> (@ (@ tptp.mem V3t2) A_27a) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)) tptp.c_2Ebool_2EF)) V2t1)) V3t2) V3t2))))))))) (let ((_let_5 (@ tptp.arr tptp.bool))) (let ((_let_6 (@ _let_5 tptp.bool))) (let ((_let_7 (@ _let_5 _let_6))) (let ((_let_8 (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ewords_2Eword__2comp A_27a)) (@ (@ tptp.arr _let_1) _let_1)))))) (let ((_let_9 (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ewords_2En2w A_27a)) (@ (@ tptp.arr tptp.ty_2Enum_2Enum) (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a)))))) (let ((_let_10 (@ tptp.arr tptp.ty_2Enum_2Enum))) (let ((_let_11 (@ _let_10 (@ _let_10 tptp.ty_2Enum_2Enum)))) (let ((_let_12 (@ (@ tptp.mem tptp.c_2Earithmetic_2E_3C_3D) (@ _let_10 (@ _let_10 tptp.bool))))) (let ((_let_13 (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2D X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2D) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))))) (let ((_let_14 (forall ((X tptp.tp__ty_2Enum_2Enum)) (@ (@ tptp.mem (@ tptp.inj__ty_2Enum_2Enum X)) tptp.ty_2Enum_2Enum)))) (let ((_let_15 (@ tptp.p tptp.c_2Ebool_2ET))) (let ((_let_16 (@ (@ tptp.mem tptp.c_2Ebool_2ET) tptp.bool))) (let ((_let_17 (forall ((A tptp.del) (B tptp.del) (F $$unsorted)) (=> (@ (@ tptp.mem F) (@ (@ tptp.arr A) B)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ (@ tptp.mem (@ (@ tptp.ap F) X)) B))))))) (let ((_let_18 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.bool) (= X (@ tptp.inj__o (@ tptp.p X))))))) (let ((_let_19 (forall ((A tptp.del) (B tptp.del) (F $$unsorted) (BOUND_VARIABLE_1330 $$unsorted)) (or (not (ho_8 (ho_7 k_6 F) (ho_14 (ho_13 k_12 A) B))) (not (ho_8 (ho_7 k_6 BOUND_VARIABLE_1330) A)) (ho_8 (ho_7 k_6 (ho_11 (ho_10 k_9 F) BOUND_VARIABLE_1330)) B))))) (let ((_let_20 (ho_14 (ho_13 k_18 tptp.bool) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_21 (ho_22 k_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_22 (ho_22 k_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37))) (let ((_let_23 (ho_10 k_9 tptp.c_2Earithmetic_2E_2D))) (let ((_let_24 (ho_11 (ho_10 k_9 (ho_11 _let_23 _let_22)) _let_21))) (let ((_let_25 (ho_20 k_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_26 (ho_10 k_9 _let_25))) (let ((_let_27 (ho_11 _let_26 _let_24))) (let ((_let_28 (ho_20 k_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_29 (ho_10 k_9 _let_28))) (let ((_let_30 (ho_11 _let_29 _let_27))) (let ((_let_31 (ho_8 (ho_7 k_6 _let_30) _let_20))) (let ((_let_32 (ho_8 (ho_7 k_6 _let_27) _let_20))) (let ((_let_33 (not _let_32))) (let ((_let_34 (ho_8 (ho_7 k_6 _let_28) (ho_14 (ho_13 k_12 _let_20) _let_20)))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_31))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_17)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.del) (B tptp.del) (F $$unsorted) (BOUND_VARIABLE_1330 $$unsorted)) (or (not (@ (@ tptp.mem F) (@ (@ tptp.arr A) B))) (not (@ (@ tptp.mem BOUND_VARIABLE_1330) A)) (@ (@ tptp.mem (@ (@ tptp.ap F) BOUND_VARIABLE_1330)) B))) _let_19))))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (ho_27 (ho_26 k_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_40 (ho_22 k_21 _let_39))) (let ((_let_41 (ho_8 (ho_7 k_6 (ho_11 _let_26 _let_40)) _let_20))) (let ((_let_42 (= _let_24 _let_40))) (let ((_let_43 (ho_8 (ho_7 k_6 _let_40) tptp.ty_2Enum_2Enum))) (let ((_let_44 (not _let_43))) (let ((_let_45 (ho_13 k_12 tptp.ty_2Enum_2Enum))) (let ((_let_46 (ho_8 (ho_7 k_6 _let_25) (ho_14 _let_45 _let_20)))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_44 _let_41))) (let ((_let_49 (_let_19))) (let ((_let_50 (forall ((X tptp.tp__ty_2Enum_2Enum)) (ho_8 (ho_7 k_6 (ho_22 k_21 X)) tptp.ty_2Enum_2Enum)))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_14)) (PREPROCESS :args ((= _let_14 _let_50)))))) (let ((_let_52 (_let_50))) (let ((_let_53 ((ho_22 k_21 X)))) (let ((_let_54 (forall ((A_27a tptp.del)) (ho_8 (ho_7 k_6 (ho_20 k_30 A_27a)) (ho_14 (ho_13 k_12 tptp.ty_2Enum_2Enum) (ho_14 (ho_13 k_18 tptp.bool) A_27a)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_9)) (PREPROCESS :args ((= _let_9 _let_54)))))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_20 k_30 A_27a)))) :args (_let_54))) _let_55 :args (_let_46 false _let_54)))) (let ((_let_57 (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Earithmetic_2E_2D) (ho_22 k_21 X0))) (ho_22 k_21 X1)) (ho_22 k_21 (ho_27 (ho_26 k_25 X0) X1)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_13)) (PREPROCESS :args ((= _let_13 _let_57)))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((ho_11 (ho_10 k_9 (ho_11 _let_23 (ho_22 k_21 X0))) (ho_22 k_21 X1))))) (let ((_let_61 (and _let_42 _let_41))) (let ((_let_62 (ASSUME :args (_let_41)))) (let ((_let_63 (APPLY_UF ho_8))) (let ((_let_64 (REFL :args (_let_20)))) (let ((_let_65 (APPLY_UF ho_7))) (let ((_let_66 (APPLY_UF ho_11))) (let ((_let_67 (ASSUME :args (_let_42)))) (let ((_let_68 (REFL :args (_let_26)))) (let ((_let_69 (REFL :args (k_6)))) (let ((_let_70 (ho_11 (ho_10 k_9 (ho_11 _let_23 _let_21)) _let_22))) (let ((_let_71 (ho_11 _let_26 _let_70))) (let ((_let_72 (ho_10 k_9 (ho_20 k_28 _let_20)))) (let ((_let_73 (= _let_71 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_11 _let_72 tptp.c_2Ebool_2ET)) _let_71)) _let_30)))) (let ((_let_74 (not _let_31))) (let ((_let_75 (ho_8 (ho_7 k_6 _let_71) _let_20))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_74 _let_73))) (let ((_let_78 (forall ((BOUND_VARIABLE_1953 tptp.del) (V0t1 $$unsorted) (BOUND_VARIABLE_1914 $$unsorted)) (or (not (ho_8 (ho_7 k_6 V0t1) BOUND_VARIABLE_1953)) (not (ho_8 (ho_7 k_6 BOUND_VARIABLE_1914) BOUND_VARIABLE_1953)) (= V0t1 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_20 k_28 BOUND_VARIABLE_1953)) tptp.c_2Ebool_2ET)) V0t1)) 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_let_37 :args (_let_107 false _let_19)) :args (_let_96 false _let_105 false _let_46 false _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_94 _let_102 _let_47 (not _let_103)))) _let_104 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.ty_2Enum_2Enum _let_20 _let_25 _let_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_49)) _let_37 :args (_let_103 false _let_19)) :args (_let_94 false _let_101 false _let_46 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 _let_83 _let_82 QUANTIFIERS_INST_E_MATCHING ((ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_20 k_19 A_27a)) V0v)) BOUND_VARIABLE_2004)))) :args (_let_99)))) _let_100 :args (_let_98 false _let_99)) :args (_let_87 false _let_96 false _let_94 false _let_98)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_93) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 QUANTIFIERS_INST_E_MATCHING ((ho_11 (ho_10 k_9 (ho_20 k_30 BOUND_VARIABLE_2045)) (ho_11 (ho_10 k_9 (ho_11 _let_23 (ho_22 k_21 V2m))) (ho_22 k_21 V3n)))))) :args _let_93))) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_2020 tptp.del) (V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V1n))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V0m))) (let ((_let_3 (@ tptp.ap (@ tptp.c_2Ewords_2En2w BOUND_VARIABLE_2020)))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp BOUND_VARIABLE_2020)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add BOUND_VARIABLE_2020)) (@ _let_4 (@ _let_3 _let_2)))) (@ _let_4 (@ _let_3 _let_1))) (@ _let_4 (@ _let_3 (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) _let_2)) _let_1))))))))) (forall ((BOUND_VARIABLE_2045 tptp.del) (V2m tptp.tp__ty_2Enum_2Enum) (V3n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (@ tptp.inj__ty_2Enum_2Enum V2m))) (let ((_let_2 (@ tptp.inj__ty_2Enum_2Enum V3n))) (let ((_let_3 (@ tptp.ap tptp.c_2Earithmetic_2E_2D))) (let ((_let_4 (@ tptp.ap (@ tptp.c_2Ewords_2En2w BOUND_VARIABLE_2045)))) (let ((_let_5 (@ tptp.ap (@ tptp.c_2Ewords_2Eword__2comp BOUND_VARIABLE_2045)))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ewords_2Eword__add BOUND_VARIABLE_2045)) (@ _let_4 _let_1))) (@ _let_5 (@ _let_4 _let_2))) (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) BOUND_VARIABLE_2045))) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_3C_3D) _let_2)) _let_1))) (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_1)) _let_2)))) (@ _let_5 (@ _let_4 (@ (@ tptp.ap (@ _let_3 _let_2)) _let_1)))))))))))) (and (forall ((BOUND_VARIABLE_2020 tptp.del) (V0m tptp.tp__ty_2Enum_2Enum) (V1n tptp.tp__ty_2Enum_2Enum)) (let ((_let_1 (ho_22 k_21 V1n))) (let ((_let_2 (ho_10 k_9 (ho_20 k_30 BOUND_VARIABLE_2020)))) (let ((_let_3 (ho_10 k_9 (ho_20 k_31 BOUND_VARIABLE_2020)))) (let ((_let_4 (ho_22 k_21 V0m))) (= (ho_11 _let_3 (ho_11 _let_2 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 tptp.c_2Earithmetic_2E_2B) _let_4)) _let_1))) (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_20 k_32 BOUND_VARIABLE_2020)) (ho_11 _let_3 (ho_11 _let_2 _let_4)))) (ho_11 _let_3 (ho_11 _let_2 _let_1))))))))) _let_92)))))) :args (1)) :args (_let_85 false _let_92)) :args (_let_91 true _let_90 false _let_89 false BOOLEAN_TERM_VARIABLE_5003 false _let_88 false BOOLEAN_TERM_VARIABLE_5179 false _let_87 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_79) :args (_let_20 _let_71 _let_30 QUANTIFIERS_INST_E_MATCHING ((ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_20 k_28 BOUND_VARIABLE_1953)) tptp.c_2Ebool_2ET)) V0t1)) BOUND_VARIABLE_1914)))) :args _let_79)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (forall ((BOUND_VARIABLE_1953 tptp.del) (V0t1 $$unsorted) (BOUND_VARIABLE_1914 $$unsorted)) (or (not (@ (@ tptp.mem V0t1) BOUND_VARIABLE_1953)) (not (@ (@ tptp.mem BOUND_VARIABLE_1914) BOUND_VARIABLE_1953)) (= V0t1 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND BOUND_VARIABLE_1953)) tptp.c_2Ebool_2ET)) V0t1)) BOUND_VARIABLE_1914)))) (forall ((BOUND_VARIABLE_1971 tptp.del) (V2t1 $$unsorted) (BOUND_VARIABLE_1938 $$unsorted)) (or (not (@ (@ tptp.mem V2t1) BOUND_VARIABLE_1971)) (not (@ (@ tptp.mem BOUND_VARIABLE_1938) BOUND_VARIABLE_1971)) (= BOUND_VARIABLE_1938 (@ (@ tptp.ap (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Ebool_2ECOND BOUND_VARIABLE_1971)) tptp.c_2Ebool_2EF)) V2t1)) BOUND_VARIABLE_1938))))) (and _let_78 (forall ((BOUND_VARIABLE_1971 tptp.del) (V2t1 $$unsorted) (BOUND_VARIABLE_1938 $$unsorted)) (or (not (ho_8 (ho_7 k_6 V2t1) BOUND_VARIABLE_1971)) (not (ho_8 (ho_7 k_6 BOUND_VARIABLE_1938) BOUND_VARIABLE_1971)) (= BOUND_VARIABLE_1938 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_11 (ho_10 k_9 (ho_20 k_28 BOUND_VARIABLE_1971)) tptp.c_2Ebool_2EF)) V2t1)) BOUND_VARIABLE_1938)))))))))) :args (0)) :args (_let_77 false _let_78)) :args (_let_74 false _let_75 true _let_73 false _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_62 _let_67) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG _let_69 (CONG _let_68 (SYMM (SYMM _let_67)) :args _let_66) :args _let_65) _let_64 :args _let_63) (TRUE_INTRO _let_62))) :args (_let_41 _let_42))) :args (_let_42 _let_41))) :args (true _let_61)) :args ((or (not _let_42) _let_32 (not _let_41)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_E_MATCHING _let_60)) :args _let_59)) _let_58 :args (_let_42 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_44 _let_41 (not _let_48)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_39 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_53)) :args _let_52)) _let_51 :args (_let_43 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.ty_2Enum_2Enum _let_20 _let_25 _let_40 QUANTIFIERS_INST_CBQI_PROP)) :args _let_49)) _let_37 :args (_let_48 false _let_19)) :args (_let_41 false _let_46 false _let_43 false _let_48)) :args (_let_32 false _let_42 false _let_41)) :args (_let_38 false _let_34 true _let_31 false _let_32)) _let_37 :args (false true _let_36 false _let_19)) :args ((forall ((X Bool)) (= (@ tptp.p (@ tptp.inj__o X)) X)) (forall ((X Bool)) (@ (@ tptp.mem (@ tptp.inj__o X)) tptp.bool)) _let_18 _let_17 (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 $$unsorted)) (=> (@ (@ tptp.mem X) A) (= (@ (@ tptp.ap (@ (@ tptp.lam A) F)) X) (@ F X)))) (@ (@ tptp.mem tptp.c_2Ebool_2E_7E) _let_6) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap tptp.c_2Ebool_2E_7E) Q)) (not (@ tptp.p Q))))) (@ (@ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) _let_7) (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))))))) (@ (@ tptp.mem tptp.c_2Ebool_2EF) tptp.bool) (not (@ tptp.p tptp.c_2Ebool_2EF)) _let_16 _let_15 (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Ewords_2Eword__sub A_27a)) (@ _let_2 (@ _let_2 _let_1)))))) (forall ((X tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.surj__ty_2Enum_2Enum (@ tptp.inj__ty_2Enum_2Enum X)) X)) _let_14 (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) tptp.ty_2Enum_2Enum) (= X (@ tptp.inj__ty_2Enum_2Enum (@ tptp.surj__ty_2Enum_2Enum X))))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2D) _let_11) _let_13 _let_12 (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Ebool_2ECOND A_27a)) (@ (@ tptp.arr tptp.bool) (@ _let_1 (@ _let_1 A_27a)))))) (@ (@ tptp.mem tptp.c_2Earithmetic_2E_2B) _let_11) (forall ((X0 tptp.tp__ty_2Enum_2Enum) (X1 tptp.tp__ty_2Enum_2Enum)) (= (@ tptp.inj__ty_2Enum_2Enum (@ (@ tptp.fo__c_2Earithmetic_2E_2B X0) X1)) (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Earithmetic_2E_2B) (@ tptp.inj__ty_2Enum_2Enum X0))) (@ tptp.inj__ty_2Enum_2Enum X1)))) _let_9 _let_8 (forall ((A_27a tptp.del)) (let ((_let_1 (@ (@ tptp.ty_2Efcp_2Ecart tptp.bool) A_27a))) (let ((_let_2 (@ tptp.arr _let_1))) (@ (@ tptp.mem (@ tptp.c_2Ewords_2Eword__add A_27a)) (@ _let_2 (@ _let_2 _let_1)))))) (forall ((A_27a tptp.del)) (let ((_let_1 (@ tptp.arr A_27a))) (@ (@ tptp.mem (@ tptp.c_2Emin_2E_3D A_27a)) (@ _let_1 (@ _let_1 tptp.bool))))) (forall ((A tptp.del) (X $$unsorted)) (=> (@ (@ tptp.mem X) A) (forall ((Y $$unsorted)) (=> (@ (@ tptp.mem Y) A) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap (@ tptp.c_2Emin_2E_3D A)) X)) Y)) (= X Y)))))) (forall ((A_27a tptp.del)) (@ (@ tptp.mem (@ tptp.c_2Ebool_2E_21 A_27a)) (@ (@ tptp.arr (@ (@ tptp.arr A_27a) tptp.bool)) tptp.bool))) (forall ((A tptp.del) (Q $$unsorted)) (=> (@ (@ tptp.mem Q) (@ (@ tptp.arr A) tptp.bool)) (= (@ tptp.p (@ (@ tptp.ap (@ tptp.c_2Ebool_2E_21 A)) Q)) (forall ((X $$unsorted)) (=> (@ (@ tptp.mem X) A) (@ tptp.p (@ (@ tptp.ap Q) X))))))) (@ (@ tptp.mem tptp.c_2Ebool_2E_2F_5C) _let_7) (forall ((Q $$unsorted)) (=> (@ (@ tptp.mem Q) tptp.bool) (forall ((R $$unsorted)) (=> (@ (@ tptp.mem R) tptp.bool) (= (@ tptp.p (@ (@ tptp.ap (@ (@ tptp.ap tptp.c_2Ebool_2E_2F_5C) Q)) R)) (and (@ tptp.p Q) (@ tptp.p R))))))) true (forall ((V0t $$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)))))) (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (= (= V0x V0x) true))) (forall ((A_27a tptp.del) (V0x $$unsorted)) (=> (@ (@ tptp.mem V0x) A_27a) (forall ((V1y $$unsorted)) (=> (@ (@ tptp.mem V1y) A_27a) (= (= V0x V1y) (= V1y V0x)))))) (forall ((V0t $$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)))))) (forall ((V0t1 $$unsorted)) (=> (@ (@ tptp.mem V0t1) tptp.bool) (forall ((V1t2 $$unsorted)) (=> (@ (@ tptp.mem V1t2) tptp.bool) (forall ((V2t3 $$unsorted)) (let ((_let_1 (@ tptp.p V2t3))) (let ((_let_2 (@ tptp.p V1t2))) (let ((_let_3 (@ tptp.p V0t1))) (=> (@ (@ tptp.mem V2t3) tptp.bool) (= (=> _let_3 (=> _let_2 _let_1)) (=> (and _let_3 _let_2) _let_1))))))))))) (forall ((V0x $$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 $$unsorted)) (let ((_let_1 (@ tptp.p V3y_27))) (let ((_let_2 (@ tptp.p V1x_27))) (let ((_let_3 (@ tptp.p V2y))) (let ((_let_4 (@ tptp.p V0x))) (=> (@ (@ tptp.mem V3y_27) tptp.bool) (=> (and (= _let_4 _let_2) (=> _let_2 (= _let_3 _let_1))) (= (=> _let_4 _let_3) (=> _let_2 _let_1))))))))))))))) (forall ((A_27a tptp.del) (V0P $$unsorted)) (=> (@ (@ tptp.mem V0P) tptp.bool) (forall ((V1Q $$unsorted)) (=> (@ (@ tptp.mem V1Q) tptp.bool) (forall ((V2x $$unsorted)) (=> (@ (@ tptp.mem V2x) A_27a) (forall ((V3x_27 $$unsorted)) (=> (@ (@ tptp.mem V3x_27) A_27a) (forall ((V4y $$unsorted)) (=> (@ (@ tptp.mem V4y) A_27a) (forall ((V5y_27 $$unsorted)) (let ((_let_1 (@ tptp.ap (@ tptp.c_2Ebool_2ECOND A_27a)))) (let ((_let_2 (@ tptp.p V1Q))) (=> (@ (@ tptp.mem V5y_27) A_27a) (=> (and (= (@ tptp.p V0P) _let_2) (=> _let_2 (= V2x V3x_27)) (=> (not _let_2) (= V4y V5y_27))) (= (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V0P)) V2x)) V4y) (@ (@ tptp.ap (@ (@ tptp.ap (@ _let_1 V1Q)) V3x_27)) V5y_27))))))))))))))))) _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 197.47/198.43 )
% 197.47/198.43 % SZS output end Proof for ITP013^2
% 197.47/198.43 % cvc5---1.0.5 exiting
% 197.47/198.43 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------