TSTP Solution File: ITP019^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP019^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 03:16:01 EDT 2023
% Result : Theorem 0.23s 0.60s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP019^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.08/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n007.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
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun Aug 27 16:24:57 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.51 %----Proving TH0
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 % File : ITP019^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.23/0.52 % Domain : Interactive Theorem Proving
% 0.23/0.52 % Problem : HOL4 syntactic export of thm_2Ecomplex_2ECOMPLEX__INV__NZ.p, bushy mode
% 0.23/0.52 % Version : [BG+19] axioms.
% 0.23/0.52 % English :
% 0.23/0.52
% 0.23/0.52 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.23/0.52 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.23/0.52 % Source : [BG+19]
% 0.23/0.52 % Names : thm_2Ecomplex_2ECOMPLEX__INV__NZ.p [Gau19]
% 0.23/0.52 % : HL409001^1.p [TPAP]
% 0.23/0.52
% 0.23/0.52 % Status : Theorem
% 0.23/0.52 % Rating : 0.08 v8.1.0, 0.09 v7.5.0
% 0.23/0.52 % Syntax : Number of formulae : 104 ( 31 unt; 63 typ; 0 def)
% 0.23/0.52 % Number of atoms : 67 ( 35 equ; 4 cnn)
% 0.23/0.52 % Maximal formula atoms : 8 ( 1 avg)
% 0.23/0.52 % Number of connectives : 558 ( 4 ~; 1 |; 5 &; 525 @)
% 0.23/0.52 % ( 15 <=>; 8 =>; 0 <=; 0 <~>)
% 0.23/0.52 % Maximal formula depth : 17 ( 4 avg)
% 0.23/0.52 % Number of types : 6 ( 5 usr)
% 0.23/0.52 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.23/0.52 % Number of symbols : 60 ( 58 usr; 22 con; 0-3 aty)
% 0.23/0.52 % Number of variables : 76 ( 0 ^; 75 !; 1 ?; 76 :)
% 0.23/0.52 % SPC : TH0_THM_EQU_NAR
% 0.23/0.52
% 0.23/0.52 % Comments :
% 0.23/0.52 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.23/0.52 %------------------------------------------------------------------------------
% 0.23/0.52 thf(u,type,
% 0.23/0.52 u: $tType ).
% 0.23/0.52
% 0.23/0.52 thf(d,type,
% 0.23/0.52 d: $tType ).
% 0.23/0.52
% 0.23/0.52 thf(du,type,
% 0.23/0.52 du: $tType ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Etyop_2Enum_2Enum,type,
% 0.23/0.52 mono_2Etyop_2Enum_2Enum: $tType ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.23/0.52 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
% 0.23/0.52
% 0.23/0.52 thf(tyop_2Emin_2Ebool,type,
% 0.23/0.52 tyop_2Emin_2Ebool: d ).
% 0.23/0.52
% 0.23/0.52 thf(tyop_2Emin_2Efun,type,
% 0.23/0.52 tyop_2Emin_2Efun: d > d > d ).
% 0.23/0.52
% 0.23/0.52 thf(tyop_2Enum_2Enum,type,
% 0.23/0.52 tyop_2Enum_2Enum: d ).
% 0.23/0.52
% 0.23/0.52 thf(tyop_2Epair_2Eprod,type,
% 0.23/0.52 tyop_2Epair_2Eprod: d > d > d ).
% 0.23/0.52
% 0.23/0.52 thf(tyop_2Erealax_2Ereal,type,
% 0.23/0.52 tyop_2Erealax_2Ereal: d ).
% 0.23/0.52
% 0.23/0.52 thf(s,type,
% 0.23/0.52 s: d > u > du ).
% 0.23/0.52
% 0.23/0.52 thf(app_2E2,type,
% 0.23/0.52 app_2E2: du > du > u ).
% 0.23/0.52
% 0.23/0.52 thf(combin_i_2E0,type,
% 0.23/0.52 combin_i_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(combin_k_2E0,type,
% 0.23/0.52 combin_k_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(combin_s_2E0,type,
% 0.23/0.52 combin_s_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_21_2E0,type,
% 0.23/0.52 c_2Ebool_2E_21_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_21_2E1,type,
% 0.23/0.52 c_2Ebool_2E_21_2E1: du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.23/0.52 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.23/0.52 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Enum_2E0_2E0,type,
% 0.23/0.52 c_2Enum_2E0_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Emin_2E_3D_2E0,type,
% 0.23/0.52 c_2Emin_2E_3D_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Emin_2E_3D_2E2,type,
% 0.23/0.52 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.23/0.52 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.23/0.52 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_3F_2E0,type,
% 0.23/0.52 c_2Ebool_2E_3F_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_3F_2E1,type,
% 0.23/0.52 c_2Ebool_2E_3F_2E1: du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2EF_2E0,type,
% 0.23/0.52 c_2Ebool_2EF_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2ET_2E0,type,
% 0.23/0.52 c_2Ebool_2ET_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.23/0.52 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.23/0.52 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ecomplex_2Ecomplex__inv_2E0,type,
% 0.23/0.52 c_2Ecomplex_2Ecomplex__inv_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ecomplex_2Ecomplex__inv_2E1,type,
% 0.23/0.52 c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ecomplex_2Ecomplex__of__num_2E0,type,
% 0.23/0.52 c_2Ecomplex_2Ecomplex__of__num_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ecomplex_2Ecomplex__of__num_2E1,type,
% 0.23/0.52 c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_7E_2E0,type,
% 0.23/0.52 c_2Ebool_2E_7E_2E0: u ).
% 0.23/0.52
% 0.23/0.52 thf(c_2Ebool_2E_7E_2E1,type,
% 0.23/0.52 c_2Ebool_2E_7E_2E1: du > u ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.23/0.52 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.23/0.52 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.23/0.52 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.23/0.52 mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.23/0.52 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Enum_2E0,type,
% 0.23/0.52 mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.23/0.52 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ebool_2EF,type,
% 0.23/0.52 mono_2Ec_2Ebool_2EF: $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ebool_2ET,type,
% 0.23/0.52 mono_2Ec_2Ebool_2ET: $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.23/0.52 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ecomplex_2Ecomplex__inv,type,
% 0.23/0.52 mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num,type,
% 0.23/0.52 mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.23/0.52 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.23/0.52 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.23/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.23/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.23/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.23/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Enum_2Enum,type,
% 0.23/0.52 i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
% 0.23/0.52
% 0.23/0.52 thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.23/0.52 i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.23/0.52 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.23/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.23/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.23/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.23/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Enum_2Enum,type,
% 0.23/0.52 j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
% 0.23/0.52
% 0.23/0.52 thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.23/0.52 j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.23/0.52 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.23/0.52 ( ! [V2x_2E0: u] :
% 0.23/0.52 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.23/0.52 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.23/0.52 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.23/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.23/0.52 ! [A_27a: d,V0x_2E0: u] :
% 0.23/0.52 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.23/0.52 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.23/0.52 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) )
% 0.23/0.52 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Eho_2Es__thm,axiom,
% 0.23/0.52 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) )
% 0.23/0.52 = ( 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 ) ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.23/0.52 ! [V0: $o,V1: $o] :
% 0.23/0.52 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.23/0.52 <=> ( V0
% 0.23/0.52 & V1 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.23/0.52 ! [V0: $o,V1: $o] :
% 0.23/0.52 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.23/0.52 <=> ( V0
% 0.23/0.52 | V1 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Elogic_2E_7E,axiom,
% 0.23/0.52 ! [V0: $o] :
% 0.23/0.52 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.23/0.52 <=> ( (~) @ V0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.23/0.52 ! [V0: $o,V1: $o] :
% 0.23/0.52 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.23/0.52 <=> ( V0
% 0.23/0.52 => V1 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Elogic_2E_3D,axiom,
% 0.23/0.52 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.23/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.23/0.52 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.23/0.52 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Equant_2E_21,axiom,
% 0.23/0.52 ! [A_27a: d,V0f_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) ) )
% 0.23/0.52 <=> ! [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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(reserved_2Equant_2E_3F,axiom,
% 0.23/0.52 ! [A_27a: d,V0f_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) ) )
% 0.23/0.52 <=> ? [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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.23/0.52 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) ) )
% 0.23/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) ) )
% 0.23/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 0.23/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 0.23/0.52 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
% 0.23/0.52 = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.23/0.52 ! [V0_2E0: u] :
% 0.23/0.52 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 0.23/0.52 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.52 ! [V0: $o] :
% 0.23/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.52 ! [V0: $o > $o] :
% 0.23/0.52 ( ( 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 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.23/0.52 ! [V0: $o > $o > $o] :
% 0.23/0.52 ( ( 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 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.23/0.52 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.52 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.23/0.52 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.52 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
% 0.23/0.52 ! [V0: mono_2Etyop_2Enum_2Enum] :
% 0.23/0.52 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.23/0.52 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.52 ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 0.23/0.52 = V0 ) ).
% 0.23/0.52
% 0.23/0.52 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) ) )
% 0.23/0.52 = ( 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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.23/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.23/0.52 ( ( ( s @ A_27a @ X0_2E0 )
% 0.23/0.52 = ( s @ A_27a @ X1_2E0 ) )
% 0.23/0.52 <=> ( 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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.23/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.23/0.52 ( ( 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 ) ) ) )
% 0.23/0.52 = ( 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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.52 ! [V0: $o > $o,V1: $o] :
% 0.23/0.52 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.23/0.52 = ( 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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.52 ! [V0: $o > $o > $o,V1: $o] :
% 0.23/0.52 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.23/0.52 = ( 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 ) ) ) ) ) ).
% 0.23/0.52
% 0.23/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.23/0.52 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
% 0.23/0.52 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 0.23/0.52 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.23/0.54 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.54 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 0.23/0.54 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.23/0.54 ! [V0: $o > $o,V1: $o] :
% 0.23/0.54 ( ( V0 @ V1 )
% 0.23/0.54 = ( V0 @ V1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.23/0.54 ! [V0: $o > $o > $o,V1: $o] :
% 0.23/0.54 ( ( V0 @ V1 )
% 0.23/0.54 = ( V0 @ V1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.23/0.54 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
% 0.23/0.54 ( ( V0 @ V1 )
% 0.23/0.54 = ( V0 @ V1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.23/0.54 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.54 ( ( V0 @ V1 )
% 0.23/0.54 = ( V0 @ V1 ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.23/0.54 mono_2Ec_2Ebool_2ET ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.23/0.54 ! [A_27a: d,V0t: $o] :
% 0.23/0.54 ( ! [V1x_2E0: u] : V0t
% 0.23/0.54 <=> V0t ) ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.23/0.54 ! [V0t: $o] :
% 0.23/0.54 ( ( ( mono_2Ec_2Ebool_2ET
% 0.23/0.54 => V0t )
% 0.23/0.54 <=> V0t )
% 0.23/0.54 & ( ( V0t
% 0.23/0.54 => mono_2Ec_2Ebool_2ET )
% 0.23/0.54 <=> mono_2Ec_2Ebool_2ET )
% 0.23/0.54 & ( ( mono_2Ec_2Ebool_2EF
% 0.23/0.54 => V0t )
% 0.23/0.54 <=> mono_2Ec_2Ebool_2ET )
% 0.23/0.54 & ( ( V0t
% 0.23/0.54 => V0t )
% 0.23/0.54 <=> mono_2Ec_2Ebool_2ET )
% 0.23/0.54 & ( ( V0t
% 0.23/0.54 => mono_2Ec_2Ebool_2EF )
% 0.23/0.54 <=> ( (~) @ V0t ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
% 0.23/0.54 ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.54 ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.23/0.54 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
% 0.23/0.54 <=> ( V0z
% 0.23/0.54 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
% 0.23/0.54 ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.23/0.54 ( ( (~)
% 0.23/0.54 @ ( V0z
% 0.23/0.54 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
% 0.23/0.54 => ( (~)
% 0.23/0.54 @ ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.23/0.54 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.OCBBuDEJT6/cvc5---1.0.5_25589.p...
% 0.23/0.54 (declare-sort $$unsorted 0)
% 0.23/0.54 (declare-sort tptp.u 0)
% 0.23/0.54 (declare-sort tptp.d 0)
% 0.23/0.54 (declare-sort tptp.du 0)
% 0.23/0.54 (declare-sort tptp.mono_2Etyop_2Enum_2Enum 0)
% 0.23/0.54 (declare-sort tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 0)
% 0.23/0.54 (declare-fun tptp.tyop_2Emin_2Ebool () tptp.d)
% 0.23/0.54 (declare-fun tptp.tyop_2Emin_2Efun (tptp.d tptp.d) tptp.d)
% 0.23/0.54 (declare-fun tptp.tyop_2Enum_2Enum () tptp.d)
% 0.23/0.54 (declare-fun tptp.tyop_2Epair_2Eprod (tptp.d tptp.d) tptp.d)
% 0.23/0.54 (declare-fun tptp.tyop_2Erealax_2Ereal () tptp.d)
% 0.23/0.54 (declare-fun tptp.s (tptp.d tptp.u) tptp.du)
% 0.23/0.54 (declare-fun tptp.app_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.combin_i_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.combin_k_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.combin_s_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_21_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_21_2E1 (tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Enum_2E0_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Emin_2E_3D_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Emin_2E_3D_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_3F_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_3F_2E1 (tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2EF_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2ET_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E2 (tptp.du tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ecomplex_2Ecomplex__inv_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ecomplex_2Ecomplex__inv_2E1 (tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ecomplex_2Ecomplex__of__num_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ecomplex_2Ecomplex__of__num_2E1 (tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_7E_2E0 () tptp.u)
% 0.23/0.54 (declare-fun tptp.c_2Ebool_2E_7E_2E1 (tptp.du) tptp.u)
% 0.23/0.54 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ((-> Bool Bool) Bool) Bool)
% 0.23/0.54 (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)
% 0.23/0.54 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ((-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.mono_2Etyop_2Enum_2Enum) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ((-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2E_2F_5C (Bool Bool) Bool)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Enum_2E0 () tptp.mono_2Etyop_2Enum_2Enum)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Emin_2E_3D_3D_3E (Bool Bool) Bool)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2EF () Bool)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2ET () Bool)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2E_5C_2F (Bool Bool) Bool)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv (tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num (tptp.mono_2Etyop_2Enum_2Enum) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (declare-fun tptp.mono_2Ec_2Ebool_2E_7E (Bool) Bool)
% 0.23/0.54 (declare-fun tptp.i_mono_2Etyop_2Emin_2Ebool (Bool) tptp.u)
% 0.23/0.54 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((-> Bool Bool)) tptp.u)
% 0.23/0.54 (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)
% 0.23/0.54 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ((-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) tptp.u)
% 0.23/0.54 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ((-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) tptp.u)
% 0.23/0.54 (declare-fun tptp.i_mono_2Etyop_2Enum_2Enum (tptp.mono_2Etyop_2Enum_2Enum) tptp.u)
% 0.23/0.54 (declare-fun tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.u)
% 0.23/0.54 (declare-fun tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.du) Bool)
% 0.23/0.54 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.du Bool) Bool)
% 0.23/0.54 (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)
% 0.23/0.54 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (tptp.du tptp.mono_2Etyop_2Enum_2Enum) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (tptp.du tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (declare-fun tptp.j_mono_2Etyop_2Enum_2Enum (tptp.du) tptp.mono_2Etyop_2Enum_2Enum)
% 0.23/0.54 (declare-fun tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (tptp.du) tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)
% 0.23/0.54 (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))))))
% 0.23/0.54 (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)))))
% 0.23/0.54 (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))))))
% 0.23/0.54 (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)))))))))))))))))
% 0.23/0.54 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))))
% 0.23/0.54 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))))
% 0.23/0.54 (assert (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))))
% 0.23/0.54 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))))
% 0.23/0.54 (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)))))))
% 0.23/0.54 (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))))))))
% 0.23/0.54 (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))))))))
% 0.23/0.54 (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)))))
% 0.23/0.54 (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)))))
% 0.23/0.54 (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))))))
% 0.23/0.54 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum) (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 _let_2))) _let_2)))))
% 0.23/0.54 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 _let_3))) _let_3))))))
% 0.23/0.54 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s tptp.tyop_2Enum_2Enum))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Enum_2Enum (@ tptp.j_mono_2Etyop_2Enum_2Enum _let_2))) _let_2)))))
% 0.23/0.54 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 _let_2))) _let_2)))))
% 0.23/0.54 (assert (forall ((V0 Bool)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) V0)))
% 0.23/0.54 (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)))
% 0.23/0.54 (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))))
% 0.23/0.54 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum) (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) V0)))
% 0.23/0.54 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29))) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) V0))))
% 0.23/0.54 (assert (forall ((V0 tptp.mono_2Etyop_2Enum_2Enum)) (= (@ tptp.j_mono_2Etyop_2Enum_2Enum (@ (@ tptp.s tptp.tyop_2Enum_2Enum) (@ tptp.i_mono_2Etyop_2Enum_2Enum V0))) V0)))
% 0.23/0.54 (assert (forall ((V0 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (= (@ tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal)) (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 V0))) V0)))
% 0.23/0.54 (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)))))))))
% 0.23/0.54 (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)))))))))))
% 0.23/0.54 (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)))))))))
% 0.23/0.54 (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))))))))
% 0.23/0.54 (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))))))))))
% 0.23/0.54 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (let ((_let_2 (@ tptp.s _let_1))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ V0 V1))) (@ _let_2 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum) _let_1)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Enum_2Enum) (@ tptp.i_mono_2Etyop_2Enum_2Enum V1)))))))))
% 0.23/0.54 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (let ((_let_2 (@ tptp.s _let_1))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ V0 V1))) (@ _let_2 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) (@ _let_2 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 V1)))))))))
% 0.23/0.54 (assert (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.23/0.54 (assert (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.23/0.54 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.23/0.54 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.23/0.54 (assert tptp.mono_2Ec_2Ebool_2ET)
% 0.23/0.54 (assert (forall ((A_27a tptp.d) (V0t Bool)) (= (forall ((V1x_2E0 tptp.u)) V0t) V0t)))
% 0.23/0.54 (assert (forall ((V0t Bool)) (and (= (=> tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (=> V0t tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2ET) (= (=> tptp.mono_2Ec_2Ebool_2EF V0t) tptp.mono_2Ec_2Ebool_2ET) (= (=> V0t V0t) tptp.mono_2Ec_2Ebool_2ET) (= (=> V0t tptp.mono_2Ec_2Ebool_2EF) (not V0t)))))
% 0.23/0.60 (assert (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num tptp.mono_2Ec_2Enum_2E0))) (= (= (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv V0z) _let_1) (= V0z _let_1)))))
% 0.23/0.60 (assert (not (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num tptp.mono_2Ec_2Enum_2E0))) (=> (not (= V0z _let_1)) (not (= (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv V0z) _let_1)))))))
% 0.23/0.60 (set-info :filename cvc5---1.0.5_25589)
% 0.23/0.60 (check-sat-assuming ( true ))
% 0.23/0.60 ------- get file name : TPTP file name is ITP019^1
% 0.23/0.60 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25589.smt2...
% 0.23/0.60 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.60 % SZS status Theorem for ITP019^1
% 0.23/0.60 % SZS output start Proof for ITP019^1
% 0.23/0.60 (
% 0.23/0.60 (let ((_let_1 (not (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num tptp.mono_2Ec_2Enum_2E0))) (=> (not (= V0z _let_1)) (not (= (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv V0z) _let_1)))))))) (let ((_let_2 (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num tptp.mono_2Ec_2Enum_2E0))) (= (= (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv V0z) _let_1) (= V0z _let_1)))))) (let ((_let_3 (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (ho_49 k_52 tptp.mono_2Ec_2Enum_2E0))) (= (= V0z _let_1) (= (ho_50 k_51 V0z) _let_1)))))) (let ((_let_4 (ho_49 k_52 tptp.mono_2Ec_2Enum_2E0))) (let ((_let_5 (= _let_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53))) (let ((_let_6 (= _let_4 (ho_50 k_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53)))) (let ((_let_7 (= _let_6 _let_5))) (let ((_let_8 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num tptp.mono_2Ec_2Enum_2E0))) (= (= V0z _let_1) (= _let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv V0z))))) _let_3))))))) (let ((_let_9 (not _let_7))) (let ((_let_10 (not _let_6))) (let ((_let_11 (or _let_5 _let_10))) (let ((_let_12 (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (ho_49 k_52 tptp.mono_2Ec_2Enum_2E0))) (or (= V0z _let_1) (not (= _let_1 (ho_50 k_51 V0z)))))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (not _let_12))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((V0z tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__of__num tptp.mono_2Ec_2Enum_2E0))) (or (= _let_1 V0z) (not (= _let_1 (@ tptp.mono_2Ec_2Ecomplex_2Ecomplex__inv V0z))))))) _let_14))))))) (let ((_let_16 (or))) (let ((_let_17 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_15) :args (_let_14)) (REWRITE :args ((=> _let_14 (not (or (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 _let_4) _let_10))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_12))) (REFL :args (_let_13)) :args _let_16)) _let_15 :args (_let_13 true _let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_8 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_53 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_3)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_7)) :args ((or _let_10 _let_5 _let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 1)) (CONG (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_6))) :args _let_16)) :args ((or _let_6 _let_11))) _let_17 :args (_let_6 true _let_11)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_11 0)) _let_17 :args ((not _let_5) true _let_11)) :args (_let_9 false _let_6 true _let_5)) _let_8 :args (false true _let_7 false _let_3)) :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_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum) (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 _let_3))) _let_3))))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s tptp.tyop_2Enum_2Enum))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Enum_2Enum (@ tptp.j_mono_2Etyop_2Enum_2Enum _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 _let_2))) _let_2)))) (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 ((V0 (-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum) (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) V0)) (forall ((V0 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29))) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) V0))) (forall ((V0 tptp.mono_2Etyop_2Enum_2Enum)) (= (@ tptp.j_mono_2Etyop_2Enum_2Enum (@ (@ tptp.s tptp.tyop_2Enum_2Enum) (@ tptp.i_mono_2Etyop_2Enum_2Enum V0))) V0)) (forall ((V0 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (= (@ tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal)) (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_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)))))))) (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 (-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (let ((_let_2 (@ tptp.s _let_1))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ V0 V1))) (@ _let_2 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Enum_2Enum) _let_1)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Enum_2Enum) (@ tptp.i_mono_2Etyop_2Enum_2Enum V1)))))))) (forall ((V0 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ (@ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal))) (let ((_let_2 (@ tptp.s _let_1))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (@ V0 V1))) (@ _let_2 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun _let_1) _let_1)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 V0))) (@ _let_2 (@ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 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))) (forall ((V0 (-> tptp.mono_2Etyop_2Enum_2Enum tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Enum_2Enum)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) (forall ((V0 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (V1 tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) tptp.mono_2Ec_2Ebool_2ET (forall ((A_27a tptp.d) (V0t Bool)) (= (forall ((V1x_2E0 tptp.u)) V0t) V0t)) (forall ((V0t Bool)) (and (= (=> tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (=> V0t tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2ET) (= (=> tptp.mono_2Ec_2Ebool_2EF V0t) tptp.mono_2Ec_2Ebool_2ET) (= (=> V0t V0t) tptp.mono_2Ec_2Ebool_2ET) (= (=> V0t tptp.mono_2Ec_2Ebool_2EF) (not V0t)))) _let_2 _let_1 true))))))))))))))))))))
% 0.23/0.61 )
% 0.23/0.61 % SZS output end Proof for ITP019^1
% 0.23/0.61 % cvc5---1.0.5 exiting
% 0.23/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------