TSTP Solution File: ITP021^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP021^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 03:16:26 EDT 2023
% Result : Theorem 1.87s 2.16s
% Output : Proof 1.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP021^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 13:51:29 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 % File : ITP021^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.22/0.50 % Domain : Interactive Theorem Proving
% 0.22/0.50 % Problem : HOL4 syntactic export of thm_2Eextreal_2Emax__le.p, bushy mode
% 0.22/0.50 % Version : [BG+19] axioms.
% 0.22/0.50 % English :
% 0.22/0.50
% 0.22/0.50 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.22/0.50 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.22/0.50 % Source : [BG+19]
% 0.22/0.50 % Names : thm_2Eextreal_2Emax__le.p [Gau19]
% 0.22/0.50 % : HL410001^1.p [TPAP]
% 0.22/0.50
% 0.22/0.50 % Status : Theorem
% 0.22/0.50 % Rating : 0.54 v8.1.0, 0.55 v7.5.0
% 0.22/0.50 % Syntax : Number of formulae : 145 ( 48 unt; 68 typ; 0 def)
% 0.22/0.50 % Number of atoms : 163 ( 55 equ; 45 cnn)
% 0.22/0.50 % Maximal formula atoms : 8 ( 2 avg)
% 0.22/0.50 % Number of connectives : 991 ( 45 ~; 36 |; 27 &; 813 @)
% 0.22/0.50 % ( 39 <=>; 31 =>; 0 <=; 0 <~>)
% 0.22/0.50 % Maximal formula depth : 17 ( 5 avg)
% 0.22/0.50 % Number of types : 5 ( 4 usr)
% 0.22/0.50 % Number of type conns : 147 ( 147 >; 0 *; 0 +; 0 <<)
% 0.22/0.50 % Number of symbols : 66 ( 64 usr; 20 con; 0-4 aty)
% 0.22/0.50 % Number of variables : 146 ( 0 ^; 145 !; 1 ?; 146 :)
% 0.22/0.50 % SPC : TH0_THM_EQU_NAR
% 0.22/0.50
% 0.22/0.50 % Comments :
% 0.22/0.50 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 thf(u,type,
% 0.22/0.50 u: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(d,type,
% 0.22/0.50 d: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(du,type,
% 0.22/0.50 du: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Etyop_2Eextreal_2Eextreal,type,
% 0.22/0.50 mono_2Etyop_2Eextreal_2Eextreal: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(tyop_2Eextreal_2Eextreal,type,
% 0.22/0.50 tyop_2Eextreal_2Eextreal: d ).
% 0.22/0.50
% 0.22/0.50 thf(tyop_2Emin_2Ebool,type,
% 0.22/0.50 tyop_2Emin_2Ebool: d ).
% 0.22/0.50
% 0.22/0.50 thf(tyop_2Emin_2Efun,type,
% 0.22/0.50 tyop_2Emin_2Efun: d > d > d ).
% 0.22/0.50
% 0.22/0.50 thf(s,type,
% 0.22/0.50 s: d > u > du ).
% 0.22/0.50
% 0.22/0.50 thf(app_2E2,type,
% 0.22/0.50 app_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(combin_i_2E0,type,
% 0.22/0.50 combin_i_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(combin_k_2E0,type,
% 0.22/0.50 combin_k_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(combin_s_2E0,type,
% 0.22/0.50 combin_s_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_21_2E0,type,
% 0.22/0.50 c_2Ebool_2E_21_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_21_2E1,type,
% 0.22/0.50 c_2Ebool_2E_21_2E1: du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.22/0.50 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.22/0.50 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Emin_2E_3D_2E0,type,
% 0.22/0.50 c_2Emin_2E_3D_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Emin_2E_3D_2E2,type,
% 0.22/0.50 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.22/0.50 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.22/0.50 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_3F_2E0,type,
% 0.22/0.50 c_2Ebool_2E_3F_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_3F_2E1,type,
% 0.22/0.50 c_2Ebool_2E_3F_2E1: du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2ECOND_2E0,type,
% 0.22/0.50 c_2Ebool_2ECOND_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2ECOND_2E3,type,
% 0.22/0.50 c_2Ebool_2ECOND_2E3: du > du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2EF_2E0,type,
% 0.22/0.50 c_2Ebool_2EF_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2ET_2E0,type,
% 0.22/0.50 c_2Ebool_2ET_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.22/0.50 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.22/0.50 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Eextreal_2Eextreal__le_2E0,type,
% 0.22/0.50 c_2Eextreal_2Eextreal__le_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Eextreal_2Eextreal__le_2E2,type,
% 0.22/0.50 c_2Eextreal_2Eextreal__le_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Eextreal_2Eextreal__max_2E0,type,
% 0.22/0.50 c_2Eextreal_2Eextreal__max_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Eextreal_2Eextreal__max_2E2,type,
% 0.22/0.50 c_2Eextreal_2Eextreal__max_2E2: du > du > u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_7E_2E0,type,
% 0.22/0.50 c_2Ebool_2E_7E_2E0: u ).
% 0.22/0.50
% 0.22/0.50 thf(c_2Ebool_2E_7E_2E1,type,
% 0.22/0.50 c_2Ebool_2E_7E_2E1: du > u ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: ( $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ) > $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Eextreal_2Eextreal > $o ) > mono_2Etyop_2Eextreal_2Eextreal > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ) > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
% 0.22/0.50 mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.22/0.50 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.22/0.50 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal,type,
% 0.22/0.50 mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal: $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Ebool_2EF,type,
% 0.22/0.50 mono_2Ec_2Ebool_2EF: $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Ebool_2ET,type,
% 0.22/0.50 mono_2Ec_2Ebool_2ET: $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.22/0.50 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Eextreal_2Eextreal__le,type,
% 0.22/0.50 mono_2Ec_2Eextreal_2Eextreal__le: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Eextreal_2Eextreal__max,type,
% 0.22/0.50 mono_2Ec_2Eextreal_2Eextreal__max: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.22/0.50 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Eextreal_2Eextreal,type,
% 0.22/0.50 i_mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Eextreal_2Eextreal > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29: ( $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eextreal_2Eextreal > $o ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,type,
% 0.22/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: ( mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ) > u ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Eextreal_2Eextreal,type,
% 0.22/0.50 j_mono_2Etyop_2Eextreal_2Eextreal: du > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29: du > $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Eextreal_2Eextreal > $o ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: du > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ).
% 0.22/0.50
% 0.22/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,type,
% 0.22/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: du > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.22/0.50 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.22/0.50 ( ! [V2x_2E0: u] :
% 0.22/0.50 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.22/0.50 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.22/0.50 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.22/0.50 ! [A_27a: d,V0x_2E0: u] :
% 0.22/0.50 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.22/0.50 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.22/0.50 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) )
% 0.22/0.50 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Eho_2Es__thm,axiom,
% 0.22/0.50 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) )
% 0.22/0.50 = ( 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 ) ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.22/0.50 ! [V0: $o,V1: $o] :
% 0.22/0.50 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.22/0.50 <=> ( V0
% 0.22/0.50 & V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.22/0.50 ! [V0: $o,V1: $o] :
% 0.22/0.50 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.22/0.50 <=> ( V0
% 0.22/0.50 | V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Elogic_2E_7E,axiom,
% 0.22/0.50 ! [V0: $o] :
% 0.22/0.50 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.22/0.50 <=> ( (~) @ V0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.22/0.50 ! [V0: $o,V1: $o] :
% 0.22/0.50 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.22/0.50 <=> ( V0
% 0.22/0.50 => V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Elogic_2E_3D,axiom,
% 0.22/0.50 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.22/0.50 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.22/0.50 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Equant_2E_21,axiom,
% 0.22/0.50 ! [A_27a: d,V0f_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) ) )
% 0.22/0.50 <=> ! [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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(reserved_2Equant_2E_3F,axiom,
% 0.22/0.50 ! [A_27a: d,V0f_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) ) )
% 0.22/0.50 <=> ? [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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( j_mono_2Etyop_2Eextreal_2Eextreal @ ( s @ tyop_2Eextreal_2Eextreal @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ tyop_2Eextreal_2Eextreal @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,axiom,
% 0.22/0.50 ! [V0_2E0: u] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ V0_2E0 ) ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ V0_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.50 ! [V0: $o] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Eextreal_2Eextreal @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0: $o > $o] :
% 0.22/0.50 ( ( 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 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.22/0.50 ! [V0: $o > $o > $o] :
% 0.22/0.50 ( ( 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 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29,axiom,
% 0.22/0.50 ! [V0: $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > $o] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ V0 ) ) )
% 0.22/0.50 = V0 ) ).
% 0.22/0.50
% 0.22/0.50 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.22/0.50 ! [A_27a: d,X0_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) ) )
% 0.22/0.50 = ( 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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.22/0.50 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.22/0.50 ( ( ( s @ A_27a @ X0_2E0 )
% 0.22/0.50 = ( s @ A_27a @ X1_2E0 ) )
% 0.22/0.50 <=> ( 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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.22/0.50 ! [A_27a: d,X0_2E0: u] :
% 0.22/0.50 ( ( 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 ) ) ) )
% 0.22/0.50 = ( 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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
% 0.22/0.50 ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
% 0.22/0.50 ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
% 0.22/0.50 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.50 ! [V0: $o > $o,V1: $o] :
% 0.22/0.50 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( 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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0: $o > $o > $o,V1: $o] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( 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 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,axiom,
% 0.22/0.50 ! [V0: $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal,V1: $o] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > $o,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( s @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 @ ( V0 @ V1 ) ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
% 0.22/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal ) )
% 0.22/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
% 0.22/0.50 ! [V0: $o,V1: mono_2Etyop_2Eextreal_2Eextreal,V2: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ V0 @ V1 @ V2 ) ) )
% 0.22/0.50 = ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V1 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ V2 ) ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.50 ! [V0: $o > $o,V1: $o] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0: $o > $o > $o,V1: $o] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,axiom,
% 0.22/0.50 ! [V0: $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal,V1: $o] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > $o,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
% 0.22/0.50 ! [V0: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal,V1: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( V0 @ V1 )
% 0.22/0.50 = ( V0 @ V1 ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.22/0.50 mono_2Ec_2Ebool_2ET ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.22/0.50 ! [V0t1: $o,V1t2: $o] :
% 0.22/0.50 ( ( V0t1
% 0.22/0.50 => V1t2 )
% 0.22/0.50 => ( ( V1t2
% 0.22/0.50 => V0t1 )
% 0.22/0.50 => ( V0t1 = V1t2 ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EFALSITY,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( mono_2Ec_2Ebool_2EF
% 0.22/0.50 => V0t ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( V0t
% 0.22/0.50 | ( (~) @ V0t ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EIMP__F,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( ( V0t
% 0.22/0.50 => mono_2Ec_2Ebool_2EF )
% 0.22/0.50 => ( (~) @ V0t ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EF__IMP,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( ( (~) @ V0t )
% 0.22/0.50 => ( V0t
% 0.22/0.50 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( ( ( mono_2Ec_2Ebool_2ET
% 0.22/0.50 => V0t )
% 0.22/0.50 <=> V0t )
% 0.22/0.50 & ( ( V0t
% 0.22/0.50 => mono_2Ec_2Ebool_2ET )
% 0.22/0.50 <=> mono_2Ec_2Ebool_2ET )
% 0.22/0.50 & ( ( mono_2Ec_2Ebool_2EF
% 0.22/0.50 => V0t )
% 0.22/0.50 <=> mono_2Ec_2Ebool_2ET )
% 0.22/0.50 & ( ( V0t
% 0.22/0.50 => V0t )
% 0.22/0.50 <=> mono_2Ec_2Ebool_2ET )
% 0.22/0.50 & ( ( V0t
% 0.22/0.50 => mono_2Ec_2Ebool_2EF )
% 0.22/0.50 <=> ( (~) @ V0t ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.22/0.50 ( ! [V0t: $o] :
% 0.22/0.50 ( ( (~) @ ( (~) @ V0t ) )
% 0.22/0.50 <=> V0t )
% 0.22/0.50 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 0.22/0.50 <=> mono_2Ec_2Ebool_2EF )
% 0.22/0.50 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 0.22/0.50 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.22/0.50 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 0.22/0.50 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.22/0.50 = ( s @ A_27a @ V1y_2E0 ) )
% 0.22/0.50 <=> ( ( s @ A_27a @ V1y_2E0 )
% 0.22/0.50 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 0.22/0.50 <=> V0t )
% 0.22/0.50 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 0.22/0.50 <=> V0t )
% 0.22/0.50 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 0.22/0.50 <=> ( (~) @ V0t ) )
% 0.22/0.50 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 0.22/0.50 <=> ( (~) @ V0t ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2ECOND__CLAUSES,axiom,
% 0.22/0.50 ! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
% 0.22/0.50 ( ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) )
% 0.22/0.50 = ( s @ A_27a @ V0t1_2E0 ) )
% 0.22/0.50 & ( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ A_27a @ V0t1_2E0 ) @ ( s @ A_27a @ V1t2_2E0 ) ) )
% 0.22/0.50 = ( s @ A_27a @ V1t2_2E0 ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
% 0.22/0.50 ! [V0A: $o,V1B: $o,V2C: $o] :
% 0.22/0.50 ( ( V0A
% 0.22/0.50 | V1B
% 0.22/0.50 | V2C )
% 0.22/0.50 <=> ( V0A
% 0.22/0.50 | V1B
% 0.22/0.50 | V2C ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EDISJ__SYM,axiom,
% 0.22/0.50 ! [V0A: $o,V1B: $o] :
% 0.22/0.50 ( ( V0A
% 0.22/0.50 | V1B )
% 0.22/0.50 <=> ( V1B
% 0.22/0.50 | V0A ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 0.22/0.50 ! [V0A: $o,V1B: $o] :
% 0.22/0.50 ( ( ( (~)
% 0.22/0.50 @ ( V0A
% 0.22/0.50 & V1B ) )
% 0.22/0.50 <=> ( ( (~) @ V0A )
% 0.22/0.50 | ( (~) @ V1B ) ) )
% 0.22/0.50 & ( ( (~)
% 0.22/0.50 @ ( V0A
% 0.22/0.50 | V1B ) )
% 0.22/0.50 <=> ( ( (~) @ V0A )
% 0.22/0.50 & ( (~) @ V1B ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Eextreal_2Ele__trans,axiom,
% 0.22/0.50 ! [V0x: mono_2Etyop_2Eextreal_2Eextreal,V1y: mono_2Etyop_2Eextreal_2Eextreal,V2z: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y )
% 0.22/0.50 & ( mono_2Ec_2Eextreal_2Eextreal__le @ V1y @ V2z ) )
% 0.22/0.50 => ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V2z ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Eextreal_2Ele__total,axiom,
% 0.22/0.50 ! [V0x: mono_2Etyop_2Eextreal_2Eextreal,V1y: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y )
% 0.22/0.50 | ( mono_2Ec_2Eextreal_2Eextreal__le @ V1y @ V0x ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Eextreal_2Eextreal__max__def,axiom,
% 0.22/0.50 ! [V0x: mono_2Etyop_2Eextreal_2Eextreal,V1y: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.50 ( ( mono_2Ec_2Eextreal_2Eextreal__max @ V0x @ V1y )
% 0.22/0.50 = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ V0x @ V1y ) @ V1y @ V0x ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Esat_2ENOT__NOT,axiom,
% 0.22/0.50 ! [V0t: $o] :
% 0.22/0.50 ( ( (~) @ ( (~) @ V0t ) )
% 0.22/0.50 <=> V0t ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 0.22/0.50 ! [V0A: $o] :
% 0.22/0.50 ( V0A
% 0.22/0.50 => ( ( (~) @ V0A )
% 0.22/0.50 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.22/0.50
% 0.22/0.50 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 0.22/0.50 ! [V0B: $o,V1A: $o] :
% 0.22/0.50 ( ( ( (~)
% 0.22/0.50 @ ( V1A
% 0.22/0.50 | V0B ) )
% 0.22/0.50 => mono_2Ec_2Ebool_2EF )
% 0.22/0.50 <=> ( ( V1A
% 0.22/0.50 => mono_2Ec_2Ebool_2EF )
% 0.22/0.50 => ( ( (~) @ V0B )
% 0.22/0.53 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 0.22/0.53 ! [V0B: $o,V1A: $o] :
% 0.22/0.53 ( ( ( (~)
% 0.22/0.53 @ ( ( (~) @ V1A )
% 0.22/0.53 | V0B ) )
% 0.22/0.53 => mono_2Ec_2Ebool_2EF )
% 0.22/0.53 <=> ( V1A
% 0.22/0.53 => ( ( (~) @ V0B )
% 0.22/0.53 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2EAND__INV2,axiom,
% 0.22/0.53 ! [V0A: $o] :
% 0.22/0.53 ( ( ( (~) @ V0A )
% 0.22/0.53 => mono_2Ec_2Ebool_2EF )
% 0.22/0.53 => ( ( V0A
% 0.22/0.53 => mono_2Ec_2Ebool_2EF )
% 0.22/0.53 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2Edc__eq,axiom,
% 0.22/0.53 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.22/0.53 ( ( V2p
% 0.22/0.53 <=> ( V1q = V0r ) )
% 0.22/0.53 <=> ( ( V2p
% 0.22/0.53 | V1q
% 0.22/0.53 | V0r )
% 0.22/0.53 & ( V2p
% 0.22/0.53 | ( (~) @ V0r )
% 0.22/0.53 | ( (~) @ V1q ) )
% 0.22/0.53 & ( V1q
% 0.22/0.53 | ( (~) @ V0r )
% 0.22/0.53 | ( (~) @ V2p ) )
% 0.22/0.53 & ( V0r
% 0.22/0.53 | ( (~) @ V1q )
% 0.22/0.53 | ( (~) @ V2p ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2Edc__conj,axiom,
% 0.22/0.53 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.22/0.53 ( ( V2p
% 0.22/0.53 <=> ( V1q
% 0.22/0.53 & V0r ) )
% 0.22/0.53 <=> ( ( V2p
% 0.22/0.53 | ( (~) @ V1q )
% 0.22/0.53 | ( (~) @ V0r ) )
% 0.22/0.53 & ( V1q
% 0.22/0.53 | ( (~) @ V2p ) )
% 0.22/0.53 & ( V0r
% 0.22/0.53 | ( (~) @ V2p ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2Edc__disj,axiom,
% 0.22/0.53 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.22/0.53 ( ( V2p
% 0.22/0.53 <=> ( V1q
% 0.22/0.53 | V0r ) )
% 0.22/0.53 <=> ( ( V2p
% 0.22/0.53 | ( (~) @ V1q ) )
% 0.22/0.53 & ( V2p
% 0.22/0.53 | ( (~) @ V0r ) )
% 0.22/0.53 & ( V1q
% 0.22/0.53 | V0r
% 0.22/0.53 | ( (~) @ V2p ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2Edc__imp,axiom,
% 0.22/0.53 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.22/0.53 ( ( V2p
% 0.22/0.53 <=> ( V1q
% 0.22/0.53 => V0r ) )
% 0.22/0.53 <=> ( ( V2p
% 0.22/0.53 | V1q )
% 0.22/0.53 & ( V2p
% 0.22/0.53 | ( (~) @ V0r ) )
% 0.22/0.53 & ( ( (~) @ V1q )
% 0.22/0.53 | V0r
% 0.22/0.53 | ( (~) @ V2p ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Esat_2Edc__neg,axiom,
% 0.22/0.53 ! [V0q: $o,V1p: $o] :
% 0.22/0.53 ( ( V1p
% 0.22/0.53 <=> ( (~) @ V0q ) )
% 0.22/0.53 <=> ( ( V1p
% 0.22/0.53 | V0q )
% 0.22/0.53 & ( ( (~) @ V0q )
% 0.22/0.53 | ( (~) @ V1p ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(thm_2Eextreal_2Emax__le,conjecture,
% 0.22/0.53 ! [V0z: mono_2Etyop_2Eextreal_2Eextreal,V1x: mono_2Etyop_2Eextreal_2Eextreal,V2y: mono_2Etyop_2Eextreal_2Eextreal] :
% 0.22/0.53 ( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ V1x @ V2y ) @ V0z )
% 0.22/0.53 <=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ V1x @ V0z )
% 0.22/0.53 & ( mono_2Ec_2Eextreal_2Eextreal__le @ V2y @ V0z ) ) ) ).
% 0.22/0.53
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.YqhDloVxR9/cvc5---1.0.5_17294.p...
% 0.22/0.53 (declare-sort $$unsorted 0)
% 0.22/0.53 (declare-sort tptp.u 0)
% 0.22/0.53 (declare-sort tptp.d 0)
% 0.22/0.53 (declare-sort tptp.du 0)
% 0.22/0.53 (declare-sort tptp.mono_2Etyop_2Eextreal_2Eextreal 0)
% 0.22/0.53 (declare-fun tptp.tyop_2Eextreal_2Eextreal () tptp.d)
% 0.22/0.53 (declare-fun tptp.tyop_2Emin_2Ebool () tptp.d)
% 0.22/0.53 (declare-fun tptp.tyop_2Emin_2Efun (tptp.d tptp.d) tptp.d)
% 0.22/0.53 (declare-fun tptp.s (tptp.d tptp.u) tptp.du)
% 0.22/0.53 (declare-fun tptp.app_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.combin_i_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.combin_k_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.combin_s_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_21_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_21_2E1 (tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_2F_5C_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Emin_2E_3D_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Emin_2E_3D_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Emin_2E_3D_3D_3E_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_3F_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_3F_2E1 (tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2ECOND_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2ECOND_2E3 (tptp.du tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2EF_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2ET_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_5C_2F_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Eextreal_2Eextreal__le_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Eextreal_2Eextreal__le_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Eextreal_2Eextreal__max_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Eextreal_2Eextreal__max_2E2 (tptp.du tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_7E_2E0 () tptp.u)
% 0.22/0.53 (declare-fun tptp.c_2Ebool_2E_7E_2E1 (tptp.du) tptp.u)
% 0.22/0.53 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ((-> Bool Bool) Bool) Bool)
% 0.22/0.53 (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)
% 0.22/0.53 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool) tptp.mono_2Etyop_2Eextreal_2Eextreal) Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool) tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Eapp_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Ebool_2E_2F_5C (Bool Bool) Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Emin_2E_3D_3D_3E (Bool Bool) Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal (Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Ebool_2EF () Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Ebool_2ET () Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Ebool_2E_5C_2F (Bool Bool) Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Eextreal_2Eextreal__le (tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) Bool)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Eextreal_2Eextreal__max (tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.mono_2Ec_2Ebool_2E_7E (Bool) Bool)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Ebool (Bool) tptp.u)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Eextreal_2Eextreal (tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.u)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ((-> Bool Bool)) tptp.u)
% 0.22/0.53 (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)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 ((-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) tptp.u)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) tptp.u)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) tptp.u)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) tptp.u)
% 0.22/0.53 (declare-fun tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ((-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) tptp.u)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Ebool (tptp.du) Bool)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Eextreal_2Eextreal (tptp.du) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (tptp.du Bool) Bool)
% 0.22/0.53 (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)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (tptp.du Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (tptp.du tptp.mono_2Etyop_2Eextreal_2Eextreal) Bool)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (tptp.du tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (tptp.du tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) Bool)
% 0.22/0.53 (declare-fun tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (tptp.du tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal) tptp.mono_2Etyop_2Eextreal_2Eextreal)
% 0.22/0.53 (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))))))
% 0.22/0.53 (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)))))
% 0.22/0.53 (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))))))
% 0.22/0.53 (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)))))))))))))))))
% 0.22/0.53 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))))
% 0.22/0.53 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))))
% 0.22/0.53 (assert (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))))
% 0.22/0.53 (assert (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))))
% 0.22/0.53 (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)))))))
% 0.22/0.53 (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))))))))
% 0.22/0.53 (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))))))))
% 0.22/0.53 (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)))))
% 0.22/0.53 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal (@ tptp.j_mono_2Etyop_2Eextreal_2Eextreal _let_2))) _let_2)))))
% 0.22/0.53 (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)))))
% 0.22/0.53 (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))))))
% 0.22/0.53 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 _let_3))) _let_3))))))
% 0.22/0.53 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))))
% 0.22/0.53 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Eextreal_2Eextreal)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 _let_2))) _let_2)))))
% 0.22/0.53 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (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_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 _let_3))) _let_3))))))
% 0.22/0.53 (assert (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal))))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 _let_3))) _let_3))))))
% 0.22/0.53 (assert (forall ((V0 Bool)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) V0)))
% 0.22/0.53 (assert (forall ((V0 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (@ tptp.j_mono_2Etyop_2Eextreal_2Eextreal (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V0))) V0)))
% 0.22/0.53 (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)))
% 0.22/0.53 (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))))
% 0.22/0.53 (assert (forall ((V0 (-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0))) V0))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) V0)))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Eextreal_2Eextreal)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) V0)))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (@ (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) V0))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (@ (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0))) V0))))
% 0.22/0.53 (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)))))))))
% 0.22/0.53 (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)))))))))))
% 0.22/0.53 (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)))))))))
% 0.22/0.53 (assert (forall ((A_27a tptp.d) (X0 Bool) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 X2_2E0))) (let ((_let_3 (@ _let_1 X1_2E0))) (let ((_let_4 (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool X0)))) (let ((_let_5 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_6 (@ _let_5 A_27a))) (let ((_let_7 (@ _let_5 _let_6))) (= (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 _let_4) _let_3) _let_2)) (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) _let_7)) tptp.c_2Ebool_2ECOND_2E0)) _let_4))) _let_3))) _let_2))))))))))))
% 0.22/0.53 (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))))))))
% 0.22/0.53 (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))))))))))
% 0.22/0.53 (assert (forall ((V0 (-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 Bool)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1))))))))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (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_2Eextreal_2Eextreal) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.s tptp.tyop_2Eextreal_2Eextreal))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal (@ V0 V1))) (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Eextreal_2Eextreal)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (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_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))))))
% 0.22/0.53 (assert (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal)) (@ _let_2 tptp.c_2Ebool_2ECOND_2E0)))))
% 0.22/0.53 (assert (forall ((V0 Bool) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.s tptp.tyop_2Eextreal_2Eextreal))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal (@ (@ (@ tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal V0) V1) V2))) (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V2))))))))
% 0.22/0.53 (assert (forall ((V0 (-> Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0 (-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))))
% 0.22/0.53 (assert tptp.mono_2Ec_2Ebool_2ET)
% 0.22/0.53 (assert (forall ((V0t1 Bool) (V1t2 Bool)) (=> (=> V0t1 V1t2) (=> (=> V1t2 V0t1) (= V0t1 V1t2)))))
% 0.22/0.53 (assert (forall ((V0t Bool)) (=> tptp.mono_2Ec_2Ebool_2EF V0t)))
% 0.22/0.53 (assert (forall ((V0t Bool)) (or V0t (not V0t))))
% 0.22/0.53 (assert (forall ((V0t Bool)) (=> (=> V0t tptp.mono_2Ec_2Ebool_2EF) (not V0t))))
% 0.22/0.53 (assert (forall ((V0t Bool)) (=> (not V0t) (=> V0t tptp.mono_2Ec_2Ebool_2EF))))
% 0.22/0.53 (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)))))
% 0.22/0.53 (assert (and (forall ((V0t Bool)) (= (not (not V0t)) V0t)) (= (not tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2EF) (= (not tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2ET)))
% 0.22/0.53 (assert (forall ((A_27a 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 (@ _let_1 V1y_2E0))) (= (= _let_2 _let_3) (= _let_3 _let_2)))))))
% 0.22/0.53 (assert (forall ((V0t Bool)) (let ((_let_1 (not V0t))) (and (= (= tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (= V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (= tptp.mono_2Ec_2Ebool_2EF V0t) _let_1) (= (= V0t tptp.mono_2Ec_2Ebool_2EF) _let_1)))))
% 0.22/0.53 (assert (forall ((A_27a tptp.d) (V0t1_2E0 tptp.u) (V1t2_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V1t2_2E0))) (let ((_let_3 (@ _let_1 V0t1_2E0))) (let ((_let_4 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (and (= (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ _let_4 (@ tptp.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2ET))) _let_3) _let_2)) _let_3) (= (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ _let_4 (@ tptp.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2EF))) _let_3) _let_2)) _let_2))))))))
% 0.22/0.53 (assert (forall ((V0A Bool) (V1B Bool) (V2C Bool)) (let ((_let_1 (or V0A V1B V2C))) (= _let_1 _let_1))))
% 0.22/0.53 (assert (forall ((V0A Bool) (V1B Bool)) (= (or V0A V1B) (or V1B V0A))))
% 0.22/0.53 (assert (forall ((V0A Bool) (V1B Bool)) (let ((_let_1 (not V1B))) (let ((_let_2 (not V0A))) (and (= (not (and V0A V1B)) (or _let_2 _let_1)) (= (not (or V0A V1B)) (and _let_2 _let_1)))))))
% 0.22/0.53 (assert (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2z tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V0x))) (=> (and (@ _let_1 V1y) (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V1y) V2z)) (@ _let_1 V2z)))))
% 0.22/0.53 (assert (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (or (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y) (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V1y) V0x))))
% 1.87/2.16 (assert (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__max V0x) V1y) (@ (@ (@ tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) V1y) V0x))))
% 1.87/2.16 (assert (forall ((V0t Bool)) (= (not (not V0t)) V0t)))
% 1.87/2.16 (assert (forall ((V0A Bool)) (=> V0A (=> (not V0A) tptp.mono_2Ec_2Ebool_2EF))))
% 1.87/2.16 (assert (forall ((V0B Bool) (V1A Bool)) (= (=> (not (or V1A V0B)) tptp.mono_2Ec_2Ebool_2EF) (=> (=> V1A tptp.mono_2Ec_2Ebool_2EF) (=> (not V0B) tptp.mono_2Ec_2Ebool_2EF)))))
% 1.87/2.16 (assert (forall ((V0B Bool) (V1A Bool)) (= (=> (not (or (not V1A) V0B)) tptp.mono_2Ec_2Ebool_2EF) (=> V1A (=> (not V0B) tptp.mono_2Ec_2Ebool_2EF)))))
% 1.87/2.16 (assert (forall ((V0A Bool)) (=> (=> (not V0A) tptp.mono_2Ec_2Ebool_2EF) (=> (=> V0A tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2EF))))
% 1.87/2.16 (assert (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (let ((_let_1 (not V2p))) (let ((_let_2 (not V1q))) (let ((_let_3 (not V0r))) (= (= V2p (= V1q V0r)) (and (or V2p V1q V0r) (or V2p _let_3 _let_2) (or V1q _let_3 _let_1) (or V0r _let_2 _let_1))))))))
% 1.87/2.16 (assert (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (let ((_let_1 (not V2p))) (= (= V2p (and V1q V0r)) (and (or V2p (not V1q) (not V0r)) (or V1q _let_1) (or V0r _let_1))))))
% 1.87/2.16 (assert (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (= (= V2p (or V1q V0r)) (and (or V2p (not V1q)) (or V2p (not V0r)) (or V1q V0r (not V2p))))))
% 1.87/2.16 (assert (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (= (= V2p (=> V1q V0r)) (and (or V2p V1q) (or V2p (not V0r)) (or (not V1q) V0r (not V2p))))))
% 1.87/2.16 (assert (forall ((V0q Bool) (V1p Bool)) (let ((_let_1 (not V0q))) (= (= V1p _let_1) (and (or V1p V0q) (or _let_1 (not V1p)))))))
% 1.87/2.16 (assert (not (forall ((V0z tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z) (and (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z) (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))))
% 1.87/2.16 (set-info :filename cvc5---1.0.5_17294)
% 1.87/2.16 (check-sat-assuming ( true ))
% 1.87/2.16 ------- get file name : TPTP file name is ITP021^1
% 1.87/2.16 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17294.smt2...
% 1.87/2.16 --- Run --ho-elim --full-saturate-quant at 10...
% 1.87/2.16 % SZS status Theorem for ITP021^1
% 1.87/2.16 % SZS output start Proof for ITP021^1
% 1.87/2.16 (
% 1.87/2.16 (let ((_let_1 (not (forall ((V0z tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__max V1x) V2y)) V0z) (and (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V1x) V0z) (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V2y) V0z))))))) (let ((_let_2 (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__max V0x) V1y) (@ (@ (@ tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y)) V1y) V0x))))) (let ((_let_3 (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (or (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V0x) V1y) (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V1y) V0x))))) (let ((_let_4 (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2z tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V0x))) (=> (and (@ _let_1 V1y) (@ (@ tptp.mono_2Ec_2Eextreal_2Eextreal__le V1y) V2z)) (@ _let_1 V2z)))))) (let ((_let_5 (forall ((A_27a tptp.d) (V0t1_2E0 tptp.u) (V1t2_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V1t2_2E0))) (let ((_let_3 (@ _let_1 V0t1_2E0))) (let ((_let_4 (@ tptp.s tptp.tyop_2Emin_2Ebool))) (and (= (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ _let_4 (@ tptp.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2ET))) _let_3) _let_2)) _let_3) (= (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ _let_4 (@ tptp.i_mono_2Etyop_2Emin_2Ebool tptp.mono_2Ec_2Ebool_2EF))) _let_3) _let_2)) _let_2))))))))) (let ((_let_6 (forall ((V0t Bool)) (=> tptp.mono_2Ec_2Ebool_2EF V0t)))) (let ((_let_7 (forall ((V0 Bool) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.s tptp.tyop_2Eextreal_2Eextreal))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal (@ (@ (@ tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal V0) V1) V2))) (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V2))))))))) (let ((_let_8 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_9 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ _let_8 (@ _let_8 tptp.tyop_2Eextreal_2Eextreal)))))) (let ((_let_10 (forall ((V0 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (@ tptp.j_mono_2Etyop_2Eextreal_2Eextreal (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V0))) V0)))) (let ((_let_11 (ho_58 (ho_60 (ho_56 k_63 BOOLEAN_TERM_VARIABLE_8648) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73))) (let ((_let_12 (ho_58 (ho_60 k_65 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74))) (let ((_let_13 (= _let_12 _let_11))) (let ((_let_14 (ho_27 k_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73))) (let ((_let_15 (ho_6 k_5 tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_16 (ho_7 _let_15 _let_14))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 (ho_25 k_24 _let_16)))) (let ((_let_18 (= _let_12 (ho_25 k_24 (ho_7 _let_15 (ho_27 k_26 _let_12)))))) (let ((_let_19 (ho_27 k_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74))) (let ((_let_20 (ho_7 _let_15 _let_19))) (let ((_let_21 (ho_6 k_5 tptp.tyop_2Emin_2Ebool))) (let ((_let_22 (= (ho_7 _let_15 (ho_27 k_26 _let_11)) (ho_7 _let_15 (ho_10 (ho_9 (ho_62 k_61 (ho_7 _let_21 (ho_23 k_22 BOOLEAN_TERM_VARIABLE_8648))) _let_20) _let_16))))) (let ((_let_23 (ho_62 k_61 (ho_7 _let_21 (ho_23 k_22 BOOLEAN_TERM_VARIABLE_8369))))) (let ((_let_24 (= _let_16 (ho_7 _let_15 (ho_10 (ho_9 _let_23 _let_20) _let_16))))) (let ((_let_25 (ho_59 k_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73))) (let ((_let_26 (ho_57 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_27 (ho_57 (ho_59 k_64 _let_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_28 ((= BOOLEAN_TERM_VARIABLE_8369 false)))) (let ((_let_29 (MACRO_SR_PRED_INTRO :args _let_28))) (let ((_let_30 (EQ_RESOLVE _let_29 (REWRITE :args _let_28)))) (let ((_let_31 (forall ((V0x tptp.mono_2Etyop_2Eextreal_2Eextreal) (V1y tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= (ho_58 (ho_60 (ho_56 k_63 (ho_57 (ho_59 k_64 V0x) V1y)) V1y) V0x) (ho_58 (ho_60 k_65 V0x) V1y))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_31)))))) (let ((_let_33 (=>))) (let ((_let_34 (=))) (let ((_let_35 (APPLY_UF ho_58))) (let ((_let_36 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73)))) (let ((_let_37 (APPLY_UF ho_60))) (let ((_let_38 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74)))) (let ((_let_39 (APPLY_UF ho_56))) (let ((_let_40 (ho_57 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74))) (let ((_let_41 (MACRO_SR_PRED_INTRO :args ((= _let_40 BOOLEAN_TERM_VARIABLE_8648))))) (let ((_let_42 (REFL :args (k_63)))) (let ((_let_43 (_let_31))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 QUANTIFIERS_INST_E_MATCHING ((ho_58 (ho_60 k_65 V0x) V1y)))) :args _let_43)) (CONG (REFL :args _let_43) (CONG (REFL :args (_let_12)) (CONG (CONG (CONG _let_42 _let_41 :args _let_39) _let_38 :args _let_37) _let_36 :args _let_35) :args _let_34) :args _let_33))) _let_32 :args (_let_13 false _let_31)))) (let ((_let_45 (forall ((V0 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= V0 (ho_25 k_24 (ho_7 (ho_6 k_5 tptp.tyop_2Eextreal_2Eextreal) (ho_27 k_26 V0))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((V0 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (= V0 (@ tptp.j_mono_2Etyop_2Eextreal_2Eextreal (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V0))))) _let_45))))))) (let ((_let_47 (_let_45))) (let ((_let_48 ((ho_27 k_26 V0)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47)) _let_46 :args (_let_17 false _let_45)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47)) _let_46 :args (_let_18 false _let_45)))) (let ((_let_51 (forall ((V0 Bool) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal) (V2 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (ho_6 k_5 tptp.tyop_2Eextreal_2Eextreal))) (= (ho_7 _let_1 (ho_10 (ho_9 (ho_62 k_61 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_23 k_22 V0))) (ho_7 _let_1 (ho_27 k_26 V1))) (ho_7 _let_1 (ho_27 k_26 V2)))) (ho_7 _let_1 (ho_27 k_26 (ho_58 (ho_60 (ho_56 k_63 V0) V1) V2)))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_51)))))) (let ((_let_53 (_let_51))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (BOOLEAN_TERM_VARIABLE_8648 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 QUANTIFIERS_INST_E_MATCHING ((ho_58 (ho_60 (ho_56 k_63 V0) V1) V2)))) :args _let_53))) _let_52 :args (_let_22 false _let_51)))) (let ((_let_55 (forall ((BOUND_VARIABLE_1838 tptp.d) (BOUND_VARIABLE_1840 tptp.u) (BOUND_VARIABLE_1842 tptp.u)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_1838))) (let ((_let_2 (ho_7 _let_1 BOUND_VARIABLE_1842))) (= _let_2 (ho_7 _let_1 (ho_10 (ho_9 (ho_62 k_61 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_23 k_22 false))) (ho_7 _let_1 BOUND_VARIABLE_1840)) _let_2)))))))) (let ((_let_56 (forall ((BOUND_VARIABLE_1823 tptp.d) (BOUND_VARIABLE_1825 tptp.u) (BOUND_VARIABLE_1827 tptp.u)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_1823))) (let ((_let_2 (ho_7 _let_1 BOUND_VARIABLE_1825))) (= _let_2 (ho_7 _let_1 (ho_10 (ho_9 (ho_62 k_61 (ho_7 (ho_6 k_5 tptp.tyop_2Emin_2Ebool) (ho_23 k_22 true))) _let_2) (ho_7 _let_1 BOUND_VARIABLE_1827))))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.mono_2Ec_2Ebool_2EF false))) (MACRO_SR_PRED_TRANSFORM (ASSUME :args (tptp.mono_2Ec_2Ebool_2ET)) :args ((= tptp.mono_2Ec_2Ebool_2ET true)))) :args ((and (forall ((BOUND_VARIABLE_1823 tptp.d) (BOUND_VARIABLE_1825 tptp.u) (BOUND_VARIABLE_1827 tptp.u)) (let ((_let_1 (@ tptp.s BOUND_VARIABLE_1823))) (let ((_let_2 (@ _let_1 BOUND_VARIABLE_1825))) (= _let_2 (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 (@ (@ tptp.s 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_let_190 _let_174 _let_172 _let_30 _let_191 _let_168 _let_166 _let_136 _let_141 _let_186) :args (_let_26 _let_83 _let_162 _let_188 _let_13 _let_109 _let_17 _let_18 _let_22 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_187 (CONG (CONG _let_144 (TRANS _let_143 (CONG _let_140 (TRANS _let_185 _let_184 (CONG _let_69 (CONG (CONG (TRANS (CONG _let_68 (CONG _let_67 (TRANS _let_193 (SYMM _let_192)) :args _let_58) :args _let_63) (CONG _let_68 (CONG _let_67 _let_192 :args _let_58) :args _let_63)) _let_62 :args _let_61) _let_60 :args _let_59) :args _let_58) _let_173) :args _let_129) _let_175) :args _let_126) _let_125 :args _let_124) (TRUE_INTRO _let_190))) :args (_let_26 _let_17 _let_24 _let_162 _let_188 _let_109 _let_22 _let_13 _let_18 _let_83)) :args ((not (and _let_26 _let_83 _let_162 _let_188 _let_13 _let_109 _let_17 _let_18 _let_22 _let_24)) SB_LITERAL))) (CONG (REFL :args _let_189) _let_180 _let_163 (MACRO_SR_PRED_INTRO :args ((= (not _let_188) BOOLEAN_TERM_VARIABLE_8529))) _let_115 _let_160 _let_159 _let_113 _let_158 _let_157 :args _let_94)) :args ((or _let_27 _let_75 BOOLEAN_TERM_VARIABLE_8369 BOOLEAN_TERM_VARIABLE_8529 BOOLEAN_TERM_VARIABLE_8648 _let_110 _let_156 _let_107 _let_155 _let_153))) _let_72 _let_54 _let_50 _let_49 _let_44 _let_30 (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_181 _let_127 _let_130 _let_99 _let_182 _let_134 _let_166 _let_136 _let_141 _let_186) :args (_let_74 _let_83 BOOLEAN_TERM_VARIABLE_8349 BOOLEAN_TERM_VARIABLE_8486 BOOLEAN_TERM_VARIABLE_8648 _let_13 _let_78 _let_18 _let_22 _let_81)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_187 (CONG (CONG _let_144 (TRANS _let_143 (CONG _let_140 (TRANS _let_185 _let_184 (CONG _let_69 (CONG (CONG (CONG _let_68 (TRANS (CONG _let_67 (TRANS (CONG _let_66 _let_135 :args _let_64) (SYMM _let_183)) :args _let_58) (CONG _let_67 _let_183 :args _let_58)) :args _let_63) _let_62 :args _let_61) _let_60 :args _let_59) :args _let_58) _let_131) :args _let_129) _let_128) :args _let_126) _let_125 :args _let_124) (TRUE_INTRO _let_181))) :args (_let_74 _let_78 _let_81 BOOLEAN_TERM_VARIABLE_8349 BOOLEAN_TERM_VARIABLE_8486 BOOLEAN_TERM_VARIABLE_8648 _let_22 _let_13 _let_18 _let_83)) :args ((not (and _let_74 _let_83 BOOLEAN_TERM_VARIABLE_8349 BOOLEAN_TERM_VARIABLE_8486 BOOLEAN_TERM_VARIABLE_8648 _let_13 _let_78 _let_18 _let_22 _let_81)) SB_LITERAL))) (CONG (REFL :args _let_122) _let_180 _let_118 (REFL :args _let_179) _let_117 _let_115 _let_114 _let_113 _let_158 _let_112 :args _let_94)) :args ((or _let_27 _let_119 _let_111 _let_178 _let_110 _let_109 _let_108 _let_107 _let_155 _let_106))) _let_104 _let_54 _let_50 _let_100 _let_44 _let_99 (EQUIV_ELIM2 (SYMM (MACRO_SR_PRED_INTRO :args ((= BOOLEAN_TERM_VARIABLE_8529 _let_27))))) (CNF_EQUIV_NEG2 :args _let_96) _let_95 (CNF_AND_NEG :args (_let_76)) (EQUIV_ELIM1 _let_177) :args ((or _let_75 _let_119) false _let_24 false _let_22 false _let_18 false _let_17 false _let_13 true BOOLEAN_TERM_VARIABLE_8369 true BOOLEAN_TERM_VARIABLE_8648 false _let_81 false _let_22 false _let_18 false _let_78 false _let_13 false BOOLEAN_TERM_VARIABLE_8349 true BOOLEAN_TERM_VARIABLE_8529 true _let_27 true _let_77 false _let_76 false BOOLEAN_TERM_VARIABLE_8486)) _let_176 :args (_let_75 false _let_74)))) (let ((_let_195 (or _let_150 _let_119 _let_26))) (let ((_let_196 (ASSUME :args _let_189))) (let ((_let_197 (ASSUME :args _let_179))) (let ((_let_198 (CONG _let_66 (TRANS (FALSE_INTRO _let_197) _let_65) :args _let_64))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_196 _let_174 _let_172 _let_30 _let_197 _let_168 _let_166 _let_136 _let_141 _let_145) :args (_let_27 _let_75 _let_162 _let_178 _let_13 _let_109 _let_17 _let_18 _let_22 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_146 (CONG (CONG _let_144 (TRANS _let_143 (CONG _let_140 (TRANS _let_185 _let_184 (CONG _let_69 (CONG (CONG (CONG _let_68 (TRANS (CONG _let_67 (TRANS _let_193 (SYMM _let_198)) :args _let_58) (CONG _let_67 _let_198 :args _let_58)) :args _let_63) _let_62 :args _let_61) _let_60 :args _let_59) :args _let_58) _let_173) :args _let_129) _let_175) :args _let_126) _let_125 :args _let_124) (FALSE_INTRO _let_196))) :args (_let_75 _let_17 _let_24 _let_162 _let_178 _let_109 _let_22 _let_13 _let_18 _let_27)) :args ((not (and _let_27 _let_75 _let_162 _let_178 _let_13 _let_109 _let_17 _let_18 _let_22 _let_24)) SB_LITERAL))) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_26))) _let_163 (MACRO_SR_PRED_INTRO :args ((= (not _let_178) BOOLEAN_TERM_VARIABLE_8486))) _let_115 _let_160 _let_159 _let_113 _let_158 _let_157 :args _let_94)) :args ((or _let_26 _let_83 BOOLEAN_TERM_VARIABLE_8369 BOOLEAN_TERM_VARIABLE_8486 BOOLEAN_TERM_VARIABLE_8648 _let_110 _let_156 _let_107 _let_155 _let_153))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_41) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_195)) :args ((or _let_26 _let_119 _let_150 (not _let_195)))) _let_194 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_148 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_149)) _let_148 :args (_let_195 false _let_147)) :args (_let_150 true _let_26 false _let_74 false _let_195)) :args (_let_109 true _let_40)) (MACRO_RESOLUTION_TRUST _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_76 0)) :args ((or _let_26 _let_89))) _let_194 :args (_let_89 true _let_26)) _let_95 :args (_let_27 true _let_76 true _let_77)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_177) _let_194 :args (_let_178 true _let_26)) _let_194 _let_72 _let_54 _let_50 _let_49 _let_44 _let_30 :args (false true BOOLEAN_TERM_VARIABLE_8648 false _let_27 true BOOLEAN_TERM_VARIABLE_8486 true _let_26 false _let_24 false _let_22 false _let_18 false _let_17 false _let_13 true BOOLEAN_TERM_VARIABLE_8369)) :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_2Eextreal_2Eextreal))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal (@ tptp.j_mono_2Etyop_2Eextreal_2Eextreal _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.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 _let_3))) _let_3))))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Emin_2Ebool)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Eextreal_2Eextreal)))) (let ((_let_2 (@ _let_1 V0_2E0))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 _let_2))) _let_2)))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (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_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 _let_3))) _let_3))))) (forall ((V0_2E0 tptp.u)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal))))) (let ((_let_3 (@ _let_2 V0_2E0))) (= (@ _let_2 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_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)) _let_10 (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 (-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0))) V0))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) V0)) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Eextreal_2Eextreal)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) V0)) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 (@ (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) V0))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal))) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (@ (@ tptp.s (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_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)))))))) (forall ((A_27a tptp.d) (X0 Bool) (X1_2E0 tptp.u) (X2_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 X2_2E0))) (let ((_let_3 (@ _let_1 X1_2E0))) (let ((_let_4 (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool X0)))) (let ((_let_5 (@ tptp.tyop_2Emin_2Efun A_27a))) (let ((_let_6 (@ _let_5 A_27a))) (let ((_let_7 (@ _let_5 _let_6))) (= (@ _let_1 (@ (@ (@ tptp.c_2Ebool_2ECOND_2E3 _let_4) _let_3) _let_2)) (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_6) (@ (@ tptp.app_2E2 (@ (@ tptp.s _let_7) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) _let_7)) tptp.c_2Ebool_2ECOND_2E0)) _let_4))) _let_3))) _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 (-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 Bool)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ _let_1 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal)))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1))))))))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (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_2Eextreal_2Eextreal) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 V0))) (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.s tptp.tyop_2Eextreal_2Eextreal))) (= (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal (@ V0 V1))) (@ _let_1 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal) tptp.tyop_2Eextreal_2Eextreal)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 V0))) (@ _let_1 (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (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_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_2 (@ _let_1 tptp.tyop_2Eextreal_2Eextreal))) (let ((_let_3 (@ tptp.s _let_2))) (= (@ _let_3 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 (@ V0 V1))) (@ _let_3 (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ _let_1 _let_2)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Eextreal_2Eextreal) (@ tptp.i_mono_2Etyop_2Eextreal_2Eextreal V1))))))))) (= (@ _let_9 (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29_29 tptp.mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal)) (@ _let_9 tptp.c_2Ebool_2ECOND_2E0)) _let_7 (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 (-> Bool tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 Bool)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal Bool)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) (forall ((V0 (-> tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal tptp.mono_2Etyop_2Eextreal_2Eextreal)) (V1 tptp.mono_2Etyop_2Eextreal_2Eextreal)) (let ((_let_1 (@ V0 V1))) (= _let_1 _let_1))) tptp.mono_2Ec_2Ebool_2ET (forall ((V0t1 Bool) (V1t2 Bool)) (=> (=> V0t1 V1t2) (=> (=> V1t2 V0t1) (= V0t1 V1t2)))) _let_6 (forall ((V0t Bool)) (or V0t (not V0t))) (forall ((V0t Bool)) (=> (=> V0t tptp.mono_2Ec_2Ebool_2EF) (not V0t))) (forall ((V0t Bool)) (=> (not V0t) (=> V0t tptp.mono_2Ec_2Ebool_2EF))) (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)))) (and (forall ((V0t Bool)) (= (not (not V0t)) V0t)) (= (not tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2EF) (= (not tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2ET)) (forall ((A_27a tptp.d) (V0x_2E0 tptp.u) (V1y_2E0 tptp.u)) (let ((_let_1 (@ tptp.s A_27a))) (let ((_let_2 (@ _let_1 V0x_2E0))) (let ((_let_3 (@ _let_1 V1y_2E0))) (= (= _let_2 _let_3) (= _let_3 _let_2)))))) (forall ((V0t Bool)) (let ((_let_1 (not V0t))) (and (= (= tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (= V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (= tptp.mono_2Ec_2Ebool_2EF V0t) _let_1) (= (= V0t tptp.mono_2Ec_2Ebool_2EF) _let_1)))) _let_5 (forall ((V0A Bool) (V1B Bool) (V2C Bool)) (let ((_let_1 (or V0A V1B V2C))) (= _let_1 _let_1))) (forall ((V0A Bool) (V1B Bool)) (= (or V0A V1B) (or V1B V0A))) (forall ((V0A Bool) (V1B Bool)) (let ((_let_1 (not V1B))) (let ((_let_2 (not V0A))) (and (= (not (and V0A V1B)) (or _let_2 _let_1)) (= (not (or V0A V1B)) (and _let_2 _let_1)))))) _let_4 _let_3 _let_2 (forall ((V0t Bool)) (= (not (not V0t)) V0t)) (forall ((V0A Bool)) (=> V0A (=> (not V0A) tptp.mono_2Ec_2Ebool_2EF))) (forall ((V0B Bool) (V1A Bool)) (= (=> (not (or V1A V0B)) tptp.mono_2Ec_2Ebool_2EF) (=> (=> V1A tptp.mono_2Ec_2Ebool_2EF) (=> (not V0B) tptp.mono_2Ec_2Ebool_2EF)))) (forall ((V0B Bool) (V1A Bool)) (= (=> (not (or (not V1A) V0B)) tptp.mono_2Ec_2Ebool_2EF) (=> V1A (=> (not V0B) tptp.mono_2Ec_2Ebool_2EF)))) (forall ((V0A Bool)) (=> (=> (not V0A) tptp.mono_2Ec_2Ebool_2EF) (=> (=> V0A tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2EF))) (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (let ((_let_1 (not V2p))) (let ((_let_2 (not V1q))) (let ((_let_3 (not V0r))) (= (= V2p (= V1q V0r)) (and (or V2p V1q V0r) (or V2p _let_3 _let_2) (or V1q _let_3 _let_1) (or V0r _let_2 _let_1))))))) (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (let ((_let_1 (not V2p))) (= (= V2p (and V1q V0r)) (and (or V2p (not V1q) (not V0r)) (or V1q _let_1) (or V0r _let_1))))) (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (= (= V2p (or V1q V0r)) (and (or V2p (not V1q)) (or V2p (not V0r)) (or V1q V0r (not V2p))))) (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (= (= V2p (=> V1q V0r)) (and (or V2p V1q) (or V2p (not V0r)) (or (not V1q) V0r (not V2p))))) (forall ((V0q Bool) (V1p Bool)) (let ((_let_1 (not V0q))) (= (= V1p _let_1) (and (or V1p V0q) (or _let_1 (not V1p)))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.87/2.16 )
% 1.87/2.16 % SZS output end Proof for ITP021^1
% 1.87/2.16 % cvc5---1.0.5 exiting
% 1.87/2.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------