TSTP Solution File: ITP004^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP004^1 : 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 03:13:57 EDT 2023
% Result : Theorem 0.22s 0.64s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : ITP004^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n017.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun Aug 27 13:13:27 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : ITP004^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.22/0.52 % Domain : Interactive Theorem Proving
% 0.22/0.52 % Problem : HOL4 syntactic export of thm_2Epred__set_2EREST__SUBSET.p, bushy mode
% 0.22/0.52 % Version : [BG+19] axioms.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.22/0.52 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.22/0.52 % Source : [BG+19]
% 0.22/0.52 % Names : thm_2Epred__set_2EREST__SUBSET.p [Gau19]
% 0.22/0.52 % : HL401501^1.p [TPAP]
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.54 v8.1.0, 0.45 v7.5.0
% 0.22/0.52 % Syntax : Number of formulae : 83 ( 25 unt; 50 typ; 0 def)
% 0.22/0.52 % Number of atoms : 58 ( 26 equ; 2 cnn)
% 0.22/0.52 % Maximal formula atoms : 4 ( 1 avg)
% 0.22/0.52 % Number of connectives : 672 ( 2 ~; 1 |; 2 &; 654 @)
% 0.22/0.52 % ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 17 ( 6 avg)
% 0.22/0.52 % Number of types : 4 ( 3 usr)
% 0.22/0.52 % Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 49 ( 47 usr; 21 con; 0-3 aty)
% 0.22/0.52 % Number of variables : 79 ( 0 ^; 78 !; 1 ?; 79 :)
% 0.22/0.52 % SPC : TH0_THM_EQU_NAR
% 0.22/0.52
% 0.22/0.52 % Comments :
% 0.22/0.52 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 thf(u,type,
% 0.22/0.52 u: $tType ).
% 0.22/0.52
% 0.22/0.52 thf(d,type,
% 0.22/0.52 d: $tType ).
% 0.22/0.52
% 0.22/0.52 thf(du,type,
% 0.22/0.52 du: $tType ).
% 0.22/0.52
% 0.22/0.52 thf(tyop_2Emin_2Ebool,type,
% 0.22/0.52 tyop_2Emin_2Ebool: d ).
% 0.22/0.52
% 0.22/0.52 thf(tyop_2Emin_2Efun,type,
% 0.22/0.52 tyop_2Emin_2Efun: d > d > d ).
% 0.22/0.52
% 0.22/0.52 thf(s,type,
% 0.22/0.52 s: d > u > du ).
% 0.22/0.52
% 0.22/0.52 thf(app_2E2,type,
% 0.22/0.52 app_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(combin_i_2E0,type,
% 0.22/0.52 combin_i_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(combin_k_2E0,type,
% 0.22/0.52 combin_k_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(combin_s_2E0,type,
% 0.22/0.52 combin_s_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_21_2E0,type,
% 0.22/0.52 c_2Ebool_2E_21_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_21_2E1,type,
% 0.22/0.52 c_2Ebool_2E_21_2E1: du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.22/0.52 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.22/0.52 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Emin_2E_3D_2E0,type,
% 0.22/0.52 c_2Emin_2E_3D_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Emin_2E_3D_2E2,type,
% 0.22/0.52 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.22/0.52 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.22/0.52 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_3F_2E0,type,
% 0.22/0.52 c_2Ebool_2E_3F_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_3F_2E1,type,
% 0.22/0.52 c_2Ebool_2E_3F_2E1: du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2ECHOICE_2E0,type,
% 0.22/0.52 c_2Epred__set_2ECHOICE_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2ECHOICE_2E1,type,
% 0.22/0.52 c_2Epred__set_2ECHOICE_2E1: du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2EDELETE_2E0,type,
% 0.22/0.52 c_2Epred__set_2EDELETE_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2EDELETE_2E2,type,
% 0.22/0.52 c_2Epred__set_2EDELETE_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2EF_2E0,type,
% 0.22/0.52 c_2Ebool_2EF_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2EIN_2E0,type,
% 0.22/0.52 c_2Ebool_2EIN_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2EIN_2E2,type,
% 0.22/0.52 c_2Ebool_2EIN_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2EREST_2E0,type,
% 0.22/0.52 c_2Epred__set_2EREST_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2EREST_2E1,type,
% 0.22/0.52 c_2Epred__set_2EREST_2E1: du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2ESUBSET_2E0,type,
% 0.22/0.52 c_2Epred__set_2ESUBSET_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Epred__set_2ESUBSET_2E2,type,
% 0.22/0.52 c_2Epred__set_2ESUBSET_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2ET_2E0,type,
% 0.22/0.52 c_2Ebool_2ET_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.22/0.52 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.22/0.52 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_7E_2E0,type,
% 0.22/0.52 c_2Ebool_2E_7E_2E0: u ).
% 0.22/0.52
% 0.22/0.52 thf(c_2Ebool_2E_7E_2E1,type,
% 0.22/0.52 c_2Ebool_2E_7E_2E1: du > u ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.52 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.52 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.22/0.52 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.22/0.52 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Ec_2Ebool_2EF,type,
% 0.22/0.52 mono_2Ec_2Ebool_2EF: $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Ec_2Ebool_2ET,type,
% 0.22/0.52 mono_2Ec_2Ebool_2ET: $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.22/0.52 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.22/0.52 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.52 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.22/0.52
% 0.22/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.22/0.52
% 0.22/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.22/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.22/0.52
% 0.22/0.52 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.52 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.22/0.52
% 0.22/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.22/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.22/0.52 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.22/0.52 ( ! [V2x_2E0: u] :
% 0.22/0.52 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.22/0.52 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.22/0.52 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.22/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.22/0.52 ! [A_27a: d,V0x_2E0: u] :
% 0.22/0.52 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.22/0.52 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.22/0.52 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) )
% 0.22/0.52 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Eho_2Es__thm,axiom,
% 0.22/0.52 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) )
% 0.22/0.52 = ( 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 ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.22/0.52 ! [V0: $o,V1: $o] :
% 0.22/0.52 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.22/0.52 <=> ( V0
% 0.22/0.52 & V1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.22/0.52 ! [V0: $o,V1: $o] :
% 0.22/0.52 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.22/0.52 <=> ( V0
% 0.22/0.52 | V1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Elogic_2E_7E,axiom,
% 0.22/0.52 ! [V0: $o] :
% 0.22/0.52 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.22/0.52 <=> ( (~) @ V0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.22/0.52 ! [V0: $o,V1: $o] :
% 0.22/0.52 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.22/0.52 <=> ( V0
% 0.22/0.52 => V1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Elogic_2E_3D,axiom,
% 0.22/0.52 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.22/0.52 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.22/0.52 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Equant_2E_21,axiom,
% 0.22/0.52 ! [A_27a: d,V0f_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) ) )
% 0.22/0.52 <=> ! [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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(reserved_2Equant_2E_3F,axiom,
% 0.22/0.52 ! [A_27a: d,V0f_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) ) )
% 0.22/0.52 <=> ? [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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.52 ! [V0_2E0: u] :
% 0.22/0.52 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.22/0.52 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.52 ! [V0_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) ) )
% 0.22/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.22/0.52 ! [V0_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) ) )
% 0.22/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.52 ! [V0: $o] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.22/0.52 = V0 ) ).
% 0.22/0.52
% 0.22/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.52 ! [V0: $o > $o] :
% 0.22/0.52 ( ( 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 ) ) )
% 0.22/0.52 = V0 ) ).
% 0.22/0.52
% 0.22/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.22/0.52 ! [V0: $o > $o > $o] :
% 0.22/0.52 ( ( 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 ) ) )
% 0.22/0.52 = V0 ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) ) )
% 0.22/0.52 = ( 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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.22/0.52 ( ( ( s @ A_27a @ X0_2E0 )
% 0.22/0.52 = ( s @ A_27a @ X1_2E0 ) )
% 0.22/0.52 <=> ( 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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.22/0.52 ( ( 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 ) ) ) )
% 0.22/0.52 = ( 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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.22/0.52 ( ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
% 0.22/0.52 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.22/0.52 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
% 0.22/0.52 = ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.22/0.52 = ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.22/0.52 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
% 0.22/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EREST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
% 0.22/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.22/0.52 = ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.52 ! [V0: $o > $o,V1: $o] :
% 0.22/0.52 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.22/0.52 = ( 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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.52 ! [V0: $o > $o > $o,V1: $o] :
% 0.22/0.52 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.22/0.52 = ( 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 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.52 ! [V0: $o > $o,V1: $o] :
% 0.22/0.52 ( ( V0 @ V1 )
% 0.22/0.52 = ( V0 @ V1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.52 ! [V0: $o > $o > $o,V1: $o] :
% 0.22/0.52 ( ( V0 @ V1 )
% 0.22/0.52 = ( V0 @ V1 ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(thm_2Epred__set_2ESUBSET__DEF,axiom,
% 0.22/0.52 ! [A_27a: d,V0s_2E0: u,V1t_2E0: u] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) )
% 0.22/0.52 <=> ! [V2x_2E0: u] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
% 0.22/0.52 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(thm_2Epred__set_2EIN__DELETE,axiom,
% 0.22/0.52 ! [A_27a: d,V0s_2E0: u,V1x_2E0: u,V2y_2E0: u] :
% 0.22/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) )
% 0.22/0.52 <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
% 0.22/0.52 & ( (~)
% 0.22/0.52 @ ( ( s @ A_27a @ V1x_2E0 )
% 0.22/0.52 = ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(thm_2Epred__set_2EREST__DEF,axiom,
% 0.22/0.52 ! [A_27a: d,V0s_2E0: u] :
% 0.22/0.52 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
% 0.22/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(thm_2Epred__set_2EREST__SUBSET,conjecture,
% 0.22/0.52 ! [A_27a: d,V0s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.zAgZByexZm/cvc5---1.0.5_29204.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-sort tptp.u 0)
% 0.22/0.54 (declare-sort tptp.d 0)
% 0.22/0.54 (declare-sort tptp.du 0)
% 0.22/0.54 (declare-fun tptp.tyop_2Emin_2Ebool () tptp.d)
% 0.22/0.54 (declare-fun tptp.tyop_2Emin_2Efun (tptp.d tptp.d) tptp.d)
% 0.22/0.54 (declare-fun tptp.s (tptp.d tptp.u) tptp.du)
% 0.22/0.54 (declare-fun tptp.app_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.combin_i_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.combin_k_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.combin_s_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_21_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_21_2E1 (tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Emin_2E_3D_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Emin_2E_3D_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_3F_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_3F_2E1 (tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2ECHOICE_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2ECHOICE_2E1 (tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2EDELETE_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2EDELETE_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2EF_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2EIN_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2EIN_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2EREST_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2EREST_2E1 (tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2ESUBSET_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Epred__set_2ESUBSET_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2ET_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_7E_2E0 () tptp.u)
% 0.22/0.54 (declare-fun tptp.c_2Ebool_2E_7E_2E1 (tptp.du) tptp.u)
% 0.22/0.54 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ((-> Bool Bool) Bool) Bool)
% 0.22/0.54 (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)
% 0.22/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2E_2F_5C (Bool Bool) Bool)
% 0.22/0.54 (declare-fun tptp.mono_2Ec_2Emin_2E_3D_3D_3E (Bool Bool) Bool)
% 0.22/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2EF () Bool)
% 0.22/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2ET () Bool)
% 0.22/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2E_5C_2F (Bool Bool) Bool)
% 0.22/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2E_7E (Bool) Bool)
% 0.22/0.54 (declare-fun tptp.i_mono_2Etyop_2Emin_2Ebool (Bool) tptp.u)
% 0.22/0.54 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((-> Bool Bool)) tptp.u)
% 0.22/0.54 (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)
% 0.22/0.54 (declare-fun tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.du) Bool)
% 0.22/0.54 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.du Bool) Bool)
% 0.22/0.54 (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)
% 0.22/0.54 (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))))))
% 0.22/0.54 (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)))))
% 0.22/0.54 (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))))))
% 0.22/0.54 (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)))))))))))))))))
% 0.22/0.54 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))))
% 0.22/0.54 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))))
% 0.22/0.54 (assert (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))))
% 0.22/0.54 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))))
% 0.22/0.54 (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)))))))
% 0.22/0.54 (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))))))))
% 0.22/0.54 (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))))))))
% 0.22/0.54 (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)))))
% 0.22/0.54 (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)))))
% 0.22/0.54 (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))))))
% 0.22/0.54 (assert (forall ((V0 Bool)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) V0)))
% 0.22/0.54 (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)))
% 0.22/0.54 (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))))
% 0.22/0.54 (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)))))))))
% 0.22/0.54 (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)))))))))))
% 0.22/0.54 (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)))))))))
% 0.22/0.54 (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 A_27a))) (= (@ _let_3 (@ tptp.c_2Epred__set_2ECHOICE_2E1 _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) A_27a)) tptp.c_2Epred__set_2ECHOICE_2E0)) _let_2))))))))
% 0.22/0.54 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) X1_2E0))) (let ((_let_2 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_3 (@ _let_2 tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (@ tptp.s _let_3))) (let ((_let_5 (@ _let_4 X0_2E0))) (let ((_let_6 (@ _let_2 _let_3))) (= (@ _let_4 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_5) _let_1)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_6)) tptp.c_2Epred__set_2EDELETE_2E0)) _let_5))) _let_1)))))))))))
% 0.22/0.54 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_2 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (let ((_let_3 (@ (@ tptp.s _let_2) X1_2E0))) (let ((_let_4 (@ (@ tptp.s A_27a) X0_2E0))) (let ((_let_5 (@ (@ tptp.tyop_2Emin_2Efun _let_2) tptp.tyop_2Emin_2Ebool))) (let ((_let_6 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_6 (@ (@ tptp.c_2Ebool_2EIN_2E2 _let_4) _let_3))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_6 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_5)) tptp.c_2Ebool_2EIN_2E0)) _let_4))) _let_3))))))))))))
% 0.22/0.54 (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))) (let ((_let_3 (@ _let_2 X0_2E0))) (= (@ _let_2 (@ tptp.c_2Epred__set_2EREST_2E1 _let_3)) (@ _let_2 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)) tptp.c_2Epred__set_2EREST_2E0)) _let_3))))))))
% 0.22/0.54 (assert (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 X1_2E0))) (let ((_let_4 (@ _let_2 X0_2E0))) (let ((_let_5 (@ tptp.tyop_2Emin_2Efun _let_1))) (let ((_let_6 (@ _let_5 tptp.tyop_2Emin_2Ebool))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 _let_4) _let_3))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_5 _let_6)) tptp.c_2Epred__set_2ESUBSET_2E0)) _let_4))) _let_3)))))))))))))
% 0.22/0.54 (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))))))))
% 0.22/0.54 (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))))))))))
% 0.22/0.54 (assert (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.54 (assert (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.54 (assert (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 (@ _let_1 V0s_2E0)) (@ _let_1 V1t_2E0)))) (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ tptp.c_2Ebool_2EIN_2E2 (@ (@ tptp.s A_27a) V2x_2E0)))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ _let_2 (@ _let_1 V0s_2E0)))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ _let_2 (@ _let_1 V1t_2E0)))))))))))))
% 0.22/0.54 (assert (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V2y_2E0))) (let ((_let_3 (@ _let_1 V1x_2E0))) (let ((_let_4 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_5 (@ _let_4 V0s_2E0))) (let ((_let_6 (@ tptp.c_2Ebool_2EIN_2E2 _let_3))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_6 (@ _let_4 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_5) _let_2))))) (and (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_6 _let_5))) (not (= _let_3 _let_2)))))))))))))
% 0.22/0.54 (assert (forall ((A_27a tptp.d) (V0s_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0s_2E0))) (= (@ _let_1 (@ tptp.c_2Epred__set_2EREST_2E1 _let_2)) (@ _let_1 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_2) (@ (@ tptp.s A_27a) (@ tptp.c_2Epred__set_2ECHOICE_2E1 _let_2)))))))))
% 0.22/0.54 (assert (not (forall ((A_27a tptp.d) (V0s_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0s_2E0))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 (@ _let_1 (@ tptp.c_2Epred__set_2EREST_2E1 _let_2))) _let_2))))))))
% 0.22/0.64 (set-info :filename cvc5---1.0.5_29204)
% 0.22/0.64 (check-sat-assuming ( true ))
% 0.22/0.64 ------- get file name : TPTP file name is ITP004^1
% 0.22/0.64 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29204.smt2...
% 0.22/0.64 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.64 % SZS status Theorem for ITP004^1
% 0.22/0.64 % SZS output start Proof for ITP004^1
% 0.22/0.64 (
% 0.22/0.64 (let ((_let_1 (not (forall ((A_27a tptp.d) (V0s_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0s_2E0))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 (@ _let_1 (@ tptp.c_2Epred__set_2EREST_2E1 _let_2))) _let_2))))))))) (let ((_let_2 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0s_2E0))) (= (@ _let_1 (@ tptp.c_2Epred__set_2EREST_2E1 _let_2)) (@ _let_1 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_2) (@ (@ tptp.s A_27a) (@ tptp.c_2Epred__set_2ECHOICE_2E1 _let_2)))))))))) (let ((_let_3 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V2y_2E0))) (let ((_let_3 (@ _let_1 V1x_2E0))) (let ((_let_4 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_5 (@ _let_4 V0s_2E0))) (let ((_let_6 (@ tptp.c_2Ebool_2EIN_2E2 _let_3))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_6 (@ _let_4 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_5) _let_2))))) (and (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_6 _let_5))) (not (= _let_3 _let_2)))))))))))))) (let ((_let_4 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 (@ _let_1 V0s_2E0)) (@ _let_1 V1t_2E0)))) (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ tptp.c_2Ebool_2EIN_2E2 (@ (@ tptp.s A_27a) V2x_2E0)))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (=> (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ _let_2 (@ _let_1 V0s_2E0)))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ _let_2 (@ _let_1 V1t_2E0)))))))))))))) (let ((_let_5 (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 A_27a))) (= (@ _let_3 (@ tptp.c_2Epred__set_2ECHOICE_2E1 _let_2)) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) A_27a)) tptp.c_2Epred__set_2ECHOICE_2E0)) _let_2))))))))) (let ((_let_6 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37) tptp.tyop_2Emin_2Ebool))) (let ((_let_7 (ho_6 k_5 _let_6))) (let ((_let_8 (ho_7 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_9 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37))) (let ((_let_10 (ho_7 _let_9 (ho_10 k_32 _let_8)))) (let ((_let_11 (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 _let_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37)) tptp.c_2Epred__set_2ECHOICE_2E0)) _let_8))) (let ((_let_12 (ho_7 _let_9 _let_11))) (let ((_let_13 (= _let_12 _let_10))) (let ((_let_14 (ho_9 k_33 _let_8))) (let ((_let_15 (ho_10 k_35 _let_8))) (let ((_let_16 (ho_7 _let_7 _let_15))) (let ((_let_17 (= _let_16 (ho_7 _let_7 (ho_10 _let_14 _let_10))))) (let ((_let_18 (ho_7 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_19 (ho_9 k_34 _let_18))) (let ((_let_20 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (let ((_let_21 (ho_19 k_18 (ho_7 _let_20 (ho_10 _let_19 _let_16))))) (let ((_let_22 (ho_19 k_18 (ho_7 _let_20 (ho_10 _let_19 (ho_7 _let_7 (ho_10 _let_14 _let_12))))))) (let ((_let_23 (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (let ((_let_1 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (ho_7 (ho_6 k_5 _let_1) X0_2E0))) (let ((_let_3 (ho_6 k_5 A_27a))) (= (ho_7 _let_3 (ho_10 (ho_9 k_8 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 _let_1) A_27a)) tptp.c_2Epred__set_2ECHOICE_2E0)) _let_2)) (ho_7 _let_3 (ho_10 k_32 _let_2))))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 _let_23)))))) (let ((_let_25 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (ho_7 _let_1 V0s_2E0))) (= (ho_7 _let_1 (ho_10 (ho_9 k_33 _let_2) (ho_7 (ho_6 k_5 A_27a) (ho_10 k_32 _let_2)))) (ho_7 _let_1 (ho_10 k_35 _let_2)))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_25)))))) (let ((_let_27 (ho_19 k_18 (ho_7 _let_20 (ho_10 _let_19 _let_8))))) (let ((_let_28 (not _let_21))) (let ((_let_29 (or _let_28 _let_27))) (let ((_let_30 (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (ho_7 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_3 (ho_9 k_34 (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37) V2x_2E0)))) (let ((_let_4 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (or (not (ho_19 k_18 (ho_7 _let_4 (ho_10 _let_3 (ho_7 _let_1 (ho_10 k_35 _let_2)))))) (ho_19 k_18 (ho_7 _let_4 (ho_10 _let_3 _let_2))))))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (ho_19 k_18 (ho_7 _let_20 (ho_10 (ho_9 k_36 _let_16) _let_8))))) (let ((_let_33 (= _let_32 _let_30))) (let ((_let_34 (not _let_30))) (let ((_let_35 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)))) (= (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (ho_9 k_34 (ho_7 (ho_6 k_5 A_27a) V2x_2E0)))) (let ((_let_3 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (or (not (ho_19 k_18 (ho_7 _let_3 (ho_10 _let_2 (ho_7 _let_1 V0s_2E0))))) (ho_19 k_18 (ho_7 _let_3 (ho_10 _let_2 (ho_7 _let_1 V1t_2E0))))))))) (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 (ho_9 k_36 (ho_7 _let_1 V0s_2E0)) (ho_7 _let_1 V1t_2E0))))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 (@ _let_1 V0s_2E0)) (@ _let_1 V1t_2E0)))) (forall ((V2x_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ tptp.c_2Ebool_2EIN_2E2 (@ (@ tptp.s A_27a) V2x_2E0)))) (let ((_let_3 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (or (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ _let_2 (@ _let_1 V0s_2E0))))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_3 (@ _let_2 (@ _let_1 V1t_2E0)))))))))))) _let_35))))))) (let ((_let_37 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_38 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (ho_7 _let_1 V0s_2E0))) (ho_19 k_18 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_10 (ho_9 k_36 (ho_7 _let_1 (ho_10 k_35 _let_2))) _let_2)))))))) (let ((_let_39 (not _let_32))) (let ((_let_40 (not _let_38))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_40)))))) (let ((_let_42 (or))) (let ((_let_43 (_let_34))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_43)) :args _let_43)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_33)) :args ((or _let_32 _let_34 (not _let_33)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_41) :args (_let_40))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_38))) (REFL :args (_let_39)) :args _let_42)) _let_41 :args (_let_39 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_E_MATCHING ((ho_10 (ho_9 k_36 (ho_7 _let_37 V0s_2E0)) (ho_7 _let_37 V1t_2E0))))) :args (_let_35)))) _let_36 :args (_let_33 false _let_35)) :args (_let_34 true _let_32 false _let_33)) :args (_let_31 true _let_30)))) (let ((_let_45 (and _let_27 (not (= _let_12 _let_18))))) (let ((_let_46 (= _let_22 _let_45))) (let ((_let_47 (not _let_22))) (let ((_let_48 (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (ho_6 k_5 A_27a))) (let ((_let_2 (ho_7 _let_1 V2y_2E0))) (let ((_let_3 (ho_7 _let_1 V1x_2E0))) (let ((_let_4 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_5 (ho_7 _let_4 V0s_2E0))) (let ((_let_6 (ho_9 k_34 _let_3))) (let ((_let_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (= (ho_19 k_18 (ho_7 _let_7 (ho_10 _let_6 (ho_7 _let_4 (ho_10 (ho_9 k_33 _let_5) _let_2))))) (and (ho_19 k_18 (ho_7 _let_7 (ho_10 _let_6 _let_5))) (not (= _let_3 _let_2)))))))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_27a tptp.d) (V0s_2E0 tptp.u) (V1x_2E0 tptp.u) (V2y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V1x_2E0))) (let ((_let_3 (@ _let_1 V2y_2E0))) (let ((_let_4 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)))) (let ((_let_5 (@ _let_4 V0s_2E0))) (let ((_let_6 (@ tptp.c_2Ebool_2EIN_2E2 _let_2))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_6 (@ _let_4 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_5) _let_3))))) (and (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ _let_6 _let_5))) (not (= _let_3 _let_2)))))))))))) _let_48))))))) (let ((_let_50 (not _let_45))) (let ((_let_51 (ASSUME :args (_let_47)))) (let ((_let_52 (APPLY_UF ho_7))) (let ((_let_53 (APPLY_UF ho_10))) (let ((_let_54 (ASSUME :args (_let_13)))) (let ((_let_55 (ASSUME :args (_let_17)))) (let ((_let_56 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_51 _let_54 _let_55 _let_56) :args (_let_13 _let_17 _let_21 _let_47)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_56)) (CONG (REFL :args (k_18)) (CONG (REFL :args (_let_20)) (CONG (REFL :args (_let_19)) (TRANS (SYMM (SYMM _let_55)) (CONG (REFL :args (_let_7)) (CONG (REFL :args (_let_14)) (SYMM _let_54) :args _let_53) :args _let_52)) :args _let_53) :args _let_52) :args (APPLY_UF ho_19)) (FALSE_INTRO _let_51))) :args (_let_47 _let_13 _let_17 _let_21)) :args ((not (and _let_13 _let_17 _let_21 _let_47)) SB_LITERAL))) (CONG (REFL :args ((not _let_13))) (REFL :args ((not _let_17))) (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_22))) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_46)) :args ((or _let_45 _let_47 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_27 _let_50))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 1)) _let_44 :args ((not _let_27) true _let_29)) :args (_let_50 true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 _let_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_48)))) _let_49 :args (_let_46 false _let_48)) :args (_let_47 true _let_45 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG (REFL :args (_let_29)) (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_21))) :args _let_42)) :args ((or _let_21 _let_29))) _let_44 :args (_let_21 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_E_MATCHING ((ho_10 k_35 (ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0))))) :args (_let_25)))) _let_26 :args (_let_17 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_E_MATCHING ((ho_7 (ho_6 k_5 (ho_4 (ho_3 k_2 A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)))) :args (_let_23))) _let_24 :args (_let_13 false _let_23)) :args (false true _let_22 false _let_21 false _let_17 false _let_13)) :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))))))) (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)))) (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) (X1_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.s A_27a) X1_2E0))) (let ((_let_2 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_3 (@ _let_2 tptp.tyop_2Emin_2Ebool))) (let ((_let_4 (@ tptp.s _let_3))) (let ((_let_5 (@ _let_4 X0_2E0))) (let ((_let_6 (@ _let_2 _let_3))) (= (@ _let_4 (@ (@ tptp.c_2Epred__set_2EDELETE_2E2 _let_5) _let_1)) (@ _let_4 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_3) _let_6)) tptp.c_2Epred__set_2EDELETE_2E0)) _let_5))) _let_1)))))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_2 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (let ((_let_3 (@ (@ tptp.s _let_2) X1_2E0))) (let ((_let_4 (@ (@ tptp.s A_27a) X0_2E0))) (let ((_let_5 (@ (@ tptp.tyop_2Emin_2Efun _let_2) tptp.tyop_2Emin_2Ebool))) (let ((_let_6 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_6 (@ (@ tptp.c_2Ebool_2EIN_2E2 _let_4) _let_3))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_6 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_5) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_5)) tptp.c_2Ebool_2EIN_2E0)) _let_4))) _let_3))))))))))) (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))) (let ((_let_3 (@ _let_2 X0_2E0))) (= (@ _let_2 (@ tptp.c_2Epred__set_2EREST_2E1 _let_3)) (@ _let_2 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)) tptp.c_2Epred__set_2EREST_2E0)) _let_3))))))) (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) (let ((_let_2 (@ tptp.s _let_1))) (let ((_let_3 (@ _let_2 X1_2E0))) (let ((_let_4 (@ _let_2 X0_2E0))) (let ((_let_5 (@ tptp.tyop_2Emin_2Efun _let_1))) (let ((_let_6 (@ _let_5 tptp.tyop_2Emin_2Ebool))) (let ((_let_7 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ (@ tptp.c_2Epred__set_2ESUBSET_2E2 _let_4) _let_3))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ _let_7 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_5 _let_6)) tptp.c_2Epred__set_2ESUBSET_2E0)) _let_4))) _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))) _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.65 )
% 0.22/0.65 % SZS output end Proof for ITP004^1
% 0.22/0.65 % cvc5---1.0.5 exiting
% 0.22/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------