%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP015_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:47:47 PM UTC 2026
% Result : Theorem 10.76s 2.27s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 70 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 37 ( 15 ~; 7 |; 14 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 50 ( 50 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 21 prp; 0-2 aty)
% Number of functors : 116 ( 116 usr; 42 con; 0-4 aty)
% Number of variables : 74 ( 0 sgn 73 !; 1 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
tyop_2Ebool_2Eitself: d > d ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(func_def_2,type,
tyop_2Einteger_2Eint: d ).
tff(func_def_3,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_4,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(func_def_5,type,
tyop_2Enum_2Enum: d ).
tff(func_def_6,type,
s: ( u * d ) > du ).
tff(func_def_7,type,
app_2E2: ( du * du ) > u ).
tff(func_def_8,type,
combin_i_2E0: u ).
tff(func_def_9,type,
combin_k_2E0: u ).
tff(func_def_10,type,
combin_s_2E0: u ).
tff(func_def_11,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_12,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(func_def_13,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_14,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(func_def_15,type,
c_2Enum_2E0_2E0: u ).
tff(func_def_16,type,
c_2Eprim__rec_2E_3C_2E0: u ).
tff(func_def_17,type,
c_2Eprim__rec_2E_3C_2E2: ( du * du ) > u ).
tff(func_def_18,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_19,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(func_def_20,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_21,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(func_def_22,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_23,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(func_def_24,type,
c_2Ebool_2ECOND_2E0: u ).
tff(func_def_25,type,
c_2Ebool_2ECOND_2E3: ( du * ( du * du ) ) > u ).
tff(func_def_26,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_27,type,
c_2Earithmetic_2EMOD_2E0: u ).
tff(func_def_28,type,
c_2Earithmetic_2EMOD_2E2: ( du * du ) > u ).
tff(func_def_29,type,
c_2Einteger_2ENum_2E0: u ).
tff(func_def_30,type,
c_2Einteger_2ENum_2E1: du > u ).
tff(func_def_31,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_32,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_33,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_34,type,
c_2Ewords_2Edimword_2E0: u ).
tff(func_def_35,type,
c_2Ewords_2Edimword_2E1: du > u ).
tff(func_def_36,type,
c_2Einteger__word_2Ei2w_2E0: u ).
tff(func_def_37,type,
c_2Einteger__word_2Ei2w_2E1: du > u ).
tff(func_def_38,type,
c_2Einteger_2Eint__lt_2E0: u ).
tff(func_def_39,type,
c_2Einteger_2Eint__lt_2E2: ( du * du ) > u ).
tff(func_def_40,type,
c_2Einteger_2Eint__neg_2E0: u ).
tff(func_def_41,type,
c_2Einteger_2Eint__neg_2E1: du > u ).
tff(func_def_42,type,
c_2Einteger_2Eint__of__num_2E0: u ).
tff(func_def_43,type,
c_2Einteger_2Eint__of__num_2E1: du > u ).
tff(func_def_44,type,
c_2Ewords_2En2w_2E0: u ).
tff(func_def_45,type,
c_2Ewords_2En2w_2E1: du > u ).
tff(func_def_46,type,
c_2Ebool_2Ethe__value_2E0: u ).
tff(func_def_47,type,
c_2Ewords_2Eword__2comp_2E0: u ).
tff(func_def_48,type,
c_2Ewords_2Eword__2comp_2E1: du > u ).
tff(func_def_49,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_50,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_51,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_52,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_53,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_54,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_55,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_56,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum ).
tff(func_def_57,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_58,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_59,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
tff(func_def_60,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 ) > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_61,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum ).
tff(func_def_62,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_63,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_64,type,
mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).
tff(func_def_65,type,
mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_66,type,
mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_67,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_68,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_69,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_70,type,
mono_2Ec_2Earithmetic_2EMOD_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).
tff(func_def_71,type,
mono_2Ec_2Earithmetic_2EMOD_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).
tff(func_def_72,type,
mono_2Ec_2Einteger_2ENum_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 ).
tff(func_def_73,type,
mono_2Ec_2Einteger_2ENum_2E1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
tff(func_def_74,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_75,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_76,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_77,type,
mono_2Ec_2Einteger_2Eint__lt_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_78,type,
mono_2Ec_2Einteger_2Eint__lt_2E2: ( mono_2Etyop_2Einteger_2Eint * mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_79,type,
mono_2Ec_2Einteger_2Eint__neg_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_80,type,
mono_2Ec_2Einteger_2Eint__neg_2E1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_81,type,
mono_2Ec_2Einteger_2Eint__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_82,type,
mono_2Ec_2Einteger_2Eint__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_83,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_84,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_85,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_86,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_87,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_88,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_89,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_90,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > u ).
tff(func_def_91,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 > u ).
tff(func_def_92,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_93,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_94,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).
tff(func_def_95,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 > u ).
tff(func_def_96,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).
tff(func_def_97,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
tff(func_def_98,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
tff(func_def_99,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_100,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_101,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_102,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_103,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_104,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_105,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 ).
tff(func_def_106,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_107,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_108,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).
tff(func_def_109,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 ).
tff(func_def_110,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
tff(func_def_111,type,
j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
tff(func_def_112,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
tff(func_def_113,type,
sK0: ( u * ( u * ( d * d ) ) ) > u ).
tff(func_def_114,type,
sK1: ( u * d ) > u ).
tff(func_def_115,type,
sK2: ( u * d ) > u ).
tff(func_def_116,type,
sK3: d ).
tff(f46,axiom,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).
tff(f53,axiom,
! [X0: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2ENum_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).
tff(f57,axiom,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__lt_2E2(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).
tff(f58,axiom,
! [X0: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__neg_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).
tff(f59,axiom,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Einteger_2Eint__of__num_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).
tff(f81,axiom,
! [X0: d] :
( ! [X3: u,X4: u] : ( s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X0,X3),s(X0,X4))) = s(X0,X4) )
& ! [X1: u,X2: u] : ( s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)),s(X0,X1),s(X0,X2))) = s(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
tff(f82,axiom,
mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
tff(f83,axiom,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) = mono_2Ec_2Ebool_2EF_2E0 )
& ( p(mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)))
<=> ( ( X1 != mono_2Ec_2Enum_2E0_2E0 )
| ( X0 != mono_2Ec_2Enum_2E0_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
tff(f84,axiom,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Einteger_2ENum_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
tff(f85,axiom,
! [X0: d,X1: mono_2Etyop_2Einteger_2Eint] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(X1)))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Einteger_2Eint__lt_2E2(X1,mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E1(mono_2Ec_2Einteger_2Eint__neg_2E1(X1)))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E1(X1))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
tff(f89,conjecture,
! [X0: d] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
tff(f90,negated_conjecture,
~ ! [X0: d] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ),
inference(negated_conjecture,[status(cth)],[f89]) ).
tff(f102,plain,
? [X0: d] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0))))) ),
inference(ennf_transformation,[],[f90]) ).
tff(f131,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) = mono_2Ec_2Ebool_2EF_2E0 )
& ( ~ p(mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)))
| ( X1 != mono_2Ec_2Enum_2E0_2E0 )
| ( X0 != mono_2Ec_2Enum_2E0_2E0 ) )
& ( ( ( mono_2Ec_2Enum_2E0_2E0 = X1 )
& ( mono_2Ec_2Enum_2E0_2E0 = X0 ) )
| p(mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) )
& ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X0,X1) ) ),
inference(nnf_transformation,[],[f83]) ).
tff(f132,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) = mono_2Ec_2Ebool_2EF_2E0 )
& ( ~ p(mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)))
| ( X1 != mono_2Ec_2Enum_2E0_2E0 )
| ( X0 != mono_2Ec_2Enum_2E0_2E0 ) )
& ( ( ( mono_2Ec_2Enum_2E0_2E0 = X1 )
& ( mono_2Ec_2Enum_2E0_2E0 = X0 ) )
| p(mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) )
& ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)) = mono_2Ec_2Eprim__rec_2E_3C_2E2(X0,X1) ) ),
inference(flattening,[],[f131]) ).
tff(f134,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f102]) ).
tff(f193,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0),X1) ),
inference(cnf_transformation,[],[f46]) ).
tff(f203,plain,
! [X0: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2ENum_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f209,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__lt_2E2(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,X0),X1) ),
inference(cnf_transformation,[],[f57]) ).
tff(f210,plain,
! [X0: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__neg_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,X0) ),
inference(cnf_transformation,[],[f58]) ).
tff(f211,plain,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Einteger_2Eint__of__num_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0) ),
inference(cnf_transformation,[],[f59]) ).
tff(f247,plain,
! [X3: u,X0: d,X4: u] : ( s(X0,X4) = s(X0,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X0,X3),s(X0,X4))) ),
inference(cnf_transformation,[],[f81]) ).
tff(f249,plain,
mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f82]) ).
tff(f250,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2EF_2E0 = mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__neg_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X1))) ),
inference(cnf_transformation,[],[f132]) ).
tff(f255,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0,X1) = mono_2Ec_2Einteger_2Eint__lt_2E2(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0),mono_2Ec_2Einteger_2Eint__of__num_2E1(X1)) ),
inference(cnf_transformation,[],[f132]) ).
tff(f256,plain,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Einteger_2ENum_2E1(mono_2Ec_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
inference(cnf_transformation,[],[f84]) ).
tff(f257,plain,
! [X0: d,X1: mono_2Etyop_2Einteger_2Eint] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(X1)))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Einteger_2Eint__lt_2E2(X1,mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E1(mono_2Ec_2Einteger_2Eint__neg_2E1(X1)))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E1(X1))))))) ),
inference(cnf_transformation,[],[f85]) ).
tff(f262,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E1(mono_2Ec_2Enum_2E0_2E0))))),
inference(cnf_transformation,[],[f134]) ).
tff(f263,plain,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)),
inference(definition_unfolding,[],[f249,f211,f210,f211]) ).
tff(f264,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0),X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0)),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X1)) ),
inference(definition_unfolding,[],[f255,f193,f209,f211,f211]) ).
tff(f269,plain,
! [X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2EF_2E0 = mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0)),mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X1))) ),
inference(definition_unfolding,[],[f250,f209,f211,f210,f211]) ).
tff(f270,plain,
! [X0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0)) = X0 ),
inference(definition_unfolding,[],[f256,f203,f211]) ).
tff(f271,plain,
! [X0: d,X1: mono_2Etyop_2Einteger_2Eint] : ( s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(X1)))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,X1),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,X1)))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,X1))))))) ),
inference(definition_unfolding,[],[f257,f209,f211,f203,f210,f203]) ).
tff(f275,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0))))),
inference(definition_unfolding,[],[f262,f211]) ).
tcf(c_144,plain,
! [X0_u: u,X0_d: d,X1_u: u] : s(X0_d,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X0_d,X0_u),s(X0_d,X1_u))) = s(X0_d,X1_u),
inference(cnf_transformation,[],[f247]) ).
tcf(c_145,plain,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0),
inference(cnf_transformation,[],[f263]) ).
tcf(c_146,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum,X1_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X1_mono_2Etyop_2Enum_2Enum)) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_mono_2Etyop_2Enum_2Enum),X1_mono_2Etyop_2Enum_2Enum),
inference(cnf_transformation,[],[f264]) ).
tcf(c_151,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum,X1_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)),mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X1_mono_2Etyop_2Enum_2Enum))) = mono_2Ec_2Ebool_2EF_2E0,
inference(cnf_transformation,[],[f269]) ).
tcf(c_152,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)) = X0_mono_2Etyop_2Enum_2Enum,
inference(cnf_transformation,[],[f270]) ).
tcf(c_153,plain,
! [X0_d: d,X0_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,X0_mono_2Etyop_2Einteger_2Eint),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_d),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,X0_mono_2Etyop_2Einteger_2Eint)))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,X0_mono_2Etyop_2Einteger_2Eint))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_d),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(X0_mono_2Etyop_2Einteger_2Eint)))),
inference(cnf_transformation,[],[f271]) ).
tcf(c_158,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),
inference(cnf_transformation,[],[f275]) ).
tcf(c_499,negated_conjecture,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0))))) != s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),
inference(subtyping,[status(esa)],[c_158]) ).
tcf(c_504,plain,
! [X0_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint,X0_iProver_tyop_2Efcp_2Ecart_2_d: iProver_tyop_2Efcp_2Ecart_2_d] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,X0_mono_2Etyop_2Einteger_2Eint),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,X0_mono_2Etyop_2Einteger_2Eint)))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,X0_mono_2Etyop_2Einteger_2Eint))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(X0_mono_2Etyop_2Einteger_2Eint)))),
inference(subtyping,[status(esa)],[c_153]) ).
tcf(c_505,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)) = X0_mono_2Etyop_2Enum_2Enum,
inference(subtyping,[status(esa)],[c_152]) ).
tcf(c_506,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum,X1_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)),mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X1_mono_2Etyop_2Enum_2Enum))) = mono_2Ec_2Ebool_2EF_2E0,
inference(subtyping,[status(esa)],[c_151]) ).
tcf(c_511,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum,X1_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X1_mono_2Etyop_2Enum_2Enum)) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_mono_2Etyop_2Enum_2Enum),X1_mono_2Etyop_2Enum_2Enum),
inference(subtyping,[status(esa)],[c_146]) ).
tcf(c_512,plain,
mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0),
inference(subtyping,[status(esa)],[c_145]) ).
tcf(c_513,plain,
! [X0_iProver_s_1_d: iProver_s_1_d,X0_iProver_s_2_u: iProver_s_2_u,X1_iProver_s_2_u: iProver_s_2_u] : s(X0_iProver_s_1_d,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EF_2E0)),s(X0_iProver_s_1_d,X0_iProver_s_2_u),s(X0_iProver_s_1_d,X1_iProver_s_2_u))) = s(X0_iProver_s_1_d,X1_iProver_s_2_u),
inference(subtyping,[status(esa)],[c_144]) ).
tcf(c_2260,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)) = mono_2Ec_2Ebool_2EF_2E0,
inference(superposition,[status(thm)],[c_512,c_506]) ).
tcf(c_2261,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum] : mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_mono_2Etyop_2Enum_2Enum),mono_2Ec_2Enum_2E0_2E0) = mono_2Ec_2Ebool_2EF_2E0,
inference(demodulation,[status(thm)],[c_2260,c_511]) ).
tcf(c_11828,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum,X0_iProver_tyop_2Efcp_2Ecart_2_d: iProver_tyop_2Efcp_2Ecart_2_d] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Einteger_2Eint__lt_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum)),mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Einteger_2ENum_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__neg_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum))))))))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_mono_2Etyop_2Enum_2Enum)))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum))))),
inference(superposition,[status(thm)],[c_505,c_504]) ).
tcf(c_11858,plain,
! [X0_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum,X0_iProver_tyop_2Efcp_2Ecart_2_d: iProver_tyop_2Efcp_2Ecart_2_d] : s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,X0_mono_2Etyop_2Enum_2Enum))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0_iProver_tyop_2Efcp_2Ecart_2_d),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_mono_2Etyop_2Enum_2Enum)))),
inference(demodulation,[status(thm)],[c_11828,c_511,c_513,c_2261]) ).
tcf(c_11950,plain,
s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint,i_mono_2Etyop_2Einteger_2Eint(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint(mono_2Ec_2Einteger_2Eint__of__num_2E0,mono_2Ec_2Enum_2E0_2E0))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),
inference(instantiation,[status(thm)],[c_11858]) ).
tcf(c_11951,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11950,c_499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP015_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 17:40:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 10.76/2.27 % SZS status Started for theBenchmark.p
% 10.76/2.27 % SZS status Theorem for theBenchmark.p
% 10.76/2.27
% 10.76/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.76/2.27
% 10.76/2.27 % ------ iProver source info
% 10.76/2.27
% 10.76/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 10.76/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.76/2.27 % git: non_committed_changes: false
% 10.76/2.27
% 10.76/2.27 % ------ Parsing...
% 10.76/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.76/2.27
% 10.76/2.27 % ------ Preprocessing... sup_sim: 1 pe_s pe_e %
% 10.76/2.27
% 10.76/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 10.76/2.27
% 10.76/2.27 % ------ Preprocessing...
% 10.76/2.27 % ------ Proving...
% 10.76/2.27 % ------ Problem Properties
% 10.76/2.27
% 10.76/2.27 %
% 10.76/2.27 % clauses 127
% 10.76/2.27 % conjectures 1
% 10.76/2.27 % EPR 5
% 10.76/2.27 % Horn 105
% 10.76/2.27 % unary 64
% 10.76/2.27 % binary 53
% 10.76/2.27 % lits 200
% 10.76/2.27 % lits eq 78
% 10.76/2.27 % fd_pure 1
% 10.76/2.27 % fd_pseudo 0
% 10.76/2.27 % fd_cond 2
% 10.76/2.27 % fd_pseudo_cond 2
% 10.76/2.27 % AC symbols 0
% 10.76/2.27
% 10.76/2.27 % ------ Input Options Time Limit: Unbounded
% 10.76/2.27
% 10.76/2.27
% 10.76/2.27 % ------
% 10.76/2.27 % Current options:
% 10.76/2.27 % ------
% 10.76/2.27
% 10.76/2.27
% 10.76/2.27 %
% 10.76/2.27
% 10.76/2.27 % ------ Proving...
% 10.76/2.27 %
% 10.76/2.27
% 10.76/2.27 % SZS status Theorem for theBenchmark.p
% 10.76/2.27
% 10.76/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.76/2.27
% 10.76/2.27
%------------------------------------------------------------------------------