TSTP Solution File: ITP011^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP011^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 03:14:38 EDT 2023
% Result : Theorem 91.43s 91.64s
% Output : Proof 91.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : ITP011^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.16 % Command : do_cvc5 %s %d
% 0.17/0.37 % Computer : n017.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sun Aug 27 15:50:57 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.23/0.53 %----Proving TH0
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 % File : ITP011^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.23/0.53 % Domain : Interactive Theorem Proving
% 0.23/0.53 % Problem : HOL4 syntactic export of thm_2Equotient__option_2EOPTION__REL__def.p, bushy mode
% 0.23/0.53 % Version : [BG+19] axioms.
% 0.23/0.53 % English :
% 0.23/0.53
% 0.23/0.53 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.23/0.53 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.23/0.53 % Source : [BG+19]
% 0.23/0.53 % Names : thm_2Equotient__option_2EOPTION__REL__def.p [Gau19]
% 0.23/0.53 % : HL405001^1.p [TPAP]
% 0.23/0.53
% 0.23/0.53 % Status : Theorem
% 0.23/0.53 % Rating : 0.69 v8.1.0, 0.45 v7.5.0
% 0.23/0.53 % Syntax : Number of formulae : 106 ( 33 unt; 58 typ; 0 def)
% 0.23/0.53 % Number of atoms : 147 ( 66 equ; 10 cnn)
% 0.23/0.53 % Maximal formula atoms : 30 ( 3 avg)
% 0.23/0.53 % Number of connectives : 1446 ( 10 ~; 7 |; 44 &;1343 @)
% 0.23/0.53 % ( 31 <=>; 11 =>; 0 <=; 0 <~>)
% 0.23/0.53 % Maximal formula depth : 28 ( 6 avg)
% 0.23/0.53 % Number of types : 4 ( 3 usr)
% 0.23/0.53 % Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% 0.23/0.53 % Number of symbols : 57 ( 55 usr; 25 con; 0-3 aty)
% 0.23/0.53 % Number of variables : 141 ( 0 ^; 137 !; 4 ?; 141 :)
% 0.23/0.53 % SPC : TH0_THM_EQU_NAR
% 0.23/0.53
% 0.23/0.53 % Comments :
% 0.23/0.53 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.23/0.53 %------------------------------------------------------------------------------
% 0.23/0.53 thf(u,type,
% 0.23/0.53 u: $tType ).
% 0.23/0.53
% 0.23/0.53 thf(d,type,
% 0.23/0.53 d: $tType ).
% 0.23/0.53
% 0.23/0.53 thf(du,type,
% 0.23/0.53 du: $tType ).
% 0.23/0.53
% 0.23/0.53 thf(tyop_2Emin_2Ebool,type,
% 0.23/0.53 tyop_2Emin_2Ebool: d ).
% 0.23/0.53
% 0.23/0.53 thf(tyop_2Emin_2Efun,type,
% 0.23/0.53 tyop_2Emin_2Efun: d > d > d ).
% 0.23/0.53
% 0.23/0.53 thf(tyop_2Eoption_2Eoption,type,
% 0.23/0.53 tyop_2Eoption_2Eoption: d > d ).
% 0.23/0.53
% 0.23/0.53 thf(s,type,
% 0.23/0.53 s: d > u > du ).
% 0.23/0.53
% 0.23/0.53 thf(app_2E2,type,
% 0.23/0.53 app_2E2: du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(combin_i_2E0,type,
% 0.23/0.53 combin_i_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(combin_k_2E0,type,
% 0.23/0.53 combin_k_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(combin_s_2E0,type,
% 0.23/0.53 combin_s_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_21_2E0,type,
% 0.23/0.53 c_2Ebool_2E_21_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_21_2E1,type,
% 0.23/0.53 c_2Ebool_2E_21_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.23/0.53 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.23/0.53 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Emin_2E_3D_2E0,type,
% 0.23/0.53 c_2Emin_2E_3D_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Emin_2E_3D_2E2,type,
% 0.23/0.53 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.23/0.53 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.23/0.53 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_3F_2E0,type,
% 0.23/0.53 c_2Ebool_2E_3F_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_3F_2E1,type,
% 0.23/0.53 c_2Ebool_2E_3F_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2EF_2E0,type,
% 0.23/0.53 c_2Ebool_2EF_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EIS__NONE_2E0,type,
% 0.23/0.53 c_2Eoption_2EIS__NONE_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EIS__NONE_2E1,type,
% 0.23/0.53 c_2Eoption_2EIS__NONE_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EIS__SOME_2E0,type,
% 0.23/0.53 c_2Eoption_2EIS__SOME_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EIS__SOME_2E1,type,
% 0.23/0.53 c_2Eoption_2EIS__SOME_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2ENONE_2E0,type,
% 0.23/0.53 c_2Eoption_2ENONE_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EOPTION__JOIN_2E0,type,
% 0.23/0.53 c_2Eoption_2EOPTION__JOIN_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EOPTION__JOIN_2E1,type,
% 0.23/0.53 c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EOPTION__MAP_2E0,type,
% 0.23/0.53 c_2Eoption_2EOPTION__MAP_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EOPTION__MAP_2E2,type,
% 0.23/0.53 c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EOPTREL_2E0,type,
% 0.23/0.53 c_2Eoption_2EOPTREL_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2EOPTREL_2E3,type,
% 0.23/0.53 c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2ESOME_2E0,type,
% 0.23/0.53 c_2Eoption_2ESOME_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2ESOME_2E1,type,
% 0.23/0.53 c_2Eoption_2ESOME_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2ET_2E0,type,
% 0.23/0.53 c_2Ebool_2ET_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2ETHE_2E0,type,
% 0.23/0.53 c_2Eoption_2ETHE_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2ETHE_2E1,type,
% 0.23/0.53 c_2Eoption_2ETHE_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.23/0.53 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.23/0.53 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2Eoption__CASE_2E0,type,
% 0.23/0.53 c_2Eoption_2Eoption__CASE_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Eoption_2Eoption__CASE_2E3,type,
% 0.23/0.53 c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_7E_2E0,type,
% 0.23/0.53 c_2Ebool_2E_7E_2E0: u ).
% 0.23/0.53
% 0.23/0.53 thf(c_2Ebool_2E_7E_2E1,type,
% 0.23/0.53 c_2Ebool_2E_7E_2E1: du > u ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.23/0.53 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.23/0.53 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.23/0.53 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.23/0.53 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Ec_2Ebool_2EF,type,
% 0.23/0.53 mono_2Ec_2Ebool_2EF: $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Ec_2Ebool_2ET,type,
% 0.23/0.53 mono_2Ec_2Ebool_2ET: $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.23/0.53 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.23/0.53 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.23/0.53 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.23/0.53
% 0.23/0.53 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.23/0.53 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.23/0.53
% 0.23/0.53 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.23/0.53 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.23/0.53
% 0.23/0.53 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.23/0.53 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.23/0.53
% 0.23/0.53 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.23/0.53 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.23/0.53 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.23/0.53 ( ! [V2x_2E0: u] :
% 0.23/0.53 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.23/0.53 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.23/0.53 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.23/0.53 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.23/0.53 ! [A_27a: d,V0x_2E0: u] :
% 0.23/0.53 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.23/0.53 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.23/0.53 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.23/0.53 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Eho_2Es__thm,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.23/0.53 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.23/0.53 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.23/0.53 ! [V0: $o,V1: $o] :
% 0.23/0.53 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.23/0.53 <=> ( V0
% 0.23/0.53 & V1 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.23/0.53 ! [V0: $o,V1: $o] :
% 0.23/0.53 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.23/0.53 <=> ( V0
% 0.23/0.53 | V1 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Elogic_2E_7E,axiom,
% 0.23/0.53 ! [V0: $o] :
% 0.23/0.53 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.23/0.53 <=> ( (~) @ V0 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.23/0.53 ! [V0: $o,V1: $o] :
% 0.23/0.53 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.23/0.53 <=> ( V0
% 0.23/0.53 => V1 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Elogic_2E_3D,axiom,
% 0.23/0.53 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.23/0.53 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.23/0.53 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Equant_2E_21,axiom,
% 0.23/0.53 ! [A_27a: d,V0f_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.23/0.53 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(reserved_2Equant_2E_3F,axiom,
% 0.23/0.53 ! [A_27a: d,V0f_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.23/0.53 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.53 ! [V0_2E0: u] :
% 0.23/0.53 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.23/0.53 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.53 ! [V0_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.23/0.53 ! [V0_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.53 ! [V0: $o] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.23/0.53 = V0 ) ).
% 0.23/0.53
% 0.23/0.53 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.53 ! [V0: $o > $o] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.23/0.53 = V0 ) ).
% 0.23/0.53
% 0.23/0.53 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.23/0.53 ! [V0: $o > $o > $o] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.23/0.53 = V0 ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.23/0.53 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.23/0.53 ( ( ( s @ A_27a @ X0_2E0 )
% 0.23/0.53 = ( s @ A_27a @ X1_2E0 ) )
% 0.23/0.53 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.23/0.53 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
% 0.23/0.53 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
% 0.23/0.53 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) )
% 0.23/0.53 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
% 0.23/0.53 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
% 0.23/0.53 ! [A_27b: d,X0_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.53 ( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
% 0.23/0.53 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ A_27a ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.23/0.53 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) )
% 0.23/0.53 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
% 0.23/0.53 ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.23/0.53 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.53 ! [V0: $o > $o,V1: $o] :
% 0.23/0.53 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.23/0.53 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.53 ! [V0: $o > $o > $o,V1: $o] :
% 0.23/0.53 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.53 ! [V0: $o > $o,V1: $o] :
% 0.23/0.53 ( ( V0 @ V1 )
% 0.23/0.53 = ( V0 @ V1 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.53 ! [V0: $o > $o > $o,V1: $o] :
% 0.23/0.53 ( ( V0 @ V1 )
% 0.23/0.53 = ( V0 @ V1 ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.23/0.53 mono_2Ec_2Ebool_2ET ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.23/0.53 ! [V0t1: $o,V1t2: $o] :
% 0.23/0.53 ( ( V0t1
% 0.23/0.53 => V1t2 )
% 0.23/0.53 => ( ( V1t2
% 0.23/0.53 => V0t1 )
% 0.23/0.53 => ( V0t1 = V1t2 ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EFALSITY,axiom,
% 0.23/0.53 ! [V0t: $o] :
% 0.23/0.53 ( mono_2Ec_2Ebool_2EF
% 0.23/0.53 => V0t ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EEXISTS__SIMP,axiom,
% 0.23/0.53 ! [A_27a: d,V0t: $o] :
% 0.23/0.53 ( ? [V1x_2E0: u] : V0t
% 0.23/0.53 <=> V0t ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EAND__CLAUSES,axiom,
% 0.23/0.53 ! [V0t: $o] :
% 0.23/0.53 ( ( ( mono_2Ec_2Ebool_2ET
% 0.23/0.53 & V0t )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( V0t
% 0.23/0.53 & mono_2Ec_2Ebool_2ET )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( mono_2Ec_2Ebool_2EF
% 0.23/0.53 & V0t )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2EF )
% 0.23/0.53 & ( ( V0t
% 0.23/0.53 & mono_2Ec_2Ebool_2EF )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2EF )
% 0.23/0.53 & ( ( V0t
% 0.23/0.53 & V0t )
% 0.23/0.53 <=> V0t ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EOR__CLAUSES,axiom,
% 0.23/0.53 ! [V0t: $o] :
% 0.23/0.53 ( ( ( mono_2Ec_2Ebool_2ET
% 0.23/0.53 | V0t )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2ET )
% 0.23/0.53 & ( ( V0t
% 0.23/0.53 | mono_2Ec_2Ebool_2ET )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2ET )
% 0.23/0.53 & ( ( mono_2Ec_2Ebool_2EF
% 0.23/0.53 | V0t )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( V0t
% 0.23/0.53 | mono_2Ec_2Ebool_2EF )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( V0t
% 0.23/0.53 | V0t )
% 0.23/0.53 <=> V0t ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.23/0.53 ( ! [V0t: $o] :
% 0.23/0.53 ( ( (~) @ ( (~) @ V0t ) )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2EF )
% 0.23/0.53 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.23/0.53 ! [A_27a: d,V0x_2E0: u] :
% 0.23/0.53 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.23/0.53 = ( s @ A_27a @ V0x_2E0 ) )
% 0.23/0.53 <=> mono_2Ec_2Ebool_2ET ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.23/0.53 ! [V0t: $o] :
% 0.23/0.53 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 0.23/0.53 <=> V0t )
% 0.23/0.53 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 0.23/0.53 <=> ( (~) @ V0t ) )
% 0.23/0.53 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 0.23/0.53 <=> ( (~) @ V0t ) ) ) ).
% 0.23/0.53
% 0.23/0.53 thf(thm_2Eoption_2Eoption__CLAUSES,axiom,
% 0.23/0.53 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1e_2E0: u,V2e_2E0: u] :
% 0.23/0.53 ( ! [V3x_2E0: u,V4y_2E0: u] :
% 0.23/0.53 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4y_2E0 ) ) ) )
% 0.23/0.53 <=> ( ( s @ A_27a @ V3x_2E0 )
% 0.23/0.53 = ( s @ A_27a @ V4y_2E0 ) ) )
% 0.23/0.53 & ! [V5x_2E0: u] :
% 0.23/0.53 ( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
% 0.23/0.53 = ( s @ A_27a @ V5x_2E0 ) )
% 0.23/0.53 & ! [V6x_2E0: u] :
% 0.23/0.53 ( (~)
% 0.23/0.53 @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) ) )
% 0.23/0.53 & ! [V7x_2E0: u] :
% 0.23/0.53 ( (~)
% 0.23/0.53 @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_2E0 ) ) )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.23/0.53 & ! [V8x_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V8x_2E0 ) ) ) ) ) )
% 0.23/0.53 = mono_2Ec_2Ebool_2ET )
% 0.23/0.53 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 0.23/0.53 = mono_2Ec_2Ebool_2EF )
% 0.23/0.53 & ! [V9x_2E0: u] :
% 0.23/0.53 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) ) ) )
% 0.23/0.53 <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 )
% 0.23/0.53 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.23/0.53 & ! [V10x_2E0: u] :
% 0.23/0.53 ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) ) ) ) )
% 0.23/0.54 <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.23/0.54 & ! [V11x_2E0: u] :
% 0.23/0.54 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) )
% 0.23/0.54 => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) )
% 0.23/0.54 & ! [V12x_2E0: u] :
% 0.23/0.54 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) )
% 0.23/0.54 & ! [V13x_2E0: u] :
% 0.23/0.54 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) )
% 0.23/0.54 & ! [V14x_2E0: u] :
% 0.23/0.54 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) ) ) )
% 0.23/0.54 => ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) @ ( s @ A_27b @ V2e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
% 0.23/0.54 = ( s @ A_27b @ V2e_2E0 ) ) )
% 0.23/0.54 & ! [V15x_2E0: u] :
% 0.23/0.54 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) )
% 0.23/0.54 => ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) @ ( s @ A_27b @ V2e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
% 0.23/0.54 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) ) ) )
% 0.23/0.54 & ! [V16x_2E0: u] :
% 0.23/0.54 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) )
% 0.23/0.54 => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) )
% 0.23/0.54 & ! [V17v_2E0: u,V18f_2E0: u] :
% 0.23/0.54 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ A_27b @ V17v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V18f_2E0 ) ) )
% 0.23/0.54 = ( s @ A_27b @ V17v_2E0 ) )
% 0.23/0.54 & ! [V19x_2E0: u,V20v_2E0: u,V21f_2E0: u] :
% 0.23/0.54 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V19x_2E0 ) ) ) @ ( s @ A_27b @ V20v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) ) )
% 0.23/0.54 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) @ ( s @ A_27a @ V19x_2E0 ) ) ) )
% 0.23/0.54 & ! [V22f_2E0: u,V23x_2E0: u] :
% 0.23/0.54 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V23x_2E0 ) ) ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ ( s @ A_27a @ V23x_2E0 ) ) ) ) ) )
% 0.23/0.54 & ! [V24f_2E0: u] :
% 0.23/0.54 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V24f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
% 0.23/0.54 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
% 0.23/0.54 & ! [V25x_2E0: u] :
% 0.23/0.54 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Eoption_2EOPTREL__def,axiom,
% 0.23/0.54 ! [A_27a: d,A_27b: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
% 0.23/0.54 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) ) ) )
% 0.23/0.54 <=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
% 0.23/0.54 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.23/0.54 | ? [V3x0_2E0: u,V4y0_2E0: u] :
% 0.23/0.54 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x0_2E0 ) ) ) )
% 0.23/0.54 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 )
% 0.23/0.54 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V4y0_2E0 ) ) ) )
% 0.23/0.54 & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Equotient__option_2EOPTION__REL__def,conjecture,
% 0.23/0.54 ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2R_2E0: u] :
% 0.23/0.54 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 0.23/0.54 = mono_2Ec_2Ebool_2ET )
% 0.23/0.54 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 0.23/0.54 = mono_2Ec_2Ebool_2EF )
% 0.23/0.54 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) )
% 0.23/0.54 = mono_2Ec_2Ebool_2EF )
% 0.23/0.54 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) )
% 0.23/0.56 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 %------------------------------------------------------------------------------
% 0.23/0.56 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.yBvZvuMS4K/cvc5---1.0.5_15716.p...
% 0.23/0.56 (declare-sort $$unsorted 0)
% 0.23/0.56 (declare-sort tptp.u 0)
% 0.23/0.56 (declare-sort tptp.d 0)
% 0.23/0.56 (declare-sort tptp.du 0)
% 0.23/0.56 (declare-fun tptp.tyop_2Emin_2Ebool () tptp.d)
% 0.23/0.56 (declare-fun tptp.tyop_2Emin_2Efun (tptp.d tptp.d) tptp.d)
% 0.23/0.56 (declare-fun tptp.tyop_2Eoption_2Eoption (tptp.d) tptp.d)
% 0.23/0.56 (declare-fun tptp.s (tptp.d tptp.u) tptp.du)
% 0.23/0.56 (declare-fun tptp.app_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.combin_i_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.combin_k_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.combin_s_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_21_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_21_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Emin_2E_3D_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Emin_2E_3D_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_3F_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_3F_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2EF_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EIS__NONE_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EIS__NONE_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EIS__SOME_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EIS__SOME_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2ENONE_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EOPTION__JOIN_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EOPTION__JOIN_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EOPTION__MAP_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EOPTION__MAP_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EOPTREL_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2EOPTREL_2E3 (tptp.du tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2ESOME_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2ESOME_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2ET_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2ETHE_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2ETHE_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2Eoption__CASE_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Eoption_2Eoption__CASE_2E3 (tptp.du tptp.du tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_7E_2E0 () tptp.u)
% 0.23/0.56 (declare-fun tptp.c_2Ebool_2E_7E_2E1 (tptp.du) tptp.u)
% 0.23/0.56 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ((-> Bool Bool) Bool) Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((-> Bool Bool Bool) Bool Bool) Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Ec_2Ebool_2E_2F_5C (Bool Bool) Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Ec_2Emin_2E_3D_3D_3E (Bool Bool) Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Ec_2Ebool_2EF () Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Ec_2Ebool_2ET () Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Ec_2Ebool_2E_5C_2F (Bool Bool) Bool)
% 0.23/0.56 (declare-fun tptp.mono_2Ec_2Ebool_2E_7E (Bool) Bool)
% 0.23/0.56 (declare-fun tptp.i_mono_2Etyop_2Emin_2Ebool (Bool) tptp.u)
% 0.23/0.56 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((-> Bool Bool)) tptp.u)
% 0.23/0.56 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ((-> Bool Bool Bool)) tptp.u)
% 0.23/0.56 (declare-fun tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.du) Bool)
% 0.23/0.56 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.du Bool) Bool)
% 0.23/0.56 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (tptp.du Bool Bool) Bool)
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)))) (=> (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V2x_2E0))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)))) (let ((_let_3 (@ tptp.s A_27b))) (= (@ _let_3 (@ (@ tptp.app_2E2 (@ _let_2 V0f_2E0)) _let_1)) (@ _let_3 (@ (@ tptp.app_2E2 (@ _let_2 V1g_2E0)) _let_1))))))) (= (@ _let_1 V0f_2E0) (@ _let_1 V1g_2E0))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0x_2E0))) (= (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27a)) tptp.combin_i_2E0)) _let_2)) _let_2)))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (V0x_2E0 tptp.u) (V1y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0x_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27a))) (= (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_3) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_3)) tptp.combin_k_2E0)) _let_2))) (@ (@ tptp.s A_27b) V1y_2E0))) _let_2))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (A_27c tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u) (V2x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V2x_2E0))) (let ((_let_2 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_3 (@ _let_2 A_27b))) (let ((_let_4 (@ (@ tptp.s _let_3) V1g_2E0))) (let ((_let_5 (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27c))) (let ((_let_6 (@ _let_2 _let_5))) (let ((_let_7 (@ (@ tptp.s _let_6) V0f_2E0))) (let ((_let_8 (@ tptp.s A_27c))) (let ((_let_9 (@ _let_2 A_27c))) (let ((_let_10 (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_9))) (= (@ _let_8 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_9) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_10) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_6) _let_10)) tptp.combin_s_2E0)) _let_7))) _let_4))) _let_1)) (@ _let_8 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 _let_7) _let_1))) (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 _let_4) _let_1)))))))))))))))))
% 0.23/0.56 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))))
% 0.23/0.56 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))))
% 0.23/0.56 (assert (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))))
% 0.23/0.56 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (V0_2E0 tptp.u) (V1_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V1_2E0))) (let ((_let_3 (@ _let_1 V0_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Emin_2E_3D_2E2 _let_3) _let_2))) (= _let_3 _let_2)))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_21_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)))) (forall ((V1x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)) (@ (@ tptp.s A_27a) V1x_2E0))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_3F_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)))) (exists ((V1x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)) (@ (@ tptp.s A_27a) V1x_2E0))))))))
% 0.23/0.56 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ tptp.j_mono_2Etyop_2Emin_2Ebool _let_2))) _let_2)))))
% 0.23/0.56 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))))
% 0.23/0.56 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Emin_2Ebool))))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 _let_3))) _let_3))))))
% 0.23/0.56 (assert (forall ((V0 Bool)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) V0)))
% 0.23/0.56 (assert (forall ((V0 (-> Bool Bool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) V0)))
% 0.23/0.56 (assert (forall ((V0 (-> Bool Bool Bool))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) V0))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Ebool_2E_21_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Ebool_2E_21_2E0)) _let_2)))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 X1_2E0))) (let ((_let_3 (@ _let_1 X0_2E0))) (let ((_let_4 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_5 (@ _let_4 tptp.tyop_2Emin_2Ebool))) (= (= _let_3 _let_2) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_4 _let_5)) tptp.c_2Emin_2E_3D_2E0)) _let_3))) _let_2)))))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Ebool_2E_3F_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Ebool_2E_3F_2E0)) _let_2)))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Eoption_2EIS__NONE_2E0)) _let_2)))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Eoption_2EIS__SOME_2E0)) _let_2)))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.tyop_2Eoption_2Eoption _let_1))) (let ((_let_3 (@ (@ tptp.s _let_2) X0_2E0))) (let ((_let_4 (@ tptp.s _let_1))) (= (@ _let_4 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 _let_3)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_2) _let_1)) tptp.c_2Eoption_2EOPTION__JOIN_2E0)) _let_3)))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X1_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b))) (let ((_let_4 (@ (@ tptp.s _let_3) X0_2E0))) (let ((_let_5 (@ tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_6 (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_5))) (let ((_let_7 (@ tptp.s _let_5))) (= (@ _let_7 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_4) _let_2)) (@ _let_7 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_6)) tptp.c_2Eoption_2EOPTION__MAP_2E0)) _let_4))) _let_2))))))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 X2_2E0))) (let ((_let_4 (@ _let_2 X1_2E0))) (let ((_let_5 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_6 (@ _let_5 (@ _let_5 tptp.tyop_2Emin_2Ebool)))) (let ((_let_7 (@ (@ tptp.s _let_6) X0_2E0))) (let ((_let_8 (@ tptp.tyop_2Emin_2Efun _let_1))) (let ((_let_9 (@ _let_8 tptp.tyop_2Emin_2Ebool))) (let ((_let_10 (@ _let_8 _let_9))) (let ((_let_11 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_11 (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 _let_7) _let_4) _let_3))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_11 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_9) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_10) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_6) _let_10)) tptp.c_2Eoption_2EOPTREL_2E0)) _let_7))) _let_4))) _let_3)))))))))))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_2 (@ (@ tptp.s _let_1) X2_2E0))) (let ((_let_3 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_4 (@ (@ tptp.s _let_3) X1_2E0))) (let ((_let_5 (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)))) (let ((_let_6 (@ (@ tptp.s _let_5) X0_2E0))) (let ((_let_7 (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool))) (let ((_let_8 (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_7))) (let ((_let_9 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_9 (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 _let_6) _let_4) _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_9 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_8) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_5) _let_8)) tptp.c_2Eoption_2EOPTREL_2E0)) _let_6))) _let_4))) _let_2)))))))))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) X0_2E0))) (let ((_let_2 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_2)) tptp.c_2Eoption_2ESOME_2E0)) _let_1))))))))
% 0.23/0.56 (assert (forall ((A_27b tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27b) X0_2E0))) (let ((_let_2 (@ tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) _let_2)) tptp.c_2Eoption_2ESOME_2E0)) _let_1))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.tyop_2Eoption_2Eoption _let_1))) (let ((_let_4 (@ tptp.s _let_3))) (= (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_3)) tptp.c_2Eoption_2ESOME_2E0)) _let_2)))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s A_27a))) (= (@ _let_3 (@ tptp.c_2Eoption_2ETHE_2E1 _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) A_27a)) tptp.c_2Eoption_2ETHE_2E0)) _let_2))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b))) (let ((_let_2 (@ (@ tptp.s _let_1) X2_2E0))) (let ((_let_3 (@ tptp.s A_27b))) (let ((_let_4 (@ _let_3 X1_2E0))) (let ((_let_5 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_6 (@ (@ tptp.s _let_5) X0_2E0))) (let ((_let_7 (@ (@ tptp.tyop_2Emin_2Efun _let_1) A_27b))) (let ((_let_8 (@ (@ tptp.tyop_2Emin_2Efun A_27b) _let_7))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_6) _let_4) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_8) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_5) _let_8)) tptp.c_2Eoption_2Eoption__CASE_2E0)) _let_6))) _let_4))) _let_2)))))))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1))) (let ((_let_3 (@ (@ tptp.s _let_2) X2_2E0))) (let ((_let_4 (@ tptp.s _let_1))) (let ((_let_5 (@ _let_4 X1_2E0))) (let ((_let_6 (@ _let_4 X0_2E0))) (let ((_let_7 (@ (@ tptp.tyop_2Emin_2Efun _let_2) _let_1))) (let ((_let_8 (@ tptp.tyop_2Emin_2Efun _let_1))) (let ((_let_9 (@ _let_8 _let_7))) (= (@ _let_4 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_6) _let_5) _let_3)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_9) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_8 _let_9)) tptp.c_2Eoption_2Eoption__CASE_2E0)) _let_6))) _let_5))) _let_3))))))))))))))
% 0.23/0.56 (assert (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ V0 V1))) (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1))))))))
% 0.23/0.56 (assert (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1))))))))))
% 0.23/0.56 (assert (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.23/0.56 (assert (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.23/0.56 (assert tptp.mono_2Ec_2Ebool_2ET)
% 0.23/0.56 (assert (forall ((V0t1 Bool) (V1t2 Bool)) (=> (=> V0t1 V1t2) (=> (=> V1t2 V0t1) (= V0t1 V1t2)))))
% 0.23/0.56 (assert (forall ((V0t Bool)) (=> tptp.mono_2Ec_2Ebool_2EF V0t)))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (V0t Bool)) (= (exists ((V1x_2E0 tptp.u)) V0t) V0t)))
% 0.23/0.56 (assert (forall ((V0t Bool)) (and (= (and tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (and V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (and tptp.mono_2Ec_2Ebool_2EF V0t) tptp.mono_2Ec_2Ebool_2EF) (= (and V0t tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2EF) (= (and V0t V0t) V0t))))
% 0.23/0.56 (assert (forall ((V0t Bool)) (and (= (or tptp.mono_2Ec_2Ebool_2ET V0t) tptp.mono_2Ec_2Ebool_2ET) (= (or V0t tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2ET) (= (or tptp.mono_2Ec_2Ebool_2EF V0t) V0t) (= (or V0t tptp.mono_2Ec_2Ebool_2EF) V0t) (= (or V0t V0t) V0t))))
% 0.23/0.56 (assert (and (forall ((V0t Bool)) (= (not (not V0t)) V0t)) (= (not tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2EF) (= (not tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2ET)))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V0x_2E0))) (= (= _let_1 _let_1) tptp.mono_2Ec_2Ebool_2ET))))
% 0.23/0.56 (assert (forall ((V0t Bool)) (let ((_let_1 (not V0t))) (and (= (= tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (= V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (= tptp.mono_2Ec_2Ebool_2EF V0t) _let_1) (= (= V0t tptp.mono_2Ec_2Ebool_2EF) _let_1)))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (V0f_2E0 tptp.u) (V1e_2E0 tptp.u) (V2e_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 tptp.c_2Eoption_2ENONE_2E0))) (and (forall ((V3x_2E0 tptp.u) (V4y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V4y_2E0))) (let ((_let_3 (@ _let_1 V3x_2E0))) (let ((_let_4 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (= (= (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_3)) (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2))) (= _let_3 _let_2))))))) (forall ((V5x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V5x_2E0))) (= (@ _let_1 (@ tptp.c_2Eoption_2ETHE_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)))) _let_2)))) (forall ((V6x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (not (= (@ _let_1 tptp.c_2Eoption_2ENONE_2E0) (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) V6x_2E0))))))) (forall ((V7x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (not (= (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) V7x_2E0))) (@ _let_1 tptp.c_2Eoption_2ENONE_2E0))))) (forall ((V8x_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) V8x_2E0)))))) tptp.mono_2Ec_2Ebool_2ET)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_3))) tptp.mono_2Ec_2Ebool_2EF) (forall ((V9x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_2 (@ _let_1 V9x_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((V10x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_2 (@ _let_1 V10x_2E0))) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)))) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((V11x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_2 (@ _let_1 V11x_2E0))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2))) (= (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) (@ tptp.c_2Eoption_2ETHE_2E1 _let_2)))) _let_2))))) (forall ((V12x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V12x_2E0))) (= (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) (@ _let_2 tptp.c_2Eoption_2ENONE_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1)) tptp.c_2Eoption_2ESOME_2E0))) _let_3))))) (forall ((V13x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V13x_2E0))) (= (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) _let_3) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1)) tptp.c_2Eoption_2ESOME_2E0))) _let_3))))) (forall ((V14x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27b))) (let ((_let_2 (@ _let_1 V2e_2E0))) (let ((_let_3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) V14x_2E0))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_3))) (= (@ _let_1 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) _let_2) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0))) _let_2)))))) (forall ((V15x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) V15x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0))) (let ((_let_3 (@ tptp.s A_27b))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_1))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_1) (@ _let_3 V2e_2E0)) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 _let_2) (@ (@ tptp.s A_27a) (@ tptp.c_2Eoption_2ETHE_2E1 _let_1)))))))))) (forall ((V16x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V16x_2E0))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_3))) (= (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) (@ _let_2 V1e_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1)) tptp.c_2Eoption_2ESOME_2E0))) _let_3)))))) (forall ((V17v_2E0 tptp.u) (V18f_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27b))) (let ((_let_2 (@ _let_1 V17v_2E0))) (= (@ _let_1 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) tptp.c_2Eoption_2ENONE_2E0)) _let_2) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V18f_2E0))) _let_2)))) (forall ((V19x_2E0 tptp.u) (V20v_2E0 tptp.u) (V21f_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V19x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0))) (let ((_let_3 (@ tptp.s A_27b))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_1))) (@ _let_3 V20v_2E0)) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 _let_2) _let_1))))))) (forall ((V22f_2E0 tptp.u) (V23x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V23x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0))) (let ((_let_3 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (= (@ _let_3 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_2) (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 _let_2) _let_1))))))))) (forall ((V24f_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (= (@ _let_1 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V24f_2E0)) (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) tptp.c_2Eoption_2ENONE_2E0))) (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))) (= (@ _let_2 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption _let_1)) tptp.c_2Eoption_2ENONE_2E0))) _let_3) (forall ((V25x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V25x_2E0))) (= (@ _let_2 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption _let_1)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_3)))) _let_3)))))))))))
% 0.23/0.56 (assert (forall ((A_27a tptp.d) (A_27b tptp.d) (V0R_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (let ((_let_2 (@ _let_1 V2y_2E0))) (let ((_let_3 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_4 (@ _let_3 V1x_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool))) V0R_2E0)) _let_4) _let_2))) (or (and (= _let_4 (@ _let_3 tptp.c_2Eoption_2ENONE_2E0)) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0))) (exists ((V3x0_2E0 tptp.u) (V4y0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27b) V4y0_2E0))) (let ((_let_2 (@ (@ tptp.s A_27a) V3x0_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (let ((_let_5 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (and (= (@ _let_5 V1x_2E0) (@ _let_5 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2))) (= (@ _let_4 V2y_2E0) (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_3) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_3)) V0R_2E0)) _let_2))) _let_1))))))))))))))))))
% 91.43/91.64 (assert (not (forall ((A_27a tptp.d) (V0y_2E0 tptp.u) (V1x_2E0 tptp.u) (V2R_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0y_2E0))) (let ((_let_3 (@ _let_1 V1x_2E0))) (let ((_let_4 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_5 (@ _let_4 tptp.tyop_2Emin_2Ebool))) (let ((_let_6 (@ (@ tptp.s (@ _let_4 _let_5)) V2R_2E0))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (let ((_let_8 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_9 (@ _let_8 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (let ((_let_10 (@ tptp.c_2Eoption_2EOPTREL_2E3 _let_6))) (let ((_let_11 (@ _let_10 (@ _let_8 (@ tptp.c_2Eoption_2ESOME_2E1 _let_3))))) (let ((_let_12 (@ _let_8 tptp.c_2Eoption_2ENONE_2E0))) (let ((_let_13 (@ _let_10 _let_12))) (and (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_13 _let_12))) tptp.mono_2Ec_2Ebool_2ET) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_11 _let_12))) tptp.mono_2Ec_2Ebool_2EF) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_13 _let_9))) tptp.mono_2Ec_2Ebool_2EF) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_11 _let_9))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 _let_6) _let_3))) _let_2)))))))))))))))))))))
% 91.43/91.64 (set-info :filename cvc5---1.0.5_15716)
% 91.43/91.64 (check-sat-assuming ( true ))
% 91.43/91.64 ------- get file name : TPTP file name is ITP011^1
% 91.43/91.64 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15716.smt2...
% 91.43/91.64 --- Run --ho-elim --full-saturate-quant at 10...
% 91.43/91.64 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 91.43/91.64 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 91.43/91.64 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 91.43/91.64 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 91.43/91.64 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 91.43/91.64 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 91.43/91.64 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 91.43/91.64 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 91.43/91.64 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 91.43/91.64 % SZS status Theorem for ITP011^1
% 91.43/91.64 % SZS output start Proof for ITP011^1
% 91.43/91.64 (
% 91.43/91.64 (let ((_let_1 (not (forall ((A_27a tptp.d) (V0y_2E0 tptp.u) (V1x_2E0 tptp.u) (V2R_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0y_2E0))) (let ((_let_3 (@ _let_1 V1x_2E0))) (let ((_let_4 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_5 (@ _let_4 tptp.tyop_2Emin_2Ebool))) (let ((_let_6 (@ (@ tptp.s (@ _let_4 _let_5)) V2R_2E0))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (let ((_let_8 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_9 (@ _let_8 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (let ((_let_10 (@ tptp.c_2Eoption_2EOPTREL_2E3 _let_6))) (let ((_let_11 (@ _let_10 (@ _let_8 (@ tptp.c_2Eoption_2ESOME_2E1 _let_3))))) (let ((_let_12 (@ _let_8 tptp.c_2Eoption_2ENONE_2E0))) (let ((_let_13 (@ _let_10 _let_12))) (and (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_13 _let_12))) tptp.mono_2Ec_2Ebool_2ET) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_11 _let_12))) tptp.mono_2Ec_2Ebool_2EF) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_13 _let_9))) tptp.mono_2Ec_2Ebool_2EF) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_11 _let_9))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 _let_6) _let_3))) _let_2)))))))))))))))))))))) (let ((_let_2 (forall ((A_27a tptp.d) (A_27b tptp.d) (V0R_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (let ((_let_2 (@ _let_1 V2y_2E0))) (let ((_let_3 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_4 (@ _let_3 V1x_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool))) V0R_2E0)) _let_4) _let_2))) (or (and (= _let_4 (@ _let_3 tptp.c_2Eoption_2ENONE_2E0)) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0))) (exists ((V3x0_2E0 tptp.u) (V4y0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27b) V4y0_2E0))) (let ((_let_2 (@ (@ tptp.s A_27a) V3x0_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (let ((_let_5 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (and (= (@ _let_5 V1x_2E0) (@ _let_5 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2))) (= (@ _let_4 V2y_2E0) (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_3) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_3)) V0R_2E0)) _let_2))) _let_1))))))))))))))))))) (let ((_let_3 (forall ((A_27a tptp.d) (A_27b tptp.d) (V0f_2E0 tptp.u) (V1e_2E0 tptp.u) (V2e_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 tptp.c_2Eoption_2ENONE_2E0))) (and (forall ((V3x_2E0 tptp.u) (V4y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V4y_2E0))) (let ((_let_3 (@ _let_1 V3x_2E0))) (let ((_let_4 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (= (= (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_3)) (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2))) (= _let_3 _let_2))))))) (forall ((V5x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V5x_2E0))) (= (@ _let_1 (@ tptp.c_2Eoption_2ETHE_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)))) _let_2)))) (forall ((V6x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (not (= (@ _let_1 tptp.c_2Eoption_2ENONE_2E0) (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) V6x_2E0))))))) (forall ((V7x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (not (= (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) V7x_2E0))) (@ _let_1 tptp.c_2Eoption_2ENONE_2E0))))) (forall ((V8x_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) V8x_2E0)))))) tptp.mono_2Ec_2Ebool_2ET)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_3))) tptp.mono_2Ec_2Ebool_2EF) (forall ((V9x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_2 (@ _let_1 V9x_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((V10x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_2 (@ _let_1 V10x_2E0))) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)))) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((V11x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_2 (@ _let_1 V11x_2E0))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2))) (= (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27a) (@ tptp.c_2Eoption_2ETHE_2E1 _let_2)))) _let_2))))) (forall ((V12x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V12x_2E0))) (= (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) (@ _let_2 tptp.c_2Eoption_2ENONE_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1)) tptp.c_2Eoption_2ESOME_2E0))) _let_3))))) (forall ((V13x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V13x_2E0))) (= (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) _let_3) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1)) tptp.c_2Eoption_2ESOME_2E0))) _let_3))))) (forall ((V14x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27b))) (let ((_let_2 (@ _let_1 V2e_2E0))) (let ((_let_3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) V14x_2E0))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_3))) (= (@ _let_1 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) _let_2) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0))) _let_2)))))) (forall ((V15x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) V15x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0))) (let ((_let_3 (@ tptp.s A_27b))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_1))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_1) (@ _let_3 V2e_2E0)) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 _let_2) (@ (@ tptp.s A_27a) (@ tptp.c_2Eoption_2ETHE_2E1 _let_1)))))))))) (forall ((V16x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V16x_2E0))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_3))) (= (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) (@ _let_2 V1e_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1)) tptp.c_2Eoption_2ESOME_2E0))) _let_3)))))) (forall ((V17v_2E0 tptp.u) (V18f_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27b))) (let ((_let_2 (@ _let_1 V17v_2E0))) (= (@ _let_1 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) tptp.c_2Eoption_2ENONE_2E0)) _let_2) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V18f_2E0))) _let_2)))) (forall ((V19x_2E0 tptp.u) (V20v_2E0 tptp.u) (V21f_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V19x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V21f_2E0))) (let ((_let_3 (@ tptp.s A_27b))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_1))) (@ _let_3 V20v_2E0)) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 _let_2) _let_1))))))) (forall ((V22f_2E0 tptp.u) (V23x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V23x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V22f_2E0))) (let ((_let_3 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (= (@ _let_3 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_2) (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 _let_2) _let_1))))))))) (forall ((V24f_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (= (@ _let_1 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V24f_2E0)) (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)) tptp.c_2Eoption_2ENONE_2E0))) (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))) (= (@ _let_2 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption _let_1)) tptp.c_2Eoption_2ENONE_2E0))) _let_3) (forall ((V25x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V25x_2E0))) (= (@ _let_2 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption _let_1)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_3)))) _let_3)))))))))))) (let ((_let_4 (forall ((V0t Bool)) (=> tptp.mono_2Ec_2Ebool_2EF V0t)))) (let ((_let_5 (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Eoption_2EIS__NONE_2E0)) _let_2)))))))))) (let ((_let_6 (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ tptp.j_mono_2Etyop_2Emin_2Ebool _let_2))) _let_2)))))) (let ((_let_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (let ((_let_8 (ho_4 k_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46))) (let ((_let_9 (ho_6 k_5 _let_8))) (let ((_let_10 (ho_7 _let_9 tptp.c_2Eoption_2ENONE_2E0))) (let ((_let_11 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46))) (let ((_let_12 (ho_10 k_39 (ho_7 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47)))) (let ((_let_13 (ho_7 _let_9 _let_12))) (let ((_let_14 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46))) (let ((_let_15 (ho_4 _let_14 tptp.tyop_2Emin_2Ebool))) (let ((_let_16 (ho_7 (ho_6 k_5 (ho_4 _let_14 _let_15)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48))) (let ((_let_17 (ho_10 (ho_9 (ho_38 k_37 _let_16) _let_13) _let_10))) (let ((_let_18 (ho_7 _let_7 _let_17))) (let ((_let_19 (= _let_18 (ho_7 _let_7 (ho_23 k_22 BOOLEAN_TERM_VARIABLE_6704))))) (let ((_let_20 (ho_19 k_18 _let_18))) (let ((_let_21 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_22 (ho_7 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (let ((_let_23 (ho_7 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))) (let ((_let_24 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_25 (ho_4 _let_24 tptp.tyop_2Emin_2Ebool))) (let ((_let_26 (ho_7 (ho_6 k_5 (ho_4 _let_24 _let_25)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70))) (let ((_let_27 (ho_9 k_8 _let_26))) (let ((_let_28 (ho_6 k_5 _let_25))) (let ((_let_29 (ho_10 (ho_9 k_8 (ho_7 _let_28 (ho_10 _let_27 _let_23))) _let_22))) (let ((_let_30 (ho_7 _let_7 _let_29))) (let ((_let_31 (= _let_30 (ho_7 _let_7 (ho_23 k_22 BOOLEAN_TERM_VARIABLE_16280))))) (let ((_let_32 (ho_10 k_39 _let_23))) (let ((_let_33 (ho_6 k_5 (ho_4 k_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67)))) (let ((_let_34 (ho_7 _let_33 _let_32))) (let ((_let_35 (= _let_23 (ho_7 _let_21 (ho_10 k_40 _let_34))))) (let ((_let_36 (ho_10 k_39 _let_22))) (let ((_let_37 (ho_7 _let_33 _let_36))) (let ((_let_38 (= _let_22 (ho_7 _let_21 (ho_10 k_40 _let_37))))) (let ((_let_39 (ho_7 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_116))) (let ((_let_40 (ho_7 _let_33 (ho_10 k_39 _let_39)))) (let ((_let_41 (= _let_34 _let_40))) (let ((_let_42 (ho_7 _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_117))) (let ((_let_43 (ho_7 _let_33 (ho_10 k_39 _let_42)))) (let ((_let_44 (= _let_37 _let_43))) (let ((_let_45 (ho_19 k_18 (ho_7 _let_7 (ho_10 (ho_9 k_8 (ho_7 _let_28 (ho_10 _let_27 _let_39))) _let_42))))) (let ((_let_46 (= _let_39 (ho_7 _let_21 (ho_10 k_40 _let_40))))) (let ((_let_47 (= _let_42 (ho_7 _let_21 (ho_10 k_40 _let_43))))) (let ((_let_48 (forall ((V0_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (ho_7 _let_1 V0_2E0))) (= _let_2 (ho_7 _let_1 (ho_23 k_22 (ho_19 k_18 _let_2))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ _let_1 V0_2E0))) (= _let_2 (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ tptp.j_mono_2Etyop_2Emin_2Ebool _let_2))))))) _let_48))))))) (let ((_let_50 (=>))) (let ((_let_51 (=))) (let ((_let_52 (APPLY_UF ho_7))) (let ((_let_53 (APPLY_UF ho_23))) (let ((_let_54 (MACRO_SR_PRED_INTRO :args ((= _let_20 BOOLEAN_TERM_VARIABLE_6704))))) (let ((_let_55 (REFL :args (k_22)))) (let ((_let_56 (REFL :args (_let_7)))) (let ((_let_57 (_let_48))) (let ((_let_58 (REFL :args _let_57))) (let ((_let_59 (forall ((V3x0_2E0 tptp.u) (V4y0_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46))) (let ((_let_2 (ho_7 _let_1 V4y0_2E0))) (let ((_let_3 (ho_7 _let_1 V3x0_2E0))) (let ((_let_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46))) (let ((_let_5 (ho_4 _let_4 tptp.tyop_2Emin_2Ebool))) (let ((_let_6 (ho_6 k_5 (ho_4 k_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46)))) (or (not (= (ho_7 _let_6 (ho_10 k_39 (ho_7 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47))) (ho_7 _let_6 (ho_10 k_39 _let_3)))) (not (= (ho_7 _let_6 tptp.c_2Eoption_2ENONE_2E0) (ho_7 _let_6 (ho_10 k_39 _let_2)))) (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 _let_5) (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 (ho_4 _let_4 _let_5)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48)) _let_3))) _let_2)))))))))))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (= _let_13 _let_10))) (let ((_let_62 (or _let_61 _let_60))) (let ((_let_63 (= _let_20 _let_62))) (let ((_let_64 (not _let_20))) (let ((_let_65 (forall ((A_27a tptp.d) (A_27b tptp.d) (V0R_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 A_27b)))) (let ((_let_2 (ho_7 _let_1 V2y_2E0))) (let ((_let_3 (ho_6 k_5 (ho_4 k_32 A_27a)))) (let ((_let_4 (ho_7 _let_3 V1x_2E0))) (= (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 (ho_9 (ho_38 k_37 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) (ho_4 (ho_3 k_2 A_27b) tptp.tyop_2Emin_2Ebool))) V0R_2E0)) _let_4) _let_2))) (or (and (= _let_4 (ho_7 _let_3 tptp.c_2Eoption_2ENONE_2E0)) (= _let_2 (ho_7 _let_1 tptp.c_2Eoption_2ENONE_2E0))) (not (forall ((V3x0_2E0 tptp.u) (V4y0_2E0 tptp.u)) (let ((_let_1 (ho_7 (ho_6 k_5 A_27b) V4y0_2E0))) (let ((_let_2 (ho_7 (ho_6 k_5 A_27a) V3x0_2E0))) (let ((_let_3 (ho_4 (ho_3 k_2 A_27b) tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (ho_6 k_5 (ho_4 k_32 A_27b)))) (let ((_let_5 (ho_6 k_5 (ho_4 k_32 A_27a)))) (or (not (= (ho_7 _let_5 (ho_10 k_39 _let_2)) (ho_7 _let_5 V1x_2E0))) (not (= (ho_7 _let_4 (ho_10 k_39 _let_1)) (ho_7 _let_4 V2y_2E0))) (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 _let_3) (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) _let_3)) V0R_2E0)) _let_2))) _let_1))))))))))))))))))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_27a tptp.d) (A_27b tptp.d) (V0R_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (let ((_let_2 (@ _let_1 V2y_2E0))) (let ((_let_3 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (let ((_let_4 (@ _let_3 V1x_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool))) V0R_2E0)) _let_4) _let_2))) (or (and (= _let_4 (@ _let_3 tptp.c_2Eoption_2ENONE_2E0)) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0))) (not (forall ((V3x0_2E0 tptp.u) (V4y0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27b) V4y0_2E0))) (let ((_let_2 (@ (@ tptp.s A_27a) V3x0_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27b)))) (let ((_let_5 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption A_27a)))) (or (not (= (@ _let_5 V1x_2E0) (@ _let_5 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)))) (not (= (@ _let_4 V2y_2E0) (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_3) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_3)) V0R_2E0)) _let_2))) _let_1))))))))))))))))))) _let_65))))))) (let ((_let_67 (_let_65))) (let ((_let_68 ((ho_10 (ho_9 (ho_38 k_37 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) (ho_4 (ho_3 k_2 A_27b) tptp.tyop_2Emin_2Ebool))) V0R_2E0)) (ho_7 (ho_6 k_5 (ho_4 k_32 A_27a)) V1x_2E0)) (ho_7 (ho_6 k_5 (ho_4 k_32 A_27b)) V2y_2E0))))) (let ((_let_69 (not _let_62))) (let ((_let_70 (ho_7 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_52))) (let ((_let_71 (ho_7 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_51))) (let ((_let_72 (= _let_10 (ho_7 _let_9 (ho_10 k_39 _let_70))))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or (not (= _let_13 (ho_7 _let_9 (ho_10 k_39 _let_71)))) _let_73 (not (ho_19 k_18 (ho_7 _let_7 (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 _let_15) (ho_10 (ho_9 k_8 _let_16) _let_71))) _let_70))))))) (let ((_let_75 (forall ((BOUND_VARIABLE_2043 tptp.d) (V6x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2043)))) (not (= (ho_7 _let_1 (ho_10 k_39 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2043) V6x_2E0))) (ho_7 _let_1 tptp.c_2Eoption_2ENONE_2E0))))))) (let ((_let_76 (forall ((BOUND_VARIABLE_2132 tptp.d) (V9x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2132)))) (let ((_let_2 (ho_7 _let_1 V9x_2E0))) (= (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_33 _let_2))) (= (ho_7 _let_1 tptp.c_2Eoption_2ENONE_2E0) _let_2))))))) (let ((_let_77 (forall ((BOUND_VARIABLE_2021 tptp.d) (V5x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_2021))) (let ((_let_2 (ho_7 _let_1 V5x_2E0))) (= _let_2 (ho_7 _let_1 (ho_10 k_40 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2021)) (ho_10 k_39 _let_2)))))))))) (let ((_let_78 (forall ((BOUND_VARIABLE_2512 tptp.d) (V25x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2512))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V25x_2E0))) (= _let_3 (@ _let_2 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption _let_1)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_3))))))))))) (let ((_let_79 (forall ((BOUND_VARIABLE_2490 tptp.d)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2490))) (let ((_let_2 (@ tptp.s _let_1))) (= (@ _let_2 tptp.c_2Eoption_2ENONE_2E0) (@ _let_2 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption _let_1)) tptp.c_2Eoption_2ENONE_2E0))))))))) (let ((_let_80 (forall ((BOUND_VARIABLE_2462 tptp.d) (BOUND_VARIABLE_2464 tptp.d) (V24f_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2464)))) (= (@ _let_1 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2462) BOUND_VARIABLE_2464)) V24f_2E0)) (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2462)) tptp.c_2Eoption_2ENONE_2E0))) (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))) (let ((_let_81 (forall ((BOUND_VARIABLE_2426 tptp.d) (BOUND_VARIABLE_2428 tptp.d) (V22f_2E0 tptp.u) (V23x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s BOUND_VARIABLE_2426) V23x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2426) BOUND_VARIABLE_2428)) V22f_2E0))) (let ((_let_3 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2428)))) (= (@ _let_3 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_2) (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2426)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)))) (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s BOUND_VARIABLE_2428) (@ (@ tptp.app_2E2 _let_2) _let_1))))))))))) (let ((_let_82 (forall ((BOUND_VARIABLE_2392 tptp.d) (BOUND_VARIABLE_2394 tptp.d) (V19x_2E0 tptp.u) (V20v_2E0 tptp.u) (V21f_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s BOUND_VARIABLE_2392) V19x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2392) BOUND_VARIABLE_2394)) V21f_2E0))) (let ((_let_3 (@ tptp.s BOUND_VARIABLE_2394))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2392)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_1))) (@ _let_3 V20v_2E0)) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 _let_2) _let_1))))))))) (let ((_let_83 (forall ((BOUND_VARIABLE_2364 tptp.d) (BOUND_VARIABLE_2366 tptp.d) (V17v_2E0 tptp.u) (V18f_2E0 tptp.u)) (let ((_let_1 (@ tptp.s BOUND_VARIABLE_2366))) (let ((_let_2 (@ _let_1 V17v_2E0))) (= _let_2 (@ _let_1 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2364)) tptp.c_2Eoption_2ENONE_2E0)) _let_2) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2364) BOUND_VARIABLE_2366)) V18f_2E0))))))))) (let ((_let_84 (forall ((BOUND_VARIABLE_2332 tptp.d) (V16x_2E0 tptp.u) (BOUND_VARIABLE_2338 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2332))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V16x_2E0))) (or (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_3)))) (= _let_3 (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) (@ _let_2 BOUND_VARIABLE_2338)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2332) _let_1)) tptp.c_2Eoption_2ESOME_2E0))))))))))) (let ((_let_85 (forall ((BOUND_VARIABLE_2293 tptp.d) (V15x_2E0 tptp.u) (BOUND_VARIABLE_2295 tptp.d) (BOUND_VARIABLE_2297 tptp.u) (BOUND_VARIABLE_2301 tptp.u)) (let ((_let_1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2293)) V15x_2E0))) (let ((_let_2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2293) BOUND_VARIABLE_2295)) BOUND_VARIABLE_2297))) (let ((_let_3 (@ tptp.s BOUND_VARIABLE_2295))) (or (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_1)))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_1) (@ _let_3 BOUND_VARIABLE_2301)) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 _let_2) (@ (@ tptp.s BOUND_VARIABLE_2293) (@ tptp.c_2Eoption_2ETHE_2E1 _let_1)))))))))))) (let ((_let_86 (forall ((BOUND_VARIABLE_2260 tptp.d) (V14x_2E0 tptp.u) (BOUND_VARIABLE_2262 tptp.d) (BOUND_VARIABLE_2264 tptp.u) (BOUND_VARIABLE_2268 tptp.u)) (let ((_let_1 (@ tptp.s BOUND_VARIABLE_2262))) (let ((_let_2 (@ _let_1 BOUND_VARIABLE_2268))) (let ((_let_3 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2260)) V14x_2E0))) (or (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_3)))) (= _let_2 (@ _let_1 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) _let_2) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2260) BOUND_VARIABLE_2262)) BOUND_VARIABLE_2264))))))))))) (let ((_let_87 (forall ((BOUND_VARIABLE_2234 tptp.d) (V13x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2234))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V13x_2E0))) (= _let_3 (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) _let_3) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2234) _let_1)) tptp.c_2Eoption_2ESOME_2E0)))))))))) (let ((_let_88 (forall ((BOUND_VARIABLE_2207 tptp.d) (V12x_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2207))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 V12x_2E0))) (= _let_3 (@ _let_2 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_3) (@ _let_2 tptp.c_2Eoption_2ENONE_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun BOUND_VARIABLE_2207) _let_1)) tptp.c_2Eoption_2ESOME_2E0)))))))))) (let ((_let_89 (forall ((BOUND_VARIABLE_2179 tptp.d) (V11x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2179)))) (let ((_let_2 (@ _let_1 V11x_2E0))) (or (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)))) (= _let_2 (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s BOUND_VARIABLE_2179) (@ tptp.c_2Eoption_2ETHE_2E1 _let_2))))))))))) (let ((_let_90 (forall ((BOUND_VARIABLE_2155 tptp.d) (V10x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2155)))) (let ((_let_2 (@ _let_1 V10x_2E0))) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2)))) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))))) (let ((_let_91 (forall ((BOUND_VARIABLE_2132 tptp.d) (V9x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2132)))) (let ((_let_2 (@ _let_1 V9x_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__NONE_2E1 _let_2))) (= _let_2 (@ _let_1 tptp.c_2Eoption_2ENONE_2E0)))))))) (let ((_let_92 (forall ((BOUND_VARIABLE_2065 tptp.d) (V7x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2065)))) (not (= (@ _let_1 tptp.c_2Eoption_2ENONE_2E0) (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s BOUND_VARIABLE_2065) V7x_2E0))))))))) (let ((_let_93 (forall ((BOUND_VARIABLE_2043 tptp.d) (V6x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2043)))) (not (= (@ _let_1 tptp.c_2Eoption_2ENONE_2E0) (@ _let_1 (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s BOUND_VARIABLE_2043) V6x_2E0))))))))) (let ((_let_94 (forall ((BOUND_VARIABLE_2021 tptp.d) (V5x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s BOUND_VARIABLE_2021))) (let ((_let_2 (@ _let_1 V5x_2E0))) (= _let_2 (@ _let_1 (@ tptp.c_2Eoption_2ETHE_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2021)) (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)))))))))) (let ((_let_95 (forall ((BOUND_VARIABLE_1996 tptp.d) (V3x_2E0 tptp.u) (V4y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s BOUND_VARIABLE_1996))) (let ((_let_2 (@ _let_1 V4y_2E0))) (let ((_let_3 (@ _let_1 V3x_2E0))) (let ((_let_4 (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_1996)))) (= (= (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_3)) (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2))) (= _let_3 _let_2))))))))) (let ((_let_96 (AND_INTRO (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.mono_2Ec_2Ebool_2EF false))) (MACRO_SR_PRED_TRANSFORM (ASSUME :args (tptp.mono_2Ec_2Ebool_2ET)) :args ((= tptp.mono_2Ec_2Ebool_2ET true)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_96 :args ((and _let_95 _let_94 _let_93 _let_92 (forall ((BOUND_VARIABLE_2088 tptp.d) (V8x_2E0 tptp.u)) (= tptp.mono_2Ec_2Ebool_2ET (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2088)) (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s BOUND_VARIABLE_2088) V8x_2E0)))))))) (forall ((BOUND_VARIABLE_2112 tptp.d)) (= tptp.mono_2Ec_2Ebool_2EF (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2112)) tptp.c_2Eoption_2ENONE_2E0)))))) _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and _let_95 _let_94 _let_93 _let_92 (forall ((BOUND_VARIABLE_2088 tptp.d) (V8x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2088)) (@ tptp.c_2Eoption_2ESOME_2E1 (@ (@ tptp.s BOUND_VARIABLE_2088) V8x_2E0))))))) (forall ((BOUND_VARIABLE_2112 tptp.d)) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Eoption_2EIS__SOME_2E1 (@ (@ tptp.s (@ tptp.tyop_2Eoption_2Eoption BOUND_VARIABLE_2112)) tptp.c_2Eoption_2ENONE_2E0)))))) _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78) (and (forall ((BOUND_VARIABLE_1996 tptp.d) (V3x_2E0 tptp.u) (V4y_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_1996))) (let ((_let_2 (ho_7 _let_1 V3x_2E0))) (let ((_let_3 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_1996)))) (let ((_let_4 (ho_7 _let_1 V4y_2E0))) (= (= _let_4 _let_2) (= (ho_7 _let_3 (ho_10 k_39 _let_4)) (ho_7 _let_3 (ho_10 k_39 _let_2))))))))) _let_77 _let_75 (forall ((BOUND_VARIABLE_2065 tptp.d) (V7x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2065)))) (not (= (ho_7 _let_1 (ho_10 k_39 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2065) V7x_2E0))) (ho_7 _let_1 tptp.c_2Eoption_2ENONE_2E0))))) (forall ((BOUND_VARIABLE_2088 tptp.d) (V8x_2E0 tptp.u)) (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_34 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2088)) (ho_10 k_39 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2088) V8x_2E0))))))) (forall ((BOUND_VARIABLE_2112 tptp.d)) (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_34 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2112)) tptp.c_2Eoption_2ENONE_2E0)))))) _let_76 (forall ((BOUND_VARIABLE_2155 tptp.d) (V10x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2155)))) (let ((_let_2 (ho_7 _let_1 V10x_2E0))) (= (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_34 _let_2)))) (= (ho_7 _let_1 tptp.c_2Eoption_2ENONE_2E0) _let_2))))) (forall ((BOUND_VARIABLE_2179 tptp.d) (V11x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2179)))) (let ((_let_2 (ho_7 _let_1 V11x_2E0))) (or (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_34 _let_2)))) (= _let_2 (ho_7 _let_1 (ho_10 k_39 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2179) (ho_10 k_40 _let_2))))))))) (forall ((BOUND_VARIABLE_2207 tptp.d) (V12x_2E0 tptp.u)) (let ((_let_1 (ho_4 k_32 BOUND_VARIABLE_2207))) (let ((_let_2 (ho_6 k_5 _let_1))) (let ((_let_3 (ho_7 _let_2 V12x_2E0))) (= _let_3 (ho_7 _let_2 (ho_10 (ho_9 (ho_38 k_41 _let_3) (ho_7 _let_2 tptp.c_2Eoption_2ENONE_2E0)) (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2207) _let_1)) tptp.c_2Eoption_2ESOME_2E0)))))))) (forall ((BOUND_VARIABLE_2234 tptp.d) (V13x_2E0 tptp.u)) (let ((_let_1 (ho_4 k_32 BOUND_VARIABLE_2234))) (let ((_let_2 (ho_6 k_5 _let_1))) (let ((_let_3 (ho_7 _let_2 V13x_2E0))) (= _let_3 (ho_7 _let_2 (ho_10 (ho_9 (ho_38 k_41 _let_3) _let_3) (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2234) _let_1)) tptp.c_2Eoption_2ESOME_2E0)))))))) (forall ((BOUND_VARIABLE_2260 tptp.d) (V14x_2E0 tptp.u) (BOUND_VARIABLE_2262 tptp.d) (BOUND_VARIABLE_2264 tptp.u) (BOUND_VARIABLE_2268 tptp.u)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_2262))) (let ((_let_2 (ho_7 _let_1 BOUND_VARIABLE_2268))) (let ((_let_3 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2260)) V14x_2E0))) (or (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_33 _let_3)))) (= _let_2 (ho_7 _let_1 (ho_10 (ho_9 (ho_38 k_41 _let_3) _let_2) (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2260) BOUND_VARIABLE_2262)) BOUND_VARIABLE_2264))))))))) (forall ((BOUND_VARIABLE_2293 tptp.d) (V15x_2E0 tptp.u) (BOUND_VARIABLE_2295 tptp.d) (BOUND_VARIABLE_2297 tptp.u) (BOUND_VARIABLE_2301 tptp.u)) (let ((_let_1 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2293) BOUND_VARIABLE_2295)) BOUND_VARIABLE_2297))) (let ((_let_2 (ho_6 k_5 BOUND_VARIABLE_2295))) (let ((_let_3 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2293)) V15x_2E0))) (or (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_34 _let_3)))) (= (ho_7 _let_2 (ho_10 (ho_9 k_8 _let_1) (ho_7 (ho_6 k_5 BOUND_VARIABLE_2293) (ho_10 k_40 _let_3)))) (ho_7 _let_2 (ho_10 (ho_9 (ho_38 k_41 _let_3) (ho_7 _let_2 BOUND_VARIABLE_2301)) _let_1)))))))) (forall ((BOUND_VARIABLE_2332 tptp.d) (V16x_2E0 tptp.u) (BOUND_VARIABLE_2338 tptp.u)) (let ((_let_1 (ho_4 k_32 BOUND_VARIABLE_2332))) (let ((_let_2 (ho_6 k_5 _let_1))) (let ((_let_3 (ho_7 _let_2 V16x_2E0))) (or (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 k_34 _let_3)))) (= _let_3 (ho_7 _let_2 (ho_10 (ho_9 (ho_38 k_41 _let_3) (ho_7 _let_2 BOUND_VARIABLE_2338)) (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2332) _let_1)) tptp.c_2Eoption_2ESOME_2E0))))))))) (forall ((BOUND_VARIABLE_2364 tptp.d) (BOUND_VARIABLE_2366 tptp.d) (V17v_2E0 tptp.u) (V18f_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_2366))) (let ((_let_2 (ho_7 _let_1 V17v_2E0))) (= _let_2 (ho_7 _let_1 (ho_10 (ho_9 (ho_38 k_41 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2364)) tptp.c_2Eoption_2ENONE_2E0)) _let_2) (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2364) BOUND_VARIABLE_2366)) V18f_2E0))))))) (forall ((BOUND_VARIABLE_2392 tptp.d) (BOUND_VARIABLE_2394 tptp.d) (V19x_2E0 tptp.u) (V20v_2E0 tptp.u) (V21f_2E0 tptp.u)) (let ((_let_1 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2392) BOUND_VARIABLE_2394)) V21f_2E0))) (let ((_let_2 (ho_6 k_5 BOUND_VARIABLE_2394))) (let ((_let_3 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2392) V19x_2E0))) (= (ho_7 _let_2 (ho_10 (ho_9 k_8 _let_1) _let_3)) (ho_7 _let_2 (ho_10 (ho_9 (ho_38 k_41 (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2392)) (ho_10 k_39 _let_3))) (ho_7 _let_2 V20v_2E0)) _let_1))))))) (forall ((BOUND_VARIABLE_2426 tptp.d) (BOUND_VARIABLE_2428 tptp.d) (V22f_2E0 tptp.u) (V23x_2E0 tptp.u)) (let ((_let_1 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2426) V23x_2E0))) (let ((_let_2 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2426) BOUND_VARIABLE_2428)) V22f_2E0))) (let ((_let_3 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2428)))) (= (ho_7 _let_3 (ho_10 k_39 (ho_7 (ho_6 k_5 BOUND_VARIABLE_2428) (ho_10 (ho_9 k_8 _let_2) _let_1)))) (ho_7 _let_3 (ho_10 (ho_9 k_36 _let_2) (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2426)) (ho_10 k_39 _let_1))))))))) (forall ((BOUND_VARIABLE_2462 tptp.d) (BOUND_VARIABLE_2464 tptp.d) (V24f_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2464)))) (= (ho_7 _let_1 tptp.c_2Eoption_2ENONE_2E0) (ho_7 _let_1 (ho_10 (ho_9 k_36 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 BOUND_VARIABLE_2462) BOUND_VARIABLE_2464)) V24f_2E0)) (ho_7 (ho_6 k_5 (ho_4 k_32 BOUND_VARIABLE_2462)) tptp.c_2Eoption_2ENONE_2E0)))))) (forall ((BOUND_VARIABLE_2490 tptp.d)) (let ((_let_1 (ho_4 k_32 BOUND_VARIABLE_2490))) (let ((_let_2 (ho_6 k_5 _let_1))) (= (ho_7 _let_2 (ho_10 k_35 (ho_7 (ho_6 k_5 (ho_4 k_32 _let_1)) tptp.c_2Eoption_2ENONE_2E0))) (ho_7 _let_2 tptp.c_2Eoption_2ENONE_2E0))))) (forall ((BOUND_VARIABLE_2512 tptp.d) (V25x_2E0 tptp.u)) (let ((_let_1 (ho_4 k_32 BOUND_VARIABLE_2512))) (let ((_let_2 (ho_6 k_5 _let_1))) (let ((_let_3 (ho_7 _let_2 V25x_2E0))) (= _let_3 (ho_7 _let_2 (ho_10 k_35 (ho_7 (ho_6 k_5 (ho_4 k_32 _let_1)) (ho_10 k_39 _let_3))))))))))))))))) (let ((_let_98 (AND_ELIM _let_97 :args (2)))) (let ((_let_99 (_let_75))) (let ((_let_100 (ASSUME :args _let_99))) (let ((_let_101 (or))) (let ((_let_102 (_let_60))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 QUANTIFIERS_INST_CBQI_PROP)) :args _let_99)) _let_98 :args ((not _let_61) false _let_75)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_63)) :args ((or _let_64 _let_62 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_60 _let_69))) _let_103 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_102)) :args _let_102)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) (REFL :args ((not _let_74))) :args _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 1)) (CONG (REFL :args (_let_74)) (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_72))) :args _let_101)) :args ((or _let_72 _let_74))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_52 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_99))) _let_98 :args (_let_73 false _let_75)) :args (_let_74 true _let_72)) :args (_let_59 false _let_74)) :args (_let_69 true _let_61 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48 _let_12 tptp.c_2Eoption_2ENONE_2E0 QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_67))) _let_66 :args (_let_63 false _let_65)) :args (_let_64 true _let_62 false _let_63)))) (let ((_let_105 (not BOOLEAN_TERM_VARIABLE_6704))) (let ((_let_106 (ho_19 k_18 (ho_7 _let_7 (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 _let_8) tptp.tyop_2Emin_2Ebool)) tptp.c_2Eoption_2EIS__NONE_2E0)) _let_13))))) (let ((_let_107 (not BOOLEAN_TERM_VARIABLE_7350))) (let ((_let_108 (ho_19 k_18 (ho_7 _let_7 (ho_10 k_33 _let_13))))) (let ((_let_109 (= _let_106 _let_108))) (let ((_let_110 (not _let_106))) (let ((_let_111 (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (ho_4 k_32 A_27a))) (let ((_let_2 (ho_7 (ho_6 k_5 _let_1) X0_2E0))) (let ((_let_3 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (= (ho_19 k_18 (ho_7 _let_3 (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Eoption_2EIS__NONE_2E0)) _let_2))) (ho_19 k_18 (ho_7 _let_3 (ho_10 k_33 _let_2)))))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_111)))))) (let ((_let_113 (= _let_61 _let_108))) (let ((_let_114 (not _let_108))) (let ((_let_115 (_let_76))) (let ((_let_116 (ho_19 k_18 _let_30))) (let ((_let_117 (MACRO_SR_PRED_INTRO :args ((= _let_116 BOOLEAN_TERM_VARIABLE_16280))))) (let ((_let_118 (AND_ELIM _let_97 :args (1)))) (let ((_let_119 (_let_77))) (let ((_let_120 (ASSUME :args _let_119))) (let ((_let_121 (not BOOLEAN_TERM_VARIABLE_16280))) (let ((_let_122 (ho_19 k_18 (ho_7 _let_7 (ho_10 (ho_9 (ho_38 k_37 _let_26) _let_34) _let_37))))) (let ((_let_123 (= _let_116 _let_122))) (let ((_let_124 (forall ((V3x0_2E0 tptp.u) (V4y0_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_2 (ho_7 _let_1 V4y0_2E0))) (let ((_let_3 (ho_7 _let_1 V3x0_2E0))) (let ((_let_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_5 (ho_4 _let_4 tptp.tyop_2Emin_2Ebool))) (let ((_let_6 (ho_6 k_5 (ho_4 k_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67)))) (or (not (= (ho_7 _let_6 (ho_10 k_39 (ho_7 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69))) (ho_7 _let_6 (ho_10 k_39 _let_3)))) (not (= (ho_7 _let_6 (ho_10 k_39 (ho_7 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68))) (ho_7 _let_6 (ho_10 k_39 _let_2)))) (not (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 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:args (_let_113 false _let_76)) :args (_let_114 true _let_61 false _let_113)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 _let_12 QUANTIFIERS_INST_E_MATCHING ((ho_7 (ho_6 k_5 (ho_4 k_32 A_27a)) X0_2E0)))) :args (_let_111))) _let_112 :args (_let_109 false _let_111)) :args (_let_110 true _let_108 false _let_109)) :args (_let_107 true _let_106)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_54) _let_104 :args (_let_105 true _let_20)) _let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_49 :args (_let_17 QUANTIFIERS_INST_E_MATCHING ((ho_19 k_18 (ho_7 _let_7 V0_2E0))))) :args _let_57) (CONG _let_58 (CONG (REFL :args (_let_18)) (CONG _let_56 (CONG _let_55 _let_54 :args _let_53) :args _let_52) :args _let_51) :args _let_50))) _let_49 :args (_let_19 false _let_48)) :args (false false _let_47 false _let_46 false _let_45 false _let_44 false _let_41 true BOOLEAN_TERM_VARIABLE_16280 false _let_38 false _let_35 false _let_31 true BOOLEAN_TERM_VARIABLE_7350 true BOOLEAN_TERM_VARIABLE_6704 true _let_20 false _let_19)) :args ((forall ((A_27a tptp.d) (A_27b tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)))) (=> (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V2x_2E0))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)))) (let ((_let_3 (@ tptp.s A_27b))) (= (@ _let_3 (@ (@ tptp.app_2E2 (@ _let_2 V0f_2E0)) _let_1)) (@ _let_3 (@ (@ tptp.app_2E2 (@ _let_2 V1g_2E0)) _let_1))))))) (= (@ _let_1 V0f_2E0) (@ _let_1 V1g_2E0))))) (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0x_2E0))) (= (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27a)) tptp.combin_i_2E0)) _let_2)) _let_2)))) (forall ((A_27a tptp.d) (A_27b tptp.d) (V0x_2E0 tptp.u) (V1y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0x_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27a))) (= (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_3) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_3)) tptp.combin_k_2E0)) _let_2))) (@ (@ tptp.s A_27b) V1y_2E0))) _let_2))))) (forall ((A_27a tptp.d) (A_27b tptp.d) (A_27c tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u) (V2x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V2x_2E0))) (let ((_let_2 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_3 (@ _let_2 A_27b))) (let ((_let_4 (@ (@ tptp.s _let_3) V1g_2E0))) (let ((_let_5 (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27c))) (let ((_let_6 (@ _let_2 _let_5))) (let ((_let_7 (@ (@ tptp.s _let_6) V0f_2E0))) (let ((_let_8 (@ tptp.s A_27c))) (let ((_let_9 (@ _let_2 A_27c))) (let ((_let_10 (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_9))) (= (@ _let_8 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_9) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_10) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_6) _let_10)) tptp.combin_s_2E0)) _let_7))) _let_4))) _let_1)) (@ _let_8 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 _let_7) _let_1))) (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 _let_4) _let_1)))))))))))))))) (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))) (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))) (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))) (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))) (forall ((A_27a tptp.d) (V0_2E0 tptp.u) (V1_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V1_2E0))) (let ((_let_3 (@ _let_1 V0_2E0))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Emin_2E_3D_2E2 _let_3) _let_2))) (= _let_3 _let_2)))))) (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_21_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)))) (forall ((V1x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)) (@ (@ tptp.s A_27a) V1x_2E0))))))) (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_3F_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)))) (exists ((V1x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)) (@ (@ tptp.s A_27a) V1x_2E0))))))) _let_6 (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Emin_2Ebool))))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 _let_3))) _let_3))))) (forall ((V0 Bool)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) V0)) (forall ((V0 (-> Bool Bool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) V0)) (forall ((V0 (-> Bool Bool Bool))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) V0))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Ebool_2E_21_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Ebool_2E_21_2E0)) _let_2)))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 X1_2E0))) (let ((_let_3 (@ _let_1 X0_2E0))) (let ((_let_4 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_5 (@ _let_4 tptp.tyop_2Emin_2Ebool))) (= (= _let_3 _let_2) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_4 _let_5)) tptp.c_2Emin_2E_3D_2E0)) _let_3))) _let_2)))))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Ebool_2E_3F_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Ebool_2E_3F_2E0)) _let_2)))))))) _let_5 (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ tptp.c_2Eoption_2EIS__SOME_2E1 _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool)) tptp.c_2Eoption_2EIS__SOME_2E0)) _let_2)))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.tyop_2Eoption_2Eoption _let_1))) (let ((_let_3 (@ (@ tptp.s _let_2) X0_2E0))) (let ((_let_4 (@ tptp.s _let_1))) (= (@ _let_4 (@ tptp.c_2Eoption_2EOPTION__JOIN_2E1 _let_3)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_2) _let_1)) tptp.c_2Eoption_2EOPTION__JOIN_2E0)) _let_3)))))))) (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X1_2E0))) (let ((_let_3 (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b))) (let ((_let_4 (@ (@ tptp.s _let_3) X0_2E0))) (let ((_let_5 (@ tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_6 (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_5))) (let ((_let_7 (@ tptp.s _let_5))) (= (@ _let_7 (@ (@ tptp.c_2Eoption_2EOPTION__MAP_2E2 _let_4) _let_2)) (@ _let_7 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_6)) tptp.c_2Eoption_2EOPTION__MAP_2E0)) _let_4))) _let_2))))))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 X2_2E0))) (let ((_let_4 (@ _let_2 X1_2E0))) (let ((_let_5 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_6 (@ _let_5 (@ _let_5 tptp.tyop_2Emin_2Ebool)))) (let ((_let_7 (@ (@ tptp.s _let_6) X0_2E0))) (let ((_let_8 (@ tptp.tyop_2Emin_2Efun _let_1))) (let ((_let_9 (@ _let_8 tptp.tyop_2Emin_2Ebool))) (let ((_let_10 (@ _let_8 _let_9))) (let ((_let_11 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_11 (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 _let_7) _let_4) _let_3))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_11 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_9) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_10) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_6) _let_10)) tptp.c_2Eoption_2EOPTREL_2E0)) _let_7))) _let_4))) _let_3)))))))))))))))) (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_2 (@ (@ tptp.s _let_1) X2_2E0))) (let ((_let_3 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_4 (@ (@ tptp.s _let_3) X1_2E0))) (let ((_let_5 (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)))) (let ((_let_6 (@ (@ tptp.s _let_5) X0_2E0))) (let ((_let_7 (@ (@ tptp.tyop_2Emin_2Efun _let_1) tptp.tyop_2Emin_2Ebool))) (let ((_let_8 (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_7))) (let ((_let_9 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_9 (@ (@ (@ tptp.c_2Eoption_2EOPTREL_2E3 _let_6) _let_4) _let_2))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_9 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_8) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_5) _let_8)) tptp.c_2Eoption_2EOPTREL_2E0)) _let_6))) _let_4))) _let_2)))))))))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) X0_2E0))) (let ((_let_2 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_2)) tptp.c_2Eoption_2ESOME_2E0)) _let_1))))))) (forall ((A_27b tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27b) X0_2E0))) (let ((_let_2 (@ tptp.tyop_2Eoption_2Eoption A_27b))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.c_2Eoption_2ESOME_2E1 _let_1)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) _let_2)) tptp.c_2Eoption_2ESOME_2E0)) _let_1))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.tyop_2Eoption_2Eoption _let_1))) (let ((_let_4 (@ tptp.s _let_3))) (= (@ _let_4 (@ tptp.c_2Eoption_2ESOME_2E1 _let_2)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_3)) tptp.c_2Eoption_2ESOME_2E0)) _let_2)))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.s _let_1) X0_2E0))) (let ((_let_3 (@ tptp.s A_27a))) (= (@ _let_3 (@ tptp.c_2Eoption_2ETHE_2E1 _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) A_27a)) tptp.c_2Eoption_2ETHE_2E0)) _let_2))))))) (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b))) (let ((_let_2 (@ (@ tptp.s _let_1) X2_2E0))) (let ((_let_3 (@ tptp.s A_27b))) (let ((_let_4 (@ _let_3 X1_2E0))) (let ((_let_5 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_6 (@ (@ tptp.s _let_5) X0_2E0))) (let ((_let_7 (@ (@ tptp.tyop_2Emin_2Efun _let_1) A_27b))) (let ((_let_8 (@ (@ tptp.tyop_2Emin_2Efun A_27b) _let_7))) (= (@ _let_3 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_6) _let_4) _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_8) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_5) _let_8)) tptp.c_2Eoption_2Eoption__CASE_2E0)) _let_6))) _let_4))) _let_2)))))))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Eoption_2Eoption A_27a))) (let ((_let_2 (@ (@ tptp.tyop_2Emin_2Efun A_27a) _let_1))) (let ((_let_3 (@ (@ tptp.s _let_2) X2_2E0))) (let ((_let_4 (@ tptp.s _let_1))) (let ((_let_5 (@ _let_4 X1_2E0))) (let ((_let_6 (@ _let_4 X0_2E0))) (let ((_let_7 (@ (@ tptp.tyop_2Emin_2Efun _let_2) _let_1))) (let ((_let_8 (@ tptp.tyop_2Emin_2Efun _let_1))) (let ((_let_9 (@ _let_8 _let_7))) (= (@ _let_4 (@ (@ (@ tptp.c_2Eoption_2Eoption__CASE_2E3 _let_6) _let_5) _let_3)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_9) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_8 _let_9)) tptp.c_2Eoption_2Eoption__CASE_2E0)) _let_6))) _let_5))) _let_3))))))))))))) (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ V0 V1))) (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1))))))) (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1))))))))) (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) tptp.mono_2Ec_2Ebool_2ET (forall ((V0t1 Bool) (V1t2 Bool)) (=> (=> V0t1 V1t2) (=> (=> V1t2 V0t1) (= V0t1 V1t2)))) _let_4 (forall ((A_27a tptp.d) (V0t Bool)) (= (exists ((V1x_2E0 tptp.u)) V0t) V0t)) (forall ((V0t Bool)) (and (= (and tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (and V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (and tptp.mono_2Ec_2Ebool_2EF V0t) tptp.mono_2Ec_2Ebool_2EF) (= (and V0t tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2EF) (= (and V0t V0t) V0t))) (forall ((V0t Bool)) (and (= (or tptp.mono_2Ec_2Ebool_2ET V0t) tptp.mono_2Ec_2Ebool_2ET) (= (or V0t tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2ET) (= (or tptp.mono_2Ec_2Ebool_2EF V0t) V0t) (= (or V0t tptp.mono_2Ec_2Ebool_2EF) V0t) (= (or V0t V0t) V0t))) (and (forall ((V0t Bool)) (= (not (not V0t)) V0t)) (= (not tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2EF) (= (not tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2ET)) (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) V0x_2E0))) (= (= _let_1 _let_1) tptp.mono_2Ec_2Ebool_2ET))) (forall ((V0t Bool)) (let ((_let_1 (not V0t))) (and (= (= tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (= V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (= tptp.mono_2Ec_2Ebool_2EF V0t) _let_1) (= (= V0t tptp.mono_2Ec_2Ebool_2EF) _let_1)))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 91.43/91.65 )
% 91.43/91.65 % SZS output end Proof for ITP011^1
% 91.43/91.65 % cvc5---1.0.5 exiting
% 91.43/91.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------