TSTP Solution File: ITP004^7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP004^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Mon May 20 22:42:10 EDT 2024
% Result : Theorem 92.33s 13.68s
% Output : Refutation 92.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP004^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat May 18 17:32:08 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (9728)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.50 % (9735)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.51 % (9731)WARNING: value z3 for option sas not known
% 0.21/0.51 % (9729)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.51 % (9732)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.51 % (9730)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.51 % (9731)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.51 % (9734)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.51 % (9733)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 1.19/0.67 % (9735)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.68/0.74 % Exception at run slice level
% 1.68/0.74 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.68/0.75 % Exception at run slice level
% 1.68/0.75 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.68/0.75 % (9736)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 1.68/0.76 % (9738)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 2.63/0.88 % Exception at run slice level
% 2.63/0.88 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 2.63/0.89 % (9739)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 2.89/0.95 % (9736)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.89/0.96 % (9738)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.20/1.06 % Exception at run slice level
% 3.20/1.06 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 3.20/1.07 % (9740)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 91.76/13.58 % (9733)First to succeed.
% 92.33/13.68 % (9733)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9728"
% 92.33/13.68 % (9733)Refutation found. Thanks to Tanya!
% 92.33/13.68 % SZS status Theorem for theBenchmark
% 92.33/13.68 % SZS output start Proof for theBenchmark
% 92.33/13.68 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 92.33/13.68 thf(type_def_6, type, tyop_2Ebool_2Eitself: $tType > $tType).
% 92.33/13.68 thf(type_def_7, type, tyop_2Emin_2Eind: $tType).
% 92.33/13.68 thf(type_def_8, type, tyop_2Enum_2Enum: $tType).
% 92.33/13.68 thf(type_def_9, type, tyop_2Eone_2Eone: $tType).
% 92.33/13.68 thf(type_def_10, type, tyop_2Esum_2Esum: ($tType * $tType) > $tType).
% 92.33/13.68 thf(type_def_11, type, tyop_2Eoption_2Eoption: $tType > $tType).
% 92.33/13.68 thf(type_def_12, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 92.33/13.68 thf(type_def_13, type, tyop_2Eind__type_2Erecspace: $tType > $tType).
% 92.33/13.68 thf(type_def_14, type, sK123: $tType).
% 92.33/13.68 thf(func_def_0, type, tyop_2Emin_2Ebool: $tType).
% 92.33/13.68 thf(func_def_1, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 92.33/13.68 thf(func_def_2, type, c_2Ebool_2E_21: !>[X0: $tType]:((X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_3, type, c_2Ebool_2E_2F_5C: $o > $o > $o).
% 92.33/13.68 thf(func_def_4, type, c_2Emin_2E_3D: !>[X0: $tType]:(X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_5, type, c_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 92.33/13.68 thf(func_def_6, type, c_2Ebool_2E_3F: !>[X0: $tType]:((X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_7, type, c_2Ebool_2E_5C_2F: $o > $o > $o).
% 92.33/13.68 thf(func_def_8, type, c_2Ebool_2E_7E: $o > $o).
% 92.33/13.68 thf(func_def_10, type, vNOT: $o > $o).
% 92.33/13.68 thf(func_def_11, type, tyop_2Ebool_2Eitself: $tType > $tType).
% 92.33/13.68 thf(func_def_12, type, tyop_2Emin_2Eind: $tType).
% 92.33/13.68 thf(func_def_13, type, c_2Ebool_2E_3F_21: !>[X0: $tType]:((X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_14, type, c_2Emin_2E_40: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.68 thf(func_def_15, type, c_2Ebool_2EARB: !>[X0: $tType]:(X0)).
% 92.33/13.68 thf(func_def_16, type, c_2Ebool_2EBOUNDED: $o > $o).
% 92.33/13.68 thf(func_def_17, type, c_2Ebool_2ECOND: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 92.33/13.68 thf(func_def_18, type, c_2Ebool_2EDATATYPE: !>[X0: $tType]:(X0 > $o)).
% 92.33/13.68 thf(func_def_19, type, c_2Ebool_2EF: $o).
% 92.33/13.68 thf(func_def_20, type, c_2Ebool_2EIN: !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_21, type, c_2Ebool_2ELET: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1)).
% 92.33/13.68 thf(func_def_22, type, c_2Ebool_2EONE__ONE: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 92.33/13.68 thf(func_def_23, type, c_2Ebool_2EONTO: !>[X0: $tType, X1: $tType]:((X0 > X1) > $o)).
% 92.33/13.68 thf(func_def_24, type, c_2Ebool_2ERES__ABSTRACT: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > X0 > X1)).
% 92.33/13.68 thf(func_def_25, type, c_2Ebool_2ERES__EXISTS: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_26, type, c_2Ebool_2ERES__EXISTS__UNIQUE: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_27, type, c_2Ebool_2ERES__FORALL: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_28, type, c_2Ebool_2ERES__SELECT: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.68 thf(func_def_29, type, c_2Ebool_2ET: $o).
% 92.33/13.68 thf(func_def_30, type, c_2Ebool_2ETYPE__DEFINITION: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > $o)).
% 92.33/13.68 thf(func_def_31, type, c_2Ebool_2Eitself__case: !>[X0: $tType, X1: $tType]:(tyop_2Ebool_2Eitself(X0) > X1 > X1)).
% 92.33/13.68 thf(func_def_32, type, c_2Ebool_2Eliteral__case: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1)).
% 92.33/13.68 thf(func_def_33, type, c_2Ebool_2Ethe__value: !>[X0: $tType]:(tyop_2Ebool_2Eitself(X0))).
% 92.33/13.68 thf(func_def_34, type, c_2EConseqConv_2EASM__MARKER: $o > $o > $o).
% 92.33/13.68 thf(func_def_35, type, c_2Emarker_2E_3A_2D: tyop_2Emin_2Eind > $o > $o).
% 92.33/13.68 thf(func_def_36, type, c_2Emarker_2EAC: $o > $o > $o).
% 92.33/13.68 thf(func_def_37, type, c_2Emarker_2EAbbrev: $o > $o).
% 92.33/13.68 thf(func_def_38, type, c_2Emarker_2ECong: $o > $o).
% 92.33/13.68 thf(func_def_39, type, c_2Emarker_2EIfCases: $o).
% 92.33/13.68 thf(func_def_40, type, c_2Emarker_2Estmarker: !>[X0: $tType]:(X0 > X0)).
% 92.33/13.68 thf(func_def_41, type, c_2Emarker_2Eunint: !>[X0: $tType]:(X0 > X0)).
% 92.33/13.68 thf(func_def_42, type, c_2EnormalForms_2EEXT__POINT: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 92.33/13.68 thf(func_def_43, type, c_2EnormalForms_2EUNIV__POINT: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.68 thf(func_def_44, type, c_2Ecombin_2E_3A_3E: !>[X0: $tType, X1: $tType]:(X1 > (X1 > X0) > X0)).
% 92.33/13.68 thf(func_def_45, type, c_2Ecombin_2EASSOC: !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 92.33/13.68 thf(func_def_46, type, c_2Ecombin_2EC: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 92.33/13.68 thf(func_def_47, type, c_2Ecombin_2ECOMM: !>[X0: $tType, X1: $tType]:((X0 > X0 > X1) > $o)).
% 92.33/13.68 thf(func_def_48, type, c_2Ecombin_2EFAIL: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 92.33/13.68 thf(func_def_49, type, c_2Ecombin_2EFCOMM: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X0) > (X2 > X0 > X0) > $o)).
% 92.33/13.68 thf(func_def_50, type, c_2Ecombin_2EI: !>[X0: $tType]:(X0 > X0)).
% 92.33/13.68 thf(func_def_51, type, c_2Ecombin_2EK: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 92.33/13.68 thf(func_def_52, type, c_2Ecombin_2ELEFT__ID: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > X0 > $o)).
% 92.33/13.68 thf(func_def_53, type, c_2Ecombin_2EMONOID: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 92.33/13.68 thf(func_def_54, type, c_2Ecombin_2ERIGHT__ID: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0) > X1 > $o)).
% 92.33/13.68 thf(func_def_55, type, c_2Ecombin_2ES: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 92.33/13.68 thf(func_def_56, type, c_2Ecombin_2EUPDATE: !>[X0: $tType, X1: $tType]:(X0 > X1 > (X0 > X1) > X0 > X1)).
% 92.33/13.68 thf(func_def_57, type, c_2Ecombin_2EW: !>[X0: $tType, X1: $tType]:((X0 > X0 > X1) > X0 > X1)).
% 92.33/13.68 thf(func_def_58, type, c_2Ecombin_2Eo: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1) > (X0 > X2) > X0 > X1)).
% 92.33/13.68 thf(func_def_59, type, tyop_2Enum_2Enum: $tType).
% 92.33/13.68 thf(func_def_60, type, c_2Enum_2E0: tyop_2Enum_2Enum).
% 92.33/13.68 thf(func_def_61, type, c_2Enum_2EABS__num: tyop_2Emin_2Eind > tyop_2Enum_2Enum).
% 92.33/13.68 thf(func_def_62, type, c_2Enum_2EIS__NUM__REP: tyop_2Emin_2Eind > $o).
% 92.33/13.68 thf(func_def_63, type, c_2Enum_2EREP__num: tyop_2Enum_2Enum > tyop_2Emin_2Eind).
% 92.33/13.68 thf(func_def_64, type, c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.68 thf(func_def_65, type, c_2Enum_2ESUC__REP: tyop_2Emin_2Eind > tyop_2Emin_2Eind).
% 92.33/13.68 thf(func_def_66, type, c_2Enum_2EZERO__REP: tyop_2Emin_2Eind).
% 92.33/13.68 thf(func_def_67, type, tyop_2Eone_2Eone: $tType).
% 92.33/13.68 thf(func_def_68, type, c_2Eone_2Eone: tyop_2Eone_2Eone).
% 92.33/13.68 thf(func_def_69, type, c_2Eone_2Eone__CASE: !>[X0: $tType]:(tyop_2Eone_2Eone > X0 > X0)).
% 92.33/13.68 thf(func_def_70, type, c_2Erelation_2ECR: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_71, type, c_2Erelation_2EEMPTY__REL: !>[X0: $tType]:(X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_72, type, c_2Erelation_2EEQC: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_73, type, c_2Erelation_2EIDEM: !>[X0: $tType]:((X0 > X0) > $o)).
% 92.33/13.68 thf(func_def_74, type, c_2Erelation_2EINDUCTIVE__INVARIANT: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1 > $o) > ((X0 > X1) > X0 > X1) > $o)).
% 92.33/13.68 thf(func_def_75, type, c_2Erelation_2EINDUCTIVE__INVARIANT__ON: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > $o) > (X0 > X1 > $o) > ((X0 > X1) > X0 > X1) > $o)).
% 92.33/13.68 thf(func_def_76, type, c_2Erelation_2EINVOL: !>[X0: $tType]:((X0 > X0) > $o)).
% 92.33/13.68 thf(func_def_77, type, c_2Erelation_2ELinearOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_78, type, c_2Erelation_2EO: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > $o) > (X0 > X1 > $o) > X0 > X2 > $o)).
% 92.33/13.68 thf(func_def_79, type, c_2Erelation_2EOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_80, type, c_2Erelation_2EPreOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_81, type, c_2Erelation_2ERC: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_82, type, c_2Erelation_2ERCOMPL: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > X1 > $o)).
% 92.33/13.68 thf(func_def_83, type, c_2Erelation_2ERDOM: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > $o)).
% 92.33/13.68 thf(func_def_84, type, c_2Erelation_2ERDOM__DELETE: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > X0 > X1 > $o)).
% 92.33/13.68 thf(func_def_85, type, c_2Erelation_2ERESTRICT: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X0 > $o) > X0 > X0 > X1)).
% 92.33/13.68 thf(func_def_86, type, c_2Erelation_2ERINTER: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0 > X1 > $o)).
% 92.33/13.68 thf(func_def_87, type, c_2Erelation_2ERRANGE: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1 > $o)).
% 92.33/13.68 thf(func_def_88, type, c_2Erelation_2ERRESTRICT: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > $o) > X0 > X1 > $o)).
% 92.33/13.68 thf(func_def_89, type, c_2Erelation_2ERSUBSET: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > $o)).
% 92.33/13.68 thf(func_def_90, type, c_2Erelation_2ERTC: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_91, type, c_2Erelation_2ERUNION: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0 > X1 > $o)).
% 92.33/13.68 thf(func_def_92, type, c_2Erelation_2ERUNIV: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 92.33/13.68 thf(func_def_93, type, c_2Erelation_2ESC: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_94, type, c_2Erelation_2ESN: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_95, type, c_2Erelation_2ESTRORD: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_96, type, c_2Erelation_2EStrongLinearOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_97, type, c_2Erelation_2EStrongOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_98, type, c_2Erelation_2ETC: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.68 thf(func_def_99, type, c_2Erelation_2EWCR: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_100, type, c_2Erelation_2EWF: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.68 thf(func_def_101, type, c_2Erelation_2EWFP: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_102, type, c_2Erelation_2EWFREC: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > ((X0 > X1) > X0 > X1) > X0 > X1)).
% 92.33/13.69 thf(func_def_103, type, c_2Erelation_2EWeakLinearOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_104, type, c_2Erelation_2EWeakOrder: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_105, type, c_2Erelation_2Eantisymmetric: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_106, type, c_2Erelation_2Eapprox: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > ((X0 > X1) > X0 > X1) > X0 > (X0 > X1) > $o)).
% 92.33/13.69 thf(func_def_107, type, c_2Erelation_2Ediag: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_108, type, c_2Erelation_2Ediamond: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_109, type, c_2Erelation_2Eequivalence: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_110, type, c_2Erelation_2Einv: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1 > X0 > $o)).
% 92.33/13.69 thf(func_def_111, type, c_2Erelation_2Einv__image: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X1) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_112, type, c_2Erelation_2Eirreflexive: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_113, type, c_2Erelation_2Enf: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_114, type, c_2Erelation_2Ercdiamond: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_115, type, c_2Erelation_2Ereflexive: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_116, type, c_2Erelation_2Esymmetric: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_117, type, c_2Erelation_2Ethe__fun: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > ((X0 > X1) > X0 > X1) > X0 > X0 > X1)).
% 92.33/13.69 thf(func_def_118, type, c_2Erelation_2Etotal: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_119, type, c_2Erelation_2Etransitive: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_120, type, c_2Erelation_2Etrichotomous: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_121, type, tyop_2Esum_2Esum: ($tType * $tType) > $tType).
% 92.33/13.69 thf(func_def_122, type, c_2Esum_2E_2B_2B: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X2) > (X1 > X3) > tyop_2Esum_2Esum(X0,X1) > tyop_2Esum_2Esum(X2,X3))).
% 92.33/13.69 thf(func_def_123, type, c_2Esum_2EABS__sum: !>[X0: $tType, X1: $tType]:(($o > X0 > X1 > $o) > tyop_2Esum_2Esum(X0,X1))).
% 92.33/13.69 thf(func_def_124, type, c_2Esum_2EINL: !>[X0: $tType, X1: $tType]:(X0 > tyop_2Esum_2Esum(X0,X1))).
% 92.33/13.69 thf(func_def_125, type, c_2Esum_2EINR: !>[X0: $tType, X1: $tType]:(X1 > tyop_2Esum_2Esum(X0,X1))).
% 92.33/13.69 thf(func_def_126, type, c_2Esum_2EISL: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > $o)).
% 92.33/13.69 thf(func_def_127, type, c_2Esum_2EISR: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > $o)).
% 92.33/13.69 thf(func_def_128, type, c_2Esum_2EIS__SUM__REP: !>[X0: $tType, X1: $tType]:(($o > X0 > X1 > $o) > $o)).
% 92.33/13.69 thf(func_def_129, type, c_2Esum_2EOUTL: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_130, type, c_2Esum_2EOUTR: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_131, type, c_2Esum_2EREP__sum: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > $o > X0 > X1 > $o)).
% 92.33/13.69 thf(func_def_132, type, c_2Esum_2ESUM__ALL: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > tyop_2Esum_2Esum(X0,X1) > $o)).
% 92.33/13.69 thf(func_def_133, type, c_2Esum_2Esum__CASE: !>[X0: $tType, X1: $tType, X2: $tType]:(tyop_2Esum_2Esum(X0,X1) > (X0 > X2) > (X1 > X2) > X2)).
% 92.33/13.69 thf(func_def_134, type, tyop_2Eoption_2Eoption: $tType > $tType).
% 92.33/13.69 thf(func_def_135, type, c_2Eoption_2EIS__NONE: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > $o)).
% 92.33/13.69 thf(func_def_136, type, c_2Eoption_2EIS__SOME: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > $o)).
% 92.33/13.69 thf(func_def_137, type, c_2Eoption_2ENONE: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_138, type, c_2Eoption_2EOPTION__ALL: !>[X0: $tType]:((X0 > $o) > tyop_2Eoption_2Eoption(X0) > $o)).
% 92.33/13.69 thf(func_def_139, type, c_2Eoption_2EOPTION__APPLY: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(sTfun(X1,X0)) > tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_140, type, c_2Eoption_2EOPTION__BIND: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X1) > (X1 > tyop_2Eoption_2Eoption(X0)) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_141, type, c_2Eoption_2EOPTION__CHOICE: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_142, type, c_2Eoption_2EOPTION__GUARD: $o > tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)).
% 92.33/13.69 thf(func_def_143, type, c_2Eoption_2EOPTION__IGNORE__BIND: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_144, type, c_2Eoption_2EOPTION__JOIN: !>[X0: $tType]:(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_145, type, c_2Eoption_2EOPTION__MAP: !>[X0: $tType, X1: $tType]:((X0 > X1) > tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X1))).
% 92.33/13.69 thf(func_def_146, type, c_2Eoption_2EOPTION__MAP2: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > X0) > tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X2) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_147, type, c_2Eoption_2EOPTION__MCOMP: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > tyop_2Eoption_2Eoption(X0)) > (X2 > tyop_2Eoption_2Eoption(X1)) > X2 > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_148, type, c_2Eoption_2EOPTREL: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X1) > $o)).
% 92.33/13.69 thf(func_def_149, type, c_2Eoption_2ESOME: !>[X0: $tType]:(X0 > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_150, type, c_2Eoption_2ETHE: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_151, type, c_2Eoption_2Eoption__ABS: !>[X0: $tType]:(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_152, type, c_2Eoption_2Eoption__CASE: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X0) > X1 > (X0 > X1) > X1)).
% 92.33/13.69 thf(func_def_153, type, c_2Eoption_2Eoption__REP: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone))).
% 92.33/13.69 thf(func_def_154, type, c_2Eoption_2Esome: !>[X0: $tType]:((X0 > $o) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_155, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 92.33/13.69 thf(func_def_156, type, c_2Epair_2E_23_23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X2) > (X1 > X3) > tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X2,X3))).
% 92.33/13.69 thf(func_def_157, type, c_2Epair_2E_2C: !>[X0: $tType, X1: $tType]:(X0 > X1 > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_158, type, c_2Epair_2EABS__prod: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_159, type, c_2Epair_2ECURRY: !>[X0: $tType, X1: $tType, X2: $tType]:((tyop_2Epair_2Eprod(X0,X1) > X2) > X0 > X1 > X2)).
% 92.33/13.69 thf(func_def_160, type, c_2Epair_2EFST: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_161, type, c_2Epair_2ELEX: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X1 > $o) > tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X0,X1) > $o)).
% 92.33/13.69 thf(func_def_162, type, c_2Epair_2EPROD__ALL: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > tyop_2Epair_2Eprod(X0,X1) > $o)).
% 92.33/13.69 thf(func_def_163, type, c_2Epair_2EREP__prod: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X0 > X1 > $o)).
% 92.33/13.69 thf(func_def_164, type, c_2Epair_2ERPROD: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X1 > $o) > tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X0,X1) > $o)).
% 92.33/13.69 thf(func_def_165, type, c_2Epair_2ESND: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_166, type, c_2Epair_2ESWAP: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_167, type, c_2Epair_2EUNCURRY: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > tyop_2Epair_2Eprod(X0,X1) > X2)).
% 92.33/13.69 thf(func_def_168, type, c_2Epair_2Epair__CASE: !>[X0: $tType, X1: $tType, X2: $tType]:(tyop_2Epair_2Eprod(X1,X2) > (X1 > X2 > X0) > X0)).
% 92.33/13.69 thf(func_def_169, type, c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_170, type, c_2Eprim__rec_2EPRE: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_171, type, c_2Eprim__rec_2EPRIM__REC: !>[X0: $tType]:(X0 > (X0 > tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_172, type, c_2Eprim__rec_2EPRIM__REC__FUN: !>[X0: $tType]:(X0 > (X0 > tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_173, type, c_2Eprim__rec_2ESIMP__REC: !>[X0: $tType]:(X0 > (X0 > X0) > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_174, type, c_2Eprim__rec_2ESIMP__REC__REL: !>[X0: $tType]:((tyop_2Enum_2Enum > X0) > X0 > (X0 > X0) > tyop_2Enum_2Enum > $o)).
% 92.33/13.69 thf(func_def_175, type, c_2Eprim__rec_2Emeasure: !>[X0: $tType]:((X0 > tyop_2Enum_2Enum) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_176, type, c_2Eprim__rec_2Ewellfounded: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_177, type, c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_178, type, c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_179, type, c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_180, type, c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_181, type, c_2Earithmetic_2E_3E: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_182, type, c_2Earithmetic_2E_3E_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_183, type, c_2Earithmetic_2EABS__DIFF: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_184, type, c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_185, type, c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_186, type, c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_187, type, c_2Earithmetic_2EDIV2: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_188, type, c_2Earithmetic_2EDIVMOD: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_189, type, c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_190, type, c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_191, type, c_2Earithmetic_2EFACT: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_192, type, c_2Earithmetic_2EFUNPOW: !>[X0: $tType]:((X0 > X0) > tyop_2Enum_2Enum > X0 > X0)).
% 92.33/13.69 thf(func_def_193, type, c_2Earithmetic_2EMAX: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_194, type, c_2Earithmetic_2EMIN: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_195, type, c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_196, type, c_2Earithmetic_2EMODEQ: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_197, type, c_2Earithmetic_2ENRC: !>[X0: $tType]:((X0 > X0 > $o) > tyop_2Enum_2Enum > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_198, type, c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_199, type, c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_200, type, c_2Earithmetic_2EZERO: tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_201, type, c_2Earithmetic_2Efindq: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_202, type, c_2Earithmetic_2Enat__elim____magic: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_203, type, c_2Earithmetic_2Enum__CASE: !>[X0: $tType]:(tyop_2Enum_2Enum > X0 > (tyop_2Enum_2Enum > X0) > X0)).
% 92.33/13.69 thf(func_def_204, type, c_2Eposet_2Ebottom: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0 > $o)).
% 92.33/13.69 thf(func_def_205, type, c_2Eposet_2Ecarrier: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0 > $o)).
% 92.33/13.69 thf(func_def_206, type, c_2Eposet_2Echain: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_207, type, c_2Eposet_2Ecomplete: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > $o)).
% 92.33/13.69 thf(func_def_208, type, c_2Eposet_2Econtinuous: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > X0) > $o)).
% 92.33/13.69 thf(func_def_209, type, c_2Eposet_2Edown__continuous: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > X0) > $o)).
% 92.33/13.69 thf(func_def_210, type, c_2Eposet_2Efunction: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > $o) > (X0 > X1) > $o)).
% 92.33/13.69 thf(func_def_211, type, c_2Eposet_2Egfp: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > X0) > X0 > $o)).
% 92.33/13.69 thf(func_def_212, type, c_2Eposet_2Eglb: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_213, type, c_2Eposet_2Elfp: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > X0) > X0 > $o)).
% 92.33/13.69 thf(func_def_214, type, c_2Eposet_2Elub: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_215, type, c_2Eposet_2Emonotonic: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > X0) > $o)).
% 92.33/13.69 thf(func_def_216, type, c_2Eposet_2Epointwise__lift: !>[X0: $tType, X1: $tType]:((X0 > $o) > tyop_2Epair_2Eprod(sTfun(X1,$o),sTfun(X1,sTfun(X1,$o))) > tyop_2Epair_2Eprod(sTfun(sTfun(X0,X1),$o),sTfun(sTfun(X0,X1),sTfun(sTfun(X0,X1),$o))))).
% 92.33/13.69 thf(func_def_217, type, c_2Eposet_2Eposet: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > $o)).
% 92.33/13.69 thf(func_def_218, type, c_2Eposet_2Erelation: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_219, type, c_2Eposet_2Etop: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0 > $o)).
% 92.33/13.69 thf(func_def_220, type, c_2Eposet_2Eup__continuous: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > (X0 > X0) > $o)).
% 92.33/13.69 thf(func_def_221, type, c_2Enumeral_2Eexactlog: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_222, type, c_2Enumeral_2EiBIT__cases: !>[X0: $tType]:(tyop_2Enum_2Enum > X0 > (tyop_2Enum_2Enum > X0) > (tyop_2Enum_2Enum > X0) > X0)).
% 92.33/13.69 thf(func_def_223, type, c_2Enumeral_2EiDUB: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_224, type, c_2Enumeral_2EiSQR: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_225, type, c_2Enumeral_2EiSUB: $o > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_226, type, c_2Enumeral_2EiZ: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_227, type, c_2Enumeral_2EiiSUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_228, type, c_2Enumeral_2Einternal__mult: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_229, type, c_2Enumeral_2Eonecount: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_230, type, c_2Enumeral_2Etexp__help: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_231, type, c_2Ewhile_2EHOARE__SPEC: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X1 > $o) > $o)).
% 92.33/13.69 thf(func_def_232, type, c_2Ewhile_2ELEAST: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_233, type, c_2Ewhile_2EOLEAST: (tyop_2Enum_2Enum > $o) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_234, type, c_2Ewhile_2EOWHILE: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > X0 > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_235, type, c_2Ewhile_2EWHILE: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > X0 > X0)).
% 92.33/13.69 thf(func_def_236, type, c_2EbasicSize_2Ebool__size: $o > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_237, type, c_2EbasicSize_2Eone__size: tyop_2Eone_2Eone > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_238, type, c_2EbasicSize_2Eoption__size: !>[X0: $tType]:((X0 > tyop_2Enum_2Enum) > tyop_2Eoption_2Eoption(X0) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_239, type, c_2EbasicSize_2Epair__size: !>[X0: $tType, X1: $tType]:((X0 > tyop_2Enum_2Enum) > (X1 > tyop_2Enum_2Enum) > tyop_2Epair_2Eprod(X0,X1) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_240, type, c_2EbasicSize_2Esum__size: !>[X0: $tType, X1: $tType]:((X0 > tyop_2Enum_2Enum) > (X1 > tyop_2Enum_2Enum) > tyop_2Esum_2Esum(X0,X1) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_241, type, c_2Edivides_2EPRIMES: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_242, type, c_2Edivides_2Edivides: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_243, type, c_2Edivides_2Eprime: tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_244, type, tyop_2Eind__type_2Erecspace: $tType > $tType).
% 92.33/13.69 thf(func_def_245, type, c_2Eind__type_2EBOTTOM: !>[X0: $tType]:(tyop_2Eind__type_2Erecspace(X0))).
% 92.33/13.69 thf(func_def_246, type, c_2Eind__type_2ECONSTR: !>[X0: $tType]:(tyop_2Enum_2Enum > X0 > (tyop_2Enum_2Enum > tyop_2Eind__type_2Erecspace(X0)) > tyop_2Eind__type_2Erecspace(X0))).
% 92.33/13.69 thf(func_def_247, type, c_2Eind__type_2EFCONS: !>[X0: $tType]:(X0 > (tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_248, type, c_2Eind__type_2EFNIL: !>[X0: $tType]:(tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_249, type, c_2Eind__type_2EINJA: !>[X0: $tType]:(X0 > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_250, type, c_2Eind__type_2EINJF: !>[X0: $tType]:((tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_251, type, c_2Eind__type_2EINJN: !>[X0: $tType]:(tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_252, type, c_2Eind__type_2EINJP: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > (tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_253, type, c_2Eind__type_2EISO: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > X0) > $o)).
% 92.33/13.69 thf(func_def_254, type, c_2Eind__type_2ENUMFST: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_255, type, c_2Eind__type_2ENUMLEFT: tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_256, type, c_2Eind__type_2ENUMPAIR: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_257, type, c_2Eind__type_2ENUMRIGHT: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_258, type, c_2Eind__type_2ENUMSND: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_259, type, c_2Eind__type_2ENUMSUM: $o > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_260, type, c_2Eind__type_2EZBOT: !>[X0: $tType]:(tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_261, type, c_2Eind__type_2EZCONSTR: !>[X0: $tType]:(tyop_2Enum_2Enum > X0 > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_262, type, c_2Eind__type_2EZRECSPACE: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_263, type, c_2Eind__type_2Edest__rec: !>[X0: $tType]:(tyop_2Eind__type_2Erecspace(X0) > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_264, type, c_2Eind__type_2Emk__rec: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > tyop_2Eind__type_2Erecspace(X0))).
% 92.33/13.69 thf(func_def_265, type, c_2Egcd_2Egcd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_266, type, c_2Egcd_2Eis__gcd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_267, type, c_2Egcd_2Elcm: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_268, type, c_2Elogroot_2ELOG: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_269, type, c_2Elogroot_2EROOT: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_270, type, c_2Elogroot_2ESQRTd: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_271, type, c_2Elogroot_2EiSQRT0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_272, type, c_2Elogroot_2EiSQRT1: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_273, type, c_2Elogroot_2EiSQRT2: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_274, type, c_2Elogroot_2EiSQRT3: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_275, type, c_2Enumpair_2Einvtri: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_276, type, c_2Enumpair_2Einvtri0: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_277, type, c_2Enumpair_2Enapp: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_278, type, c_2Enumpair_2Encons: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_279, type, c_2Enumpair_2Enfoldl: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > X0) > X0 > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_280, type, c_2Enumpair_2Enfst: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_281, type, c_2Enumpair_2Enlen: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_282, type, c_2Enumpair_2Enlistrec: !>[X0: $tType]:(X0 > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0) > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_283, type, c_2Enumpair_2Enmap: (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_284, type, c_2Enumpair_2Enpair: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_285, type, c_2Enumpair_2Ensnd: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_286, type, c_2Enumpair_2Etri: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_287, type, c_2Ebit_2EBIT: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_288, type, c_2Ebit_2EBITS: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_289, type, c_2Ebit_2EBITV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_290, type, c_2Ebit_2EBITWISE: tyop_2Enum_2Enum > ($o > $o > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_291, type, c_2Ebit_2EBIT__MODIFY: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_292, type, c_2Ebit_2EBIT__REVERSE: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_293, type, c_2Ebit_2EDIVMOD__2EXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_294, type, c_2Ebit_2EDIV__2EXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_295, type, c_2Ebit_2ELOG2: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_296, type, c_2Ebit_2ELOWEST__SET__BIT: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_297, type, c_2Ebit_2EMOD__2EXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_298, type, c_2Ebit_2EMOD__2EXP__EQ: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_299, type, c_2Ebit_2EMOD__2EXP__MAX: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_300, type, c_2Ebit_2ESBIT: $o > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_301, type, c_2Ebit_2ESIGN__EXTEND: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_302, type, c_2Ebit_2ESLICE: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_303, type, c_2Ebit_2ETIMES__2EXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_304, type, c_2Epred__set_2ECHOICE: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_305, type, c_2Epred__set_2EDELETE: !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_306, type, c_2Epred__set_2EDIFF: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_307, type, c_2Epred__set_2EDISJOINT: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_308, type, c_2Epred__set_2EEMPTY: !>[X0: $tType]:(X0 > $o)).
% 92.33/13.69 thf(func_def_309, type, c_2Epred__set_2EGSPEC: !>[X0: $tType, X1: $tType]:((X1 > tyop_2Epair_2Eprod(X0,$o)) > X0 > $o)).
% 92.33/13.69 thf(func_def_310, type, c_2Epred__set_2EINSERT: !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_311, type, c_2Epred__set_2EINTER: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_312, type, c_2Epred__set_2EPSUBSET: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_313, type, c_2Epred__set_2EREST: !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_314, type, c_2Epred__set_2ESUBSET: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_315, type, c_2Epred__set_2EUNION: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_316, type, c_2Epred__set_2EUNIV: !>[X0: $tType]:(X0 > $o)).
% 92.33/13.69 thf(func_def_319, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 92.33/13.69 thf(func_def_320, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
% 92.33/13.69 thf(func_def_321, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 92.33/13.69 thf(func_def_322, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 92.33/13.69 thf(func_def_323, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 92.33/13.69 thf(func_def_324, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_325, type, vAND: $o > $o > $o).
% 92.33/13.69 thf(func_def_326, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_327, type, vOR: $o > $o > $o).
% 92.33/13.69 thf(func_def_328, type, vIMP: $o > $o > $o).
% 92.33/13.69 thf(func_def_329, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_330, type, sP0: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_331, type, sP1: (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_332, type, sP2: tyop_2Emin_2Eind > $o).
% 92.33/13.69 thf(func_def_333, type, sP3: tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_334, type, sP4: (tyop_2Enum_2Enum > $o) > (tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) > $o) > $o).
% 92.33/13.69 thf(func_def_335, type, sP5: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_336, type, sP6: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_337, type, sP7: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_338, type, sP8: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_339, type, sP9: $o > $o > $o).
% 92.33/13.69 thf(func_def_340, type, sP10: $o > $o > $o).
% 92.33/13.69 thf(func_def_341, type, sP11: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_342, type, sP12: $o > $o > $o).
% 92.33/13.69 thf(func_def_343, type, sP13: $o > $o > $o).
% 92.33/13.69 thf(func_def_344, type, sP14: $o > $o > $o).
% 92.33/13.69 thf(func_def_345, type, sP15: $o > $o > $o).
% 92.33/13.69 thf(func_def_346, type, sP16: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_347, type, sP17: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_348, type, sP18: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_349, type, sP19: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_350, type, sP20: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_351, type, sP21: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_352, type, sP22: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_353, type, sP23: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_354, type, sP24: !>[X0: $tType]:((X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_355, type, sP25: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_356, type, sP26: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_357, type, sP27: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_358, type, sP28: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_359, type, sP29: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_360, type, sP30: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_361, type, sP31: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_362, type, sP32: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_363, type, sP33: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_364, type, sP34: $o > $o > $o).
% 92.33/13.69 thf(func_def_365, type, sP35: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_366, type, sP36: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_367, type, sP37: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_368, type, sP38: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_369, type, sP39: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_370, type, sP40: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_371, type, sP41: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_372, type, sP42: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_373, type, sP43: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_374, type, sP44: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_375, type, sP45: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_376, type, sP46: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_377, type, sP47: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_378, type, sP48: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_379, type, sP49: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_380, type, sP50: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_381, type, sP51: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_382, type, sP52: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_383, type, sP53: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_384, type, sP54: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > $o).
% 92.33/13.69 thf(func_def_385, type, sP55: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_386, type, sP56: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_387, type, sP57: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_388, type, sP58: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_389, type, sP59: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_390, type, sP60: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_391, type, sP61: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_392, type, sP62: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_393, type, sP63: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_394, type, sP64: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_395, type, sP65: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_396, type, sP66: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_397, type, sP67: $o > $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_398, type, sP68: $o > $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_399, type, sP69: $o > $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_400, type, sP70: $o > $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_401, type, sP71: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_402, type, sP72: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_403, type, sP73: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_404, type, sP74: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_405, type, sP75: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_406, type, sP76: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_407, type, sP77: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_408, type, sP78: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_409, type, sP79: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_410, type, sP80: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_411, type, sP81: $o > $o > $o).
% 92.33/13.69 thf(func_def_412, type, sP82: $o > $o > $o).
% 92.33/13.69 thf(func_def_413, type, sP83: $o > $o > $o).
% 92.33/13.69 thf(func_def_414, type, sP84: $o > $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_415, type, sP85: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_416, type, sP86: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_417, type, sP87: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_418, type, sP88: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_419, type, sP89: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_420, type, sP90: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_421, type, sP91: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_422, type, sP92: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_423, type, sP93: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0 > X2) > $o)).
% 92.33/13.69 thf(func_def_424, type, sP94: !>[X0: $tType, X1: $tType]:((X1 > X0) > $o)).
% 92.33/13.69 thf(func_def_425, type, sP95: !>[X0: $tType, X1: $tType]:((X1 > X0) > $o)).
% 92.33/13.69 thf(func_def_426, type, sP96: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_427, type, sP97: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_428, type, sP98: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_429, type, sP99: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_430, type, sP100: $o > $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_431, type, sP101: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_432, type, sP102: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_433, type, sP103: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_434, type, sP104: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > $o)).
% 92.33/13.69 thf(func_def_435, type, sP105: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_436, type, sP106: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_437, type, sP107: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_438, type, sP108: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_439, type, sP109: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_440, type, sP110: $o > $o > $o > $o).
% 92.33/13.69 thf(func_def_441, type, sP111: !>[X0: $tType]:(X0 > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > X0) > X0 > $o)).
% 92.33/13.69 thf(func_def_442, type, sP112: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0) > (X1 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_443, type, sP113: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_444, type, sP114: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_445, type, sP115: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_446, type, sP116: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_447, type, sP117: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_448, type, sP118: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_449, type, sP119: !>[X0: $tType, X1: $tType]:(X0 > tyop_2Eoption_2Eoption(X1) > (X1 > X0) > X0 > $o)).
% 92.33/13.69 thf(func_def_450, type, sP120: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X1 > $o) > (X1 > X0 > $o) > ((X1 > X0) > X1 > X0) > $o)).
% 92.33/13.69 thf(func_def_451, type, sP121: !>[X0: $tType, X1: $tType]:(X1 > X0 > X1 > X0 > (X1 > X0) > $o)).
% 92.33/13.69 thf(func_def_452, type, sP122: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > tyop_2Epair_2Eprod(X1,X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > $o)).
% 92.33/13.69 thf(func_def_453, type, sK124: sK123 > $o).
% 92.33/13.69 thf(func_def_454, type, sK125: $o).
% 92.33/13.69 thf(func_def_455, type, sK126: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_456, type, sK127: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_457, type, sK128: !>[X0: $tType]:(X0 > X0 > tyop_2Enum_2Enum > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_458, type, sK129: !>[X0: $tType]:((tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_459, type, sK130: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_460, type, sK131: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_461, type, sK132: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_462, type, sK133: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_463, type, sK134: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_464, type, sK135: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_465, type, sK136: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_466, type, sK137: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_467, type, sK138: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_468, type, sK139: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_469, type, sK140: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_470, type, sK141: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_471, type, sK142: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_472, type, sK143: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_473, type, sK144: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_474, type, sK145: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_475, type, sK146: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_476, type, sK147: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_477, type, sK148: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_478, type, sK149: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_479, type, sK150: (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_480, type, sK151: (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_481, type, sK152: (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_482, type, sK153: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_483, type, sK154: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_484, type, sK155: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_485, type, sK156: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_486, type, sK157: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_487, type, sK158: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_488, type, sK159: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_489, type, sK160: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_490, type, sK161: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_491, type, sK162: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_492, type, sK163: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_493, type, sK164: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_494, type, sK165: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_495, type, sK166: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_496, type, sK167: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_497, type, sK168: (tyop_2Eone_2Eone > $o) > tyop_2Eone_2Eone).
% 92.33/13.69 thf(func_def_498, type, sK169: ($o > $o) > $o).
% 92.33/13.69 thf(func_def_499, type, sK170: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_500, type, sK171: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_501, type, sK172: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_502, type, sK173: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_503, type, sK174: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_504, type, sK175: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_505, type, sK176: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_506, type, sK177: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_507, type, sK178: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_508, type, sK179: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_509, type, sK180: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_510, type, sK181: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_511, type, sK182: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_512, type, sK183: tyop_2Emin_2Eind > tyop_2Emin_2Eind > $o).
% 92.33/13.69 thf(func_def_513, type, sK184: (tyop_2Emin_2Eind > $o) > tyop_2Emin_2Eind).
% 92.33/13.69 thf(func_def_514, type, sK185: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_515, type, sK186: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_516, type, sK187: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_517, type, sK188: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_518, type, sK189: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_519, type, sK190: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_520, type, sK191: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_521, type, sK192: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_522, type, sK193: !>[X0: $tType]:(tyop_2Ebool_2Eitself(X0) > X0)).
% 92.33/13.69 thf(func_def_523, type, sK194: !>[X0: $tType]:(tyop_2Eind__type_2Erecspace(X0) > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_524, type, sK195: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone))).
% 92.33/13.69 thf(func_def_525, type, sK196: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_526, type, sK197: tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_527, type, sK198: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_528, type, sK199: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_529, type, sK200: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_530, type, sK201: !>[X0: $tType]:((X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_531, type, sK202: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_532, type, sK203: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_533, type, sK204: (tyop_2Enum_2Enum > $o) > (tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_534, type, sK205: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_535, type, sK206: !>[X0: $tType]:((tyop_2Eoption_2Eoption(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_536, type, sK207: (tyop_2Enum_2Enum > $o) > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_537, type, sK208: !>[X0: $tType]:((tyop_2Eind__type_2Erecspace(X0) > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_538, type, sK209: !>[X0: $tType]:((tyop_2Eind__type_2Erecspace(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_539, type, sK210: !>[X0: $tType]:((tyop_2Eind__type_2Erecspace(X0) > $o) > tyop_2Enum_2Enum > tyop_2Eind__type_2Erecspace(X0))).
% 92.33/13.69 thf(func_def_540, type, sK211: !>[X0: $tType]:((tyop_2Eoption_2Eoption(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_541, type, sK212: !>[X0: $tType]:(((tyop_2Enum_2Enum > X0 > $o) > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_542, type, sK213: !>[X0: $tType]:(((tyop_2Enum_2Enum > X0 > $o) > $o) > X0)).
% 92.33/13.69 thf(func_def_543, type, sK214: !>[X0: $tType]:(((tyop_2Enum_2Enum > X0 > $o) > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_544, type, sK215: !>[X0: $tType]:(((tyop_2Enum_2Enum > X0 > $o) > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_545, type, sK216: !>[X0: $tType]:(((tyop_2Enum_2Enum > X0 > $o) > $o) > X0)).
% 92.33/13.69 thf(func_def_546, type, sK217: !>[X0: $tType]:(((tyop_2Enum_2Enum > X0 > $o) > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_547, type, sK218: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_548, type, sK219: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_549, type, sK220: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_550, type, sK221: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_551, type, sK222: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_552, type, sK223: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_553, type, sK224: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_554, type, sK225: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_555, type, sK226: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_556, type, sK227: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_557, type, sK228: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_558, type, sK229: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_559, type, sK230: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_560, type, sK231: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_561, type, sK232: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_562, type, sK233: !>[X0: $tType]:((X0 > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0) > tyop_2Enum_2Enum > $o) > X0)).
% 92.33/13.69 thf(func_def_563, type, sK234: !>[X0: $tType]:((X0 > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0) > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0)).
% 92.33/13.69 thf(func_def_564, type, sK235: !>[X0: $tType]:((X0 > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0) > tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_565, type, sK236: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_566, type, sK237: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_567, type, sK238: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_568, type, sK239: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_569, type, sK240: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_570, type, sK241: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_571, type, sK242: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_572, type, sK243: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_573, type, sK244: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_574, type, sK245: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_575, type, sK246: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_576, type, sK247: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_577, type, sK248: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_578, type, sK249: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_579, type, sK250: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_580, type, sK251: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_581, type, sK252: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_582, type, sK253: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_583, type, sK254: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_584, type, sK255: !>[X0: $tType]:((tyop_2Ebool_2Eitself(X0) > $o) > tyop_2Ebool_2Eitself(X0))).
% 92.33/13.69 thf(func_def_585, type, sK256: !>[X0: $tType]:((tyop_2Eoption_2Eoption(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_586, type, sK257: !>[X0: $tType]:((tyop_2Eoption_2Eoption(X0) > $o) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_587, type, sK258: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_588, type, sK259: !>[X0: $tType]:((tyop_2Ebool_2Eitself(X0) > $o) > tyop_2Ebool_2Eitself(X0))).
% 92.33/13.69 thf(func_def_589, type, sK260: !>[X0: $tType]:((tyop_2Eoption_2Eoption(X0) > $o) > tyop_2Eoption_2Eoption(X0))).
% 92.33/13.69 thf(func_def_590, type, sK261: !>[X0: $tType]:((tyop_2Eoption_2Eoption(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_591, type, sK262: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_592, type, sK263: !>[X0: $tType]:(tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_593, type, sK264: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_594, type, sK265: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_595, type, sK266: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_596, type, sK267: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_597, type, sK268: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_598, type, sK269: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_599, type, sK270: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_600, type, sK271: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_601, type, sK272: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_602, type, sK273: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_603, type, sK274: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_604, type, sK275: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_605, type, sK276: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_606, type, sK277: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_607, type, sK278: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_608, type, sK279: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_609, type, sK280: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_610, type, sK281: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_611, type, sK282: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_612, type, sK283: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_613, type, sK284: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_614, type, sK285: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_615, type, sK286: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_616, type, sK287: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_617, type, sK288: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_618, type, sK289: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_619, type, sK290: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_620, type, sK291: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_621, type, sK292: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_622, type, sK293: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_623, type, sK294: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_624, type, sK295: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_625, type, sK296: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_626, type, sK297: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_627, type, sK298: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_628, type, sK299: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_629, type, sK300: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_630, type, sK301: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_631, type, sK302: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_632, type, sK303: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_633, type, sK304: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_634, type, sK305: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_635, type, sK306: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_636, type, sK307: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_637, type, sK308: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_638, type, sK309: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_639, type, sK310: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_640, type, sK311: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_641, type, sK312: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_642, type, sK313: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_643, type, sK314: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_644, type, sK315: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_645, type, sK316: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_646, type, sK317: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_647, type, sK318: !>[X0: $tType]:((X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_648, type, sK319: !>[X0: $tType]:((X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_649, type, sK320: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_650, type, sK321: !>[X0: $tType]:((tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_651, type, sK322: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_652, type, sK323: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_653, type, sK324: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > $o)).
% 92.33/13.69 thf(func_def_654, type, sK325: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_655, type, sK326: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_656, type, sK327: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_657, type, sK328: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_658, type, sK329: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_659, type, sK330: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_660, type, sK331: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_661, type, sK332: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_662, type, sK333: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_663, type, sK334: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_664, type, sK335: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_665, type, sK336: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_666, type, sK337: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_667, type, sK338: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_668, type, sK339: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_669, type, sK340: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_670, type, sK341: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_671, type, sK342: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_672, type, sK343: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_673, type, sK344: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_674, type, sK345: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_675, type, sK346: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_676, type, sK347: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_677, type, sK348: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_678, type, sK349: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_679, type, sK350: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_680, type, sK351: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_681, type, sK352: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_682, type, sK353: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_683, type, sK354: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_684, type, sK355: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_685, type, sK356: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_686, type, sK357: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_687, type, sK358: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_688, type, sK359: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_689, type, sK360: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_690, type, sK361: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_691, type, sK362: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_692, type, sK363: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_693, type, sK364: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_694, type, sK365: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_695, type, sK366: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_696, type, sK367: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_697, type, sK368: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_698, type, sK369: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_699, type, sK370: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_700, type, sK371: (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_701, type, sK372: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o).
% 92.33/13.69 thf(func_def_702, type, sK373: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_703, type, sK374: !>[X0: $tType]:(tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0 > $o)).
% 92.33/13.69 thf(func_def_704, type, sK375: !>[X0: $tType]:((X0 > $o) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_705, type, sK376: !>[X0: $tType]:((X0 > $o) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_706, type, sK377: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_707, type, sK378: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_708, type, sK379: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_709, type, sK380: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_710, type, sK381: !>[X0: $tType]:(X0)).
% 92.33/13.69 thf(func_def_711, type, sK382: !>[X0: $tType]:(X0)).
% 92.33/13.69 thf(func_def_712, type, sK383: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_713, type, sK384: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_714, type, sK385: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_715, type, sK386: !>[X0: $tType]:(X0 > X0)).
% 92.33/13.69 thf(func_def_716, type, sK387: !>[X0: $tType]:(X0 > tyop_2Eone_2Eone > X0)).
% 92.33/13.69 thf(func_def_717, type, sK388: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > $o > X0 > X1 > $o)).
% 92.33/13.69 thf(func_def_718, type, sK389: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X0 > X1 > $o)).
% 92.33/13.69 thf(func_def_719, type, sK390: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_720, type, sK391: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_721, type, sK392: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_722, type, sK393: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_723, type, sK394: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_724, type, sK395: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_725, type, sK396: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_726, type, sK397: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_727, type, sK398: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_728, type, sK399: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_729, type, sK400: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_730, type, sK401: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_731, type, sK402: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_732, type, sK403: !>[X0: $tType, X1: $tType]:(tyop_2Esum_2Esum(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_733, type, sK404: !>[X0: $tType]:((X0 > $o) > (tyop_2Eoption_2Eoption(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_734, type, sK405: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_735, type, sK406: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_736, type, sK407: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_737, type, sK408: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_738, type, sK409: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_739, type, sK410: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_740, type, sK411: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_741, type, sK412: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_742, type, sK413: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_743, type, sK414: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_744, type, sK415: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_745, type, sK416: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_746, type, sK417: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_747, type, sK418: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_748, type, sK419: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_749, type, sK420: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_750, type, sK421: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > X1)).
% 92.33/13.69 thf(func_def_751, type, sK422: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > X0)).
% 92.33/13.69 thf(func_def_752, type, sK423: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_753, type, sK424: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_754, type, sK425: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_755, type, sK426: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_756, type, sK427: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_757, type, sK428: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_758, type, sK429: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_759, type, sK430: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_760, type, sK431: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_761, type, sK432: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_762, type, sK433: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_763, type, sK434: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_764, type, sK435: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_765, type, sK436: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_766, type, sK437: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_767, type, sK438: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_768, type, sK439: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_769, type, sK440: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_770, type, sK441: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_771, type, sK442: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_772, type, sK443: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_773, type, sK444: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_774, type, sK445: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_775, type, sK446: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_776, type, sK447: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_777, type, sK448: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_778, type, sK449: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_779, type, sK450: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_780, type, sK451: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_781, type, sK452: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_782, type, sK453: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_783, type, sK454: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_784, type, sK455: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_785, type, sK456: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_786, type, sK457: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_787, type, sK458: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_788, type, sK459: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_789, type, sK460: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_790, type, sK461: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_791, type, sK462: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_792, type, sK463: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_793, type, sK464: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_794, type, sK465: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_795, type, sK466: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_796, type, sK467: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_797, type, sK468: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_798, type, sK469: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_799, type, sK470: !>[X0: $tType]:((tyop_2Enum_2Enum > X0) > (X0 > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_800, type, sK471: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_801, type, sK472: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_802, type, sK473: tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_803, type, sK474: !>[X0: $tType]:((X0 > X0) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_804, type, sK475: !>[X0: $tType]:((X0 > X0) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_805, type, sK476: !>[X0: $tType]:((X0 > X0) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_806, type, sK477: !>[X0: $tType]:((X0 > X0) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_807, type, sK478: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_808, type, sK479: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_809, type, sK480: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_810, type, sK481: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_811, type, sK482: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_812, type, sK483: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_813, type, sK484: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_814, type, sK485: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_815, type, sK486: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_816, type, sK487: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_817, type, sK488: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_818, type, sK489: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_819, type, sK490: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_820, type, sK491: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_821, type, sK492: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_822, type, sK493: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_823, type, sK494: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_824, type, sK495: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_825, type, sK496: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_826, type, sK497: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_827, type, sK498: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_828, type, sK499: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_829, type, sK500: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_830, type, sK501: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_831, type, sK502: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_832, type, sK503: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_833, type, sK504: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_834, type, sK505: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_835, type, sK506: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_836, type, sK507: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > X0)).
% 92.33/13.69 thf(func_def_837, type, sK508: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > X0)).
% 92.33/13.69 thf(func_def_838, type, sK509: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > X1)).
% 92.33/13.69 thf(func_def_839, type, sK510: !>[X0: $tType, X1: $tType]:((X0 > $o) > X1 > X0)).
% 92.33/13.69 thf(func_def_840, type, sK511: !>[X0: $tType, X1: $tType]:((X0 > $o) > X0 > X1)).
% 92.33/13.69 thf(func_def_841, type, sK512: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_842, type, sK513: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_843, type, sK514: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_844, type, sK515: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_845, type, sK516: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_846, type, sK517: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_847, type, sK518: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_848, type, sK519: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_849, type, sK520: !>[X0: $tType]:((X0 > $o) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_850, type, sK521: !>[X0: $tType]:((X0 > $o) > tyop_2Epair_2Eprod(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))) > X0)).
% 92.33/13.69 thf(func_def_851, type, sK522: !>[X0: $tType]:((X0 > $o) > (tyop_2Eoption_2Eoption(X0) > $o) > X0)).
% 92.33/13.69 thf(func_def_852, type, sK523: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_853, type, sK524: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_854, type, sK525: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_855, type, sK526: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_856, type, sK527: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_857, type, sK528: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_858, type, sK529: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_859, type, sK530: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_860, type, sK531: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_861, type, sK532: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_862, type, sK533: !>[X0: $tType]:((tyop_2Enum_2Enum > X0) > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_863, type, sK534: !>[X0: $tType]:((tyop_2Enum_2Enum > X0) > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_864, type, sK535: !>[X0: $tType]:((tyop_2Enum_2Enum > X0) > (tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_865, type, sK536: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_866, type, sK537: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_867, type, sK538: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_868, type, sK539: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_869, type, sK540: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_870, type, sK541: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_871, type, sK542: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_872, type, sK543: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_873, type, sK544: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_874, type, sK545: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_875, type, sK546: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_876, type, sK547: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_877, type, sK548: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_878, type, sK549: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_879, type, sK550: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_880, type, sK551: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > X1)).
% 92.33/13.69 thf(func_def_881, type, sK552: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_882, type, sK553: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > X1)).
% 92.33/13.69 thf(func_def_883, type, sK554: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > X0)).
% 92.33/13.69 thf(func_def_884, type, sK555: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > tyop_2Esum_2Esum(X0,X1))).
% 92.33/13.69 thf(func_def_885, type, sK556: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > X0)).
% 92.33/13.69 thf(func_def_886, type, sK557: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > X1)).
% 92.33/13.69 thf(func_def_887, type, sK558: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_888, type, sK559: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_889, type, sK560: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_890, type, sK561: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_891, type, sK562: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_892, type, sK563: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_893, type, sK564: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_894, type, sK565: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_895, type, sK566: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_896, type, sK567: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_897, type, sK568: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_898, type, sK569: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_899, type, sK570: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_900, type, sK571: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_901, type, sK572: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_902, type, sK573: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_903, type, sK574: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_904, type, sK575: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_905, type, sK576: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_906, type, sK577: !>[X0: $tType]:((X0 > $o) > $o > X0)).
% 92.33/13.69 thf(func_def_907, type, sK578: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_908, type, sK579: !>[X0: $tType]:($o > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_909, type, sK580: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_910, type, sK581: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > tyop_2Esum_2Esum(X0,X1))).
% 92.33/13.69 thf(func_def_911, type, sK582: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > X1)).
% 92.33/13.69 thf(func_def_912, type, sK583: !>[X0: $tType, X1: $tType]:((tyop_2Esum_2Esum(X0,X1) > $o) > X0)).
% 92.33/13.69 thf(func_def_913, type, sK584: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_914, type, sK585: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > X0)).
% 92.33/13.69 thf(func_def_915, type, sK586: !>[X0: $tType, X1: $tType]:((tyop_2Epair_2Eprod(X0,X1) > $o) > X1)).
% 92.33/13.69 thf(func_def_916, type, sK587: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_917, type, sK588: !>[X0: $tType]:(X0 > (X0 > tyop_2Enum_2Enum) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_918, type, sK589: !>[X0: $tType]:((X0 > tyop_2Enum_2Enum) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_919, type, sK590: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > tyop_2Epair_2Eprod(X0,X1))).
% 92.33/13.69 thf(func_def_920, type, sK591: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_921, type, sK592: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_922, type, sK593: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_923, type, sK594: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_924, type, sK595: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_925, type, sK596: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_926, type, sK597: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_927, type, sK598: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_928, type, sK599: !>[X0: $tType, X1: $tType]:((X0 > X1) > X1)).
% 92.33/13.69 thf(func_def_929, type, sK600: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_930, type, sK601: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_931, type, sK602: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_932, type, sK603: !>[X0: $tType, X1: $tType]:((X0 > X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_933, type, sK604: !>[X0: $tType, X1: $tType]:((X0 > X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_934, type, sK605: !>[X0: $tType, X1: $tType]:(($o > X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_935, type, sK606: !>[X0: $tType, X1: $tType]:(($o > X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_936, type, sK607: tyop_2Enum_2Enum > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > $o) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_937, type, sK608: !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_938, type, sK609: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_939, type, sK610: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_940, type, sK611: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_941, type, sK612: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_942, type, sK613: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_943, type, sK614: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_944, type, sK615: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_945, type, sK616: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_946, type, sK617: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_947, type, sK618: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_948, type, sK619: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_949, type, sK620: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_950, type, sK621: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_951, type, sK622: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_952, type, sK623: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_953, type, sK624: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_954, type, sK625: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_955, type, sK626: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_956, type, sK627: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_957, type, sK628: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_958, type, sK629: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_959, type, sK630: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_960, type, sK631: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_961, type, sK632: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_962, type, sK633: !>[X0: $tType, X1: $tType]:(X1 > tyop_2Ebool_2Eitself(X0) > X1)).
% 92.33/13.69 thf(func_def_963, type, sK634: !>[X0: $tType]:(X0 > X0 > $o > X0)).
% 92.33/13.69 thf(func_def_964, type, sK635: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > X0) > X0 > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_965, type, sK636: !>[X0: $tType]:((X0 > X0) > (X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_966, type, sK637: !>[X0: $tType, X1: $tType]:((tyop_2Enum_2Enum > X0 > (tyop_2Enum_2Enum > tyop_2Eind__type_2Erecspace(X0)) > (tyop_2Enum_2Enum > X1) > X1) > tyop_2Eind__type_2Erecspace(X0) > X1)).
% 92.33/13.69 thf(func_def_967, type, sK638: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_968, type, sK639: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_969, type, sK640: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_970, type, sK641: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_971, type, sK642: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_972, type, sK643: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_973, type, sK644: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_974, type, sK645: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_975, type, sK646: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_976, type, sK647: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_977, type, sK648: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_978, type, sK649: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_979, type, sK650: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_980, type, sK651: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > X0 > $o) > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_981, type, sK652: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_982, type, sK653: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_983, type, sK654: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_984, type, sK655: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_985, type, sK656: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_986, type, sK657: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_987, type, sK658: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_988, type, sK659: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_989, type, sK660: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_990, type, sK661: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_991, type, sK662: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_992, type, sK663: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_993, type, sK664: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_994, type, sK665: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_995, type, sK666: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_996, type, sK667: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_997, type, sK668: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_998, type, sK669: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_999, type, sK670: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1000, type, sK671: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0 > X2) > X1)).
% 92.33/13.69 thf(func_def_1001, type, sK672: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0 > X2) > X0)).
% 92.33/13.69 thf(func_def_1002, type, sK673: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0 > X2) > X1)).
% 92.33/13.69 thf(func_def_1003, type, sK674: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X0 > X2) > X0)).
% 92.33/13.69 thf(func_def_1004, type, sK675: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X2 > X0)).
% 92.33/13.69 thf(func_def_1005, type, sK676: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X2 > X1)).
% 92.33/13.69 thf(func_def_1006, type, sK677: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1007, type, sK678: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1008, type, sK679: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1009, type, sK680: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1010, type, sK681: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1011, type, sK682: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1012, type, sK683: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1013, type, sK684: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1014, type, sK685: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > X0 > X1)).
% 92.33/13.69 thf(func_def_1015, type, sK686: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > X0 > X1)).
% 92.33/13.69 thf(func_def_1016, type, sK687: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > X0 > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1017, type, sK688: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_1018, type, sK689: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1019, type, sK690: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1020, type, sK691: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1021, type, sK692: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1022, type, sK693: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1023, type, sK694: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1024, type, sK695: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1025, type, sK696: !>[X0: $tType, X1: $tType]:(X0 > (X1 > tyop_2Epair_2Eprod(X0,$o)) > X1)).
% 92.33/13.69 thf(func_def_1026, type, sK697: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_1027, type, sK698: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_1028, type, sK699: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_1029, type, sK700: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1 > X1) > X1)).
% 92.33/13.69 thf(func_def_1030, type, sK701: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1 > X0) > X0)).
% 92.33/13.69 thf(func_def_1031, type, sK702: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > X0)).
% 92.33/13.69 thf(func_def_1032, type, sK703: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1033, type, sK704: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1034, type, sK705: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1035, type, sK706: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1036, type, sK707: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1037, type, sK708: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > X1)).
% 92.33/13.69 thf(func_def_1038, type, sK709: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1039, type, sK710: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1040, type, sK711: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_1041, type, sK712: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1042, type, sK713: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1043, type, sK714: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1044, type, sK715: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1045, type, sK716: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_1046, type, sK717: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1047, type, sK718: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1048, type, sK719: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_1049, type, sK720: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1050, type, sK721: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1051, type, sK722: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1052, type, sK723: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1053, type, sK724: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 92.33/13.69 thf(func_def_1054, type, sK725: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 92.33/13.69 thf(func_def_1055, type, sK726: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0 > X0 > $o)).
% 92.33/13.69 thf(func_def_1056, type, sK727: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1057, type, sK728: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1058, type, sK729: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1059, type, sK730: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1060, type, sK731: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1061, type, sK732: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1062, type, sK733: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1063, type, sK734: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_1064, type, sK735: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_1065, type, sK736: !>[X0: $tType, X1: $tType]:(X0 > (X1 > tyop_2Epair_2Eprod(X0,$o)) > X1)).
% 92.33/13.69 thf(func_def_1066, type, sK737: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > X0 > X1)).
% 92.33/13.69 thf(func_def_1067, type, sK738: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > X1)).
% 92.33/13.69 thf(func_def_1068, type, sK739: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1069, type, sK740: !>[X0: $tType]:(X0 > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1070, type, sK741: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1071, type, sK742: !>[X0: $tType]:((X0 > $o) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1072, type, sK743: !>[X0: $tType]:((X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_1073, type, sK744: !>[X0: $tType]:((X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1074, type, sK745: !>[X0: $tType]:((X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > X0 > $o)).
% 92.33/13.69 thf(func_def_1075, type, sK746: !>[X0: $tType]:((X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1076, type, sK747: !>[X0: $tType]:((X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1077, type, sK748: !>[X0: $tType]:((X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1078, type, sK749: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > X0) > (tyop_2Enum_2Enum > X0 > X0) > X0 > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_1079, type, sK750: !>[X0: $tType, X1: $tType]:((X0 > X1) > X1 > tyop_2Eoption_2Eoption(X0) > X1)).
% 92.33/13.69 thf(func_def_1080, type, sK751: !>[X0: $tType]:(tyop_2Enum_2Enum > (X0 > X0) > X0 > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_1081, type, sK752: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > tyop_2Epair_2Eprod(X0,X1) > X2)).
% 92.33/13.69 thf(func_def_1082, type, sK753: !>[X0: $tType]:(tyop_2Enum_2Enum > (X0 > X0) > X0 > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_1083, type, sK754: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X1) > X1 > X0)).
% 92.33/13.69 thf(func_def_1084, type, sK755: !>[X0: $tType, X1: $tType]:((X0 > tyop_2Eoption_2Eoption(X1)) > tyop_2Eoption_2Eoption(X0) > X1 > X0)).
% 92.33/13.69 thf(func_def_1085, type, sK756: !>[X0: $tType, X1: $tType]:((X0 > tyop_2Eoption_2Eoption(X1)) > tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_1086, type, sK757: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1087, type, sK758: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1088, type, sK759: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_1089, type, sK760: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > (tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1090, type, sK761: !>[X0: $tType]:((tyop_2Enum_2Enum > X0 > $o) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1091, type, sK762: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1092, type, sK763: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1093, type, sK764: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1094, type, sK765: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1095, type, sK766: !>[X0: $tType]:((X0 > X0) > (X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1096, type, sK767: !>[X0: $tType]:((X0 > X0) > (X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1097, type, sK768: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1098, type, sK769: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1099, type, sK770: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1100, type, sK771: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1101, type, sK772: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1102, type, sK773: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1103, type, sK774: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1104, type, sK775: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1105, type, sK776: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1106, type, sK777: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1107, type, sK778: !>[X0: $tType, X1: $tType]:(X1 > tyop_2Eoption_2Eoption(X0) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1108, type, sK779: !>[X0: $tType]:(tyop_2Enum_2Enum > (tyop_2Enum_2Enum > X0) > X0 > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1109, type, sK780: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > X0) > (X0 > X1 > X0) > X2)).
% 92.33/13.69 thf(func_def_1110, type, sK781: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > X0) > (X0 > X1 > X0) > X0)).
% 92.33/13.69 thf(func_def_1111, type, sK782: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > X0) > (X0 > X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1112, type, sK783: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0) > (X1 > X0 > $o) > X1)).
% 92.33/13.69 thf(func_def_1113, type, sK784: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0) > (X1 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1114, type, sK785: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X0 > X1) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1115, type, sK786: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X1 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1116, type, sK787: !>[X0: $tType]:((X0 > X0 > $o) > tyop_2Enum_2Enum > X0 > X0 > X0)).
% 92.33/13.69 thf(func_def_1117, type, sK788: !>[X0: $tType]:(tyop_2Enum_2Enum > (X0 > X0) > (tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1118, type, sK789: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1) > (X0 > X1 > $o) > (X0 > X0 > $o) > X0 > X1)).
% 92.33/13.69 thf(func_def_1119, type, sK790: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1) > (X0 > X1 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1120, type, sK791: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1) > (X0 > X1 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1121, type, sK792: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_1122, type, sK793: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1123, type, sK794: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_1124, type, sK795: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_1125, type, sK796: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1126, type, sK797: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_1127, type, sK798: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_1128, type, sK799: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > (X0 > X0 > $o) > X0 > X0)).
% 92.33/13.69 thf(func_def_1129, type, sK800: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X2) > tyop_2Esum_2Esum(X0,X1) > X2)).
% 92.33/13.69 thf(func_def_1130, type, sK801: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1131, type, sK802: !>[X0: $tType, X1: $tType]:(X0 > (X0 > X1) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1132, type, sK803: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_1133, type, sK804: !>[X0: $tType, X1: $tType]:((X0 > tyop_2Eoption_2Eoption(X1)) > (X0 > tyop_2Eoption_2Eoption(X1)) > tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_1134, type, sK805: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 92.33/13.69 thf(func_def_1135, type, sK806: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 92.33/13.69 thf(func_def_1136, type, sK807: !>[X0: $tType]:(X0 > X0 > tyop_2Enum_2Enum > tyop_2Enum_2Enum > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1137, type, sK808: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > X0) > tyop_2Epair_2Eprod(X1,X2) > X0 > X1)).
% 92.33/13.69 thf(func_def_1138, type, sK809: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > X0) > tyop_2Epair_2Eprod(X1,X2) > X0 > X2)).
% 92.33/13.69 thf(func_def_1139, type, sK810: !>[X0: $tType, X1: $tType]:(tyop_2Eoption_2Eoption(X1) > (X1 > X0) > X0 > X1)).
% 92.33/13.69 thf(func_def_1140, type, sK811: !>[X0: $tType]:((X0 > X0 > $o) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0 > X0)).
% 92.33/13.69 thf(func_def_1141, type, sK812: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X1 > $o) > (X1 > X0 > $o) > ((X1 > X0) > X1 > X0) > X1 > X0)).
% 92.33/13.69 thf(func_def_1142, type, sK813: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X1 > $o) > (X1 > X0 > $o) > ((X1 > X0) > X1 > X0) > X1)).
% 92.33/13.69 thf(func_def_1143, type, sK814: !>[X0: $tType, X1: $tType]:(X1 > (X1 > X0) > (X1 > $o) > (X1 > X1 > $o) > (X1 > X0 > $o) > X1)).
% 92.33/13.69 thf(func_def_1144, type, sK815: !>[X0: $tType]:((tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum > (tyop_2Enum_2Enum > X0) > tyop_2Enum_2Enum)).
% 92.33/13.69 thf(func_def_1145, type, sK816: !>[X0: $tType, X1: $tType, X2: $tType]:(tyop_2Epair_2Eprod(X0,X1) > (X0 > X1 > X2) > (X0 > X1 > X2) > X0)).
% 92.33/13.69 thf(func_def_1146, type, sK817: !>[X0: $tType, X1: $tType, X2: $tType]:(tyop_2Epair_2Eprod(X0,X1) > (X0 > X1 > X2) > (X0 > X1 > X2) > X1)).
% 92.33/13.69 thf(func_def_1147, type, sK818: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > X0) > tyop_2Epair_2Eprod(X1,X2) > (X1 > X2 > X0) > X1)).
% 92.33/13.69 thf(func_def_1148, type, sK819: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > X0) > tyop_2Epair_2Eprod(X1,X2) > (X1 > X2 > X0) > X2)).
% 92.33/13.69 thf(func_def_1149, type, sK820: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1150, type, sK821: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1151, type, sK822: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1152, type, sK823: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1153, type, sK824: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X1) > X2 > X0)).
% 92.33/13.69 thf(func_def_1154, type, sK825: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > tyop_2Eoption_2Eoption(X0) > tyop_2Eoption_2Eoption(X1) > X2 > X1)).
% 92.33/13.69 thf(func_def_1155, type, sK826: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > X0 > (X0 > X1 > $o) > (X1 > X2 > $o) > X1)).
% 92.33/13.69 thf(func_def_1156, type, sK827: !>[X0: $tType, X1: $tType]:((X0 > X1) > tyop_2Eoption_2Eoption(X0) > (X0 > X1) > X0)).
% 92.33/13.69 thf(func_def_1157, type, sK828: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > $o) > tyop_2Esum_2Esum(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_1158, type, sK829: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > $o) > tyop_2Esum_2Esum(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_1159, type, sK830: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > $o) > tyop_2Epair_2Eprod(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_1160, type, sK831: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > $o) > tyop_2Epair_2Eprod(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_1161, type, sK832: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > $o) > tyop_2Epair_2Eprod(X0,X1) > X0)).
% 92.33/13.69 thf(func_def_1162, type, sK833: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > $o) > tyop_2Epair_2Eprod(X0,X1) > X1)).
% 92.33/13.69 thf(func_def_1163, type, sK834: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1164, type, sK835: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1165, type, sK836: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1166, type, sK837: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1167, type, sK838: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1 > X2) > tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0) > X0)).
% 92.33/13.69 thf(func_def_1168, type, sK839: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1 > X2) > tyop_2Eoption_2Eoption(X1) > tyop_2Eoption_2Eoption(X0) > X1)).
% 92.33/13.69 thf(func_def_1169, type, sK840: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > tyop_2Esum_2Esum(X0,X1) > (X1 > X2) > X1)).
% 92.33/13.69 thf(func_def_1170, type, sK841: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X2) > tyop_2Esum_2Esum(X0,X1) > (X0 > X2) > X0)).
% 92.33/13.69 thf(func_def_1171, type, sK842: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > tyop_2Epair_2Eprod(X1,X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > X1)).
% 92.33/13.69 thf(func_def_1172, type, sK843: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > tyop_2Epair_2Eprod(X1,X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1173, type, sK844: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > tyop_2Epair_2Eprod(X1,X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > X1)).
% 92.33/13.69 thf(func_def_1174, type, sK845: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X1,X0) > tyop_2Epair_2Eprod(X1,X0) > (X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1175, type, sK846: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X0,X1) > (X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1176, type, sK847: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X0,X1) > (X0 > X0 > $o) > (X0 > X0 > $o) > X1)).
% 92.33/13.69 thf(func_def_1177, type, sK848: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X0,X1) > (X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1178, type, sK849: !>[X0: $tType, X1: $tType]:(tyop_2Epair_2Eprod(X0,X1) > tyop_2Epair_2Eprod(X0,X1) > (X0 > X0 > $o) > (X0 > X0 > $o) > X1)).
% 92.33/13.69 thf(func_def_1179, type, sK850: tyop_2Emin_2Eind > tyop_2Emin_2Eind).
% 92.33/13.69 thf(func_def_1180, type, sK851: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum).
% 92.33/13.69 thf(func_def_1181, type, sK852: tyop_2Enum_2Enum > tyop_2Emin_2Eind).
% 92.33/13.69 thf(func_def_1182, type, sK853: tyop_2Eone_2Eone > $o).
% 92.33/13.69 thf(func_def_1184, type, sK855: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1185, type, sK856: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1186, type, sK857: !>[X0: $tType]:((X0 > $o) > X0)).
% 92.33/13.69 thf(func_def_1187, type, sK858: !>[X0: $tType]:((X0 > X0 > $o) > tyop_2Enum_2Enum > X0)).
% 92.33/13.69 thf(func_def_1188, type, sK859: (tyop_2Enum_2Enum > tyop_2Enum_2Enum) > tyop_2Enum_2Enum).
% 92.33/13.69 thf(f83470,plain,(
% 92.33/13.69 $false),
% 92.33/13.69 inference(avatar_sat_refutation,[],[f21865,f21870,f21874,f21878,f21883,f21917,f21921,f21926,f21930,f21934,f21938,f21943,f21952,f21956,f21960,f21979,f21988,f21992,f21996,f22000,f22004,f22008,f22012,f22017,f22021,f22025,f22029,f22034,f22038,f22050,f22054,f22058,f22062,f22066,f22070,f22081,f22085,f22089,f22093,f22097,f22101,f22105,f22110,f22115,f22119,f22123,f22127,f22131,f22135,f22139,f22143,f22147,f22151,f22172,f22208,f22212,f22216,f22220,f22224,f22228,f22232,f22236,f22240,f22244,f22248,f22252,f22261,f22288,f22292,f22296,f22300,f22304,f22308,f22313,f22318,f22323,f22328,f22333,f22337,f22341,f22346,f22372,f22397,f22401,f22405,f22409,f22413,f22417,f22421,f22425,f22429,f22433,f22437,f22441,f22445,f22449,f22453,f22457,f22461,f22520,f22589,f22593,f22597,f22601,f22605,f22609,f22613,f22617,f22621,f22625,f22629,f22633,f22637,f22641,f22651,f22655,f22659,f22663,f22667,f22671,f22675,f22679,f22683,f22687,f22691,f22695,f22699,f22703,f22707,f22773,f22782,f22786,f22790,f22794,f22798,f22802,f22806,f22810,f22814,f22863,f22869,f22873,f22878,f22883,f22888,f22892,f22896,f22900,f22904,f22908,f22912,f22916,f22920,f22924,f22928,f22932,f22936,f22941,f22947,f22953,f22957,f22961,f22965,f22969,f22973,f22977,f22981,f22986,f22990,f22994,f22999,f23018,f23080,f23085,f23090,f23141,f23171,f23175,f23179,f23183,f23187,f23191,f23195,f23199,f23203,f23207,f23211,f23215,f23219,f23223,f23227,f23231,f23337,f23490,f23494,f23498,f23502,f23506,f23510,f23514,f23518,f23522,f23526,f23530,f23534,f23538,f23542,f23546,f23550,f23554,f23559,f23563,f23567,f23571,f23575,f23579,f23583,f23587,f23591,f23595,f23599,f23605,f23609,f23613,f23617,f23621,f23625,f23629,f23633,f23637,f23641,f23646,f23650,f23654,f23659,f23663,f23667,f23671,f23675,f23679,f23683,f23687,f23695,f23699,f23703,f23707,f23711,f23715,f23719,f23723,f23728,f23732,f23737,f23741,f23745,f23749,f23753,f23757,f23761,f23765,f23769,f23773,f23777,f23785,f23789,f23793,f23797,f23801,f23805,f23809,f23813,f23817,f23821,f23826,f23830,f23834,f23838,f23842,f23846,f23850,f23854,f23858,f23862,f23866,f23871,f23875,f23879,f23883,f23887,f23891,f23895,f23899,f23903,f23907,f23911,f23916,f24289,f25831,f26520,f29068,f29072,f29076,f29081,f29088,f29173,f29175,f29177,f29181,f29183,f29185,f29187,f29189,f29193,f29195,f29199,f29201,f29203,f29205,f29207,f29209,f29211,f29213,f29215,f29217,f29219,f29221,f29223,f29225,f29227,f29229,f29231,f29233,f29235,f29237,f29239,f29241,f29244,f29247,f29249,f35214,f35536,f35571,f35577,f35582,f35591,f37354,f41171,f41175,f41241,f41307,f41335,f41339,f41556,f41587,f41591,f41595,f41599,f41603,f41607,f41611,f41615,f41619,f41623,f41653,f41657,f41661,f41665,f41669,f41673,f41677,f41681,f41686,f41691,f41695,f41699,f41703,f41707,f42074,f42226,f42230,f42234,f42238,f42242,f42246,f42250,f42254,f42258,f42262,f42266,f42270,f42274,f42278,f42282,f42286,f42290,f42294,f42298,f42302,f42306,f42310,f42314,f42318,f42322,f42326,f42330,f42334,f42338,f42342,f42346,f42350,f42354,f42358,f42362,f42390,f42394,f42398,f42402,f42406,f42410,f42414,f42418,f42422,f42426,f42434,f42438,f42442,f42446,f42703,f42960,f43217,f43425,f43629,f43886,f44090,f44094,f44098,f44143,f44147,f44151,f44155,f44159,f44163,f44167,f44171,f44175,f44179,f44249,f44253,f44257,f44261,f44265,f44269,f44273,f44277,f44281,f44285,f44289,f44293,f44297,f44301,f44305,f44309,f44313,f44317,f44321,f44325,f44329,f44363,f44367,f44371,f44375,f44379,f44383,f44387,f44391,f44395,f44399,f44404,f44408,f44412,f44416,f44420,f44424,f44428,f44432,f44436,f44440,f44444,f44454,f44458,f44462,f44466,f44470,f44474,f44478,f44482,f44486,f44490,f44494,f44498,f44502,f44506,f44510,f44514,f44518,f44522,f44526,f44530,f44534,f44545,f44549,f44553,f44557,f44561,f44565,f44569,f44573,f44577,f44581,f44589,f44593,f45467,f45819,f45962,f46106,f46250,f46482,f46669,f47031,f47700,f48127,f48717,f48721,f48725,f48729,f48734,f48739,f48746,f48749,f54295,f54299,f54303,f54307,f54311,f54315,f54319,f54323,f54327,f54331,f54388,f54392,f54396,f54400,f54404,f54408,f54412,f54416,f54420,f54424,f54499,f54503,f54507,f54511,f54515,f54519,f54523,f54528,f54532,f54536,f54595,f54600,f54604,f54608,f54612,f54616,f54620,f56558,f56645,f56936,f56940,f56944,f56948,f56952,f56956,f56960,f56964,f56968,f57031,f57035,f57039,f57043,f57047,f57051,f57055,f57059,f57063,f57067,f57130,f57134,f57138,f57142,f57146,f57707,f57795,f57799,f57803,f57807,f57811,f57815,f57819,f57823,f57827,f57831,f57836,f57840,f57844,f57848,f57852,f57856,f57860,f57864,f57868,f57872,f57876,f57918,f57922,f57926,f57930,f57934,f57938,f57942,f57946,f57950,f57954,f57959,f57963,f57967,f57971,f57975,f57979,f57983,f57987,f58431,f60228,f60302,f60306,f60310,f60314,f60318,f60389,f60393,f60397,f60401,f60405,f60409,f60413,f60417,f60421,f60425,f60430,f60434,f60438,f60442,f60446,f62004,f62181,f62185,f62189,f62193,f62197,f62201,f62205,f62210,f62214,f62219,f62225,f62232,f62236,f62240,f62244,f62248,f62252,f62256,f62260,f62264,f62268,f62272,f62276,f62280,f62284,f62288,f62292,f62296,f62300,f62305,f62309,f62313,f62317,f62321,f62384,f66628,f66831,f66835,f66892,f66896,f66900,f66904,f66908,f66912,f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% 92.33/13.69 thf(f83469,plain,(
% 92.33/13.69 ~spl854_937 | ~spl854_939),
% 92.33/13.69 inference(avatar_contradiction_clause,[],[f83468])).
% 92.33/13.69 thf(f83468,plain,(
% 92.33/13.69 $false | (~spl854_937 | ~spl854_939)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f83467])).
% 92.33/13.69 thf(f83467,plain,(
% 92.33/13.69 (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)) | (~spl854_937 | ~spl854_939)),
% 92.33/13.69 inference(superposition,[],[f82021,f83177])).
% 92.33/13.69 thf(f83177,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X1)))) ) | ~spl854_939),
% 92.33/13.69 inference(avatar_component_clause,[],[f83176])).
% 92.33/13.69 thf(f83176,plain,(
% 92.33/13.69 spl854_939 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_939])])).
% 92.33/13.69 thf(f82021,plain,(
% 92.33/13.69 ( ! [X0 : sK123] : ((vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP(sK123,sTfun(sK123,$o),vAPP(sTfun(sK123,$o),sTfun(sK123,sTfun(sK123,$o)),c_2Epred__set_2EDELETE(sK123),sK124),X0))) ) | ~spl854_937),
% 92.33/13.69 inference(avatar_component_clause,[],[f82020])).
% 92.33/13.69 thf(f82020,plain,(
% 92.33/13.69 spl854_937 <=> ! [X0 : sK123] : (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP(sK123,sTfun(sK123,$o),vAPP(sTfun(sK123,$o),sTfun(sK123,sTfun(sK123,$o)),c_2Epred__set_2EDELETE(sK123),sK124),X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_937])])).
% 92.33/13.69 thf(f83421,plain,(
% 92.33/13.69 spl854_969 | ~spl854_9 | ~spl854_160),
% 92.33/13.69 inference(avatar_split_clause,[],[f32094,f22950,f21928,f83419])).
% 92.33/13.69 thf(f83419,plain,(
% 92.33/13.69 spl854_969 <=> ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0)),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_969])])).
% 92.33/13.69 thf(f21928,plain,(
% 92.33/13.69 spl854_9 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = X0)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_9])])).
% 92.33/13.69 thf(f22950,plain,(
% 92.33/13.69 spl854_160 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_160])])).
% 92.33/13.69 thf(f32094,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0)),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0)) ) | (~spl854_9 | ~spl854_160)),
% 92.33/13.69 inference(forward_demodulation,[],[f18488,f29755])).
% 92.33/13.69 thf(f29755,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (~spl854_9 | ~spl854_160)),
% 92.33/13.69 inference(forward_demodulation,[],[f29754,f21929])).
% 92.33/13.69 thf(f21929,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = X0)) ) | ~spl854_9),
% 92.33/13.69 inference(avatar_component_clause,[],[f21928])).
% 92.33/13.69 thf(f29754,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ~spl854_160),
% 92.33/13.69 inference(forward_demodulation,[],[f13567,f22952])).
% 92.33/13.69 thf(f22952,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_160),
% 92.33/13.69 inference(avatar_component_clause,[],[f22950])).
% 92.33/13.69 thf(f13567,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9168,f13512,f9122])).
% 92.33/13.69 thf(f9122,plain,(
% 92.33/13.69 (c_2Enum_2E0 = vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),
% 92.33/13.69 inference(cnf_transformation,[],[f379])).
% 92.33/13.69 thf(f379,axiom,(
% 92.33/13.69 (c_2Enum_2E0 = vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EZERO__DEF)).
% 92.33/13.69 thf(f13512,plain,(
% 92.33/13.69 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = c_2Earithmetic_2EZERO)),
% 92.33/13.69 inference(definition_unfolding,[],[f9120,f9122])).
% 92.33/13.69 thf(f9120,plain,(
% 92.33/13.69 (c_2Enum_2E0 = c_2Earithmetic_2EZERO)),
% 92.33/13.69 inference(cnf_transformation,[],[f916])).
% 92.33/13.69 thf(f916,axiom,(
% 92.33/13.69 (c_2Enum_2E0 = c_2Earithmetic_2EZERO)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EALT__ZERO)).
% 92.33/13.69 thf(f9168,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,c_2Enum_2E0))),
% 92.33/13.69 inference(cnf_transformation,[],[f2034])).
% 92.33/13.69 thf(f2034,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,$o)),sCOMB,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,sTfun($o,$o))),bCOMB,c_2Ebool_2E_2F_5C),c_2Edivides_2Eprime)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,c_2Enum_2E0))),
% 92.33/13.69 inference(fool_elimination,[],[f2033])).
% 92.33/13.69 thf(f2033,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X1 : tyop_2Enum_2Enum] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0)),X1)))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f1462])).
% 92.33/13.69 thf(f1462,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X110 : tyop_2Enum_2Enum] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X110)),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X136)),X110)))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EPRIMES__def)).
% 92.33/13.69 thf(f18488,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0)),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f17958,f13567])).
% 92.33/13.69 thf(f17958,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0)) )),
% 92.33/13.69 inference(equality_proxy_clausification,[],[f17957])).
% 92.33/13.69 thf(f17957,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f13906])).
% 92.33/13.69 thf(f13906,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9623,f13538,f9122])).
% 92.33/13.69 thf(f13538,plain,(
% 92.33/13.69 (c_2Ebit_2ELOG2 = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.33/13.69 inference(definition_unfolding,[],[f9126,f13512])).
% 92.33/13.69 thf(f9126,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Ebit_2ELOG2)),
% 92.33/13.69 inference(cnf_transformation,[],[f1709])).
% 92.33/13.69 thf(f1709,axiom,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Ebit_2ELOG2)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ELOG2__def)).
% 92.33/13.69 thf(f9623,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOG2,X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5497])).
% 92.33/13.69 thf(f5497,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOG2,X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2272])).
% 92.33/13.69 thf(f2272,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0))) => ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOG2,X0)),X0)))),
% 92.33/13.69 inference(fool_elimination,[],[f2271])).
% 92.33/13.69 thf(f2271,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(c_2Enum_2E0 = X0)) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOG2,X0)),X0))),
% 92.33/13.69 inference(rectify,[],[f1830])).
% 92.33/13.69 thf(f1830,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(c_2Enum_2E0 = X136)) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOG2,X136)),X136))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__LOG2)).
% 92.33/13.69 thf(f83417,plain,(
% 92.33/13.69 spl854_968),
% 92.33/13.69 inference(avatar_split_clause,[],[f19731,f83415])).
% 92.33/13.69 thf(f83415,plain,(
% 92.33/13.69 spl854_968 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X1) != X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_968])])).
% 92.33/13.69 thf(f19731,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X1) != X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19730,f9293])).
% 92.33/13.69 thf(f9293,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = X0)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4868])).
% 92.33/13.69 thf(f4868,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = X0)),
% 92.33/13.69 inference(rectify,[],[f915])).
% 92.33/13.69 thf(f915,axiom,(
% 92.33/13.69 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X8) = X8)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENUMERAL__DEF)).
% 92.33/13.69 thf(f19730,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X1)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19729,f9293])).
% 92.33/13.69 thf(f19729,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19728,f9293])).
% 92.33/13.69 thf(f19728,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14984,f9293])).
% 92.33/13.69 thf(f14984,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11359,f9122,f9121])).
% 92.33/13.69 thf(f9121,plain,(
% 92.33/13.69 (c_2Earithmetic_2E_2A = c_2Enumeral_2Einternal__mult)),
% 92.33/13.69 inference(cnf_transformation,[],[f1375])).
% 92.33/13.69 thf(f1375,axiom,(
% 92.33/13.69 (c_2Earithmetic_2E_2A = c_2Enumeral_2Einternal__mult)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Einternal__mult__def)).
% 92.33/13.69 thf(f11359,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7686])).
% 92.33/13.69 thf(f7686,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) != X1)) & (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) = X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) != X1)) & (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))))),
% 92.33/13.69 inference(flattening,[],[f7685])).
% 92.33/13.69 thf(f7685,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1)) | ((c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) != X1))) & (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) = X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1)) | ((c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) != X1))) & (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f5219])).
% 92.33/13.69 thf(f5219,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1)) <=> ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) = X1))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1)) <=> ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = X1))))),
% 92.33/13.69 inference(rectify,[],[f1183])).
% 92.33/13.69 thf(f1183,axiom,(
% 92.33/13.69 ! [X68 : tyop_2Enum_2Enum,X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X68) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X19))),X18)) <=> ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X68)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X19)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X68)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X19))) = X18))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X19))),X18) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X68)) <=> ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X68)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X19)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X68)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X19))) = X18))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV)).
% 92.33/13.69 thf(f83413,plain,(
% 92.33/13.69 spl854_498 | spl854_967 | ~spl854_221),
% 92.33/13.69 inference(avatar_split_clause,[],[f24776,f23597,f83410,f48711])).
% 92.33/13.69 thf(f48711,plain,(
% 92.33/13.69 spl854_498 <=> ! [X0 : $o] : ($false = X0)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_498])])).
% 92.33/13.69 thf(f83410,plain,(
% 92.33/13.69 spl854_967 <=> ($true = vAPP(sTfun($o,$o),$o,sK526($o),vNOT))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_967])])).
% 92.33/13.69 thf(f23597,plain,(
% 92.33/13.69 spl854_221 <=> ! [X0 : $tType,X5 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK526(X0),X1))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_221])])).
% 92.33/13.69 thf(f24776,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK526($o),vNOT)) | ($false = X0)) ) | ~spl854_221),
% 92.33/13.69 inference(not_proxy_clausification,[],[f24775])).
% 92.33/13.69 thf(f24775,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK526($o),vNOT)) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_221),
% 92.33/13.69 inference(not_proxy_clausification,[],[f24711])).
% 92.33/13.69 thf(f24711,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK526($o),vNOT))) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_221),
% 92.33/13.69 inference(primitive_instantiation,[],[f23598])).
% 92.33/13.69 thf(f23598,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > $o,X5 : X0] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK526(X0),X1))) | ($true = vAPP(X0,$o,X1,X5))) ) | ~spl854_221),
% 92.33/13.69 inference(avatar_component_clause,[],[f23597])).
% 92.33/13.69 thf(f83408,plain,(
% 92.33/13.69 spl854_966),
% 92.33/13.69 inference(avatar_split_clause,[],[f19719,f83406])).
% 92.33/13.69 thf(f83406,plain,(
% 92.33/13.69 spl854_966 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),X1) != X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_966])])).
% 92.33/13.69 thf(f19719,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),X1) != X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19718,f9293])).
% 92.33/13.69 thf(f19718,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),X1)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19717,f9293])).
% 92.33/13.69 thf(f19717,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19716,f9293])).
% 92.33/13.69 thf(f19716,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14981,f9293])).
% 92.33/13.69 thf(f14981,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11362,f9122,f9121])).
% 92.33/13.69 thf(f11362,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7686])).
% 92.33/13.69 thf(f83404,plain,(
% 92.33/13.69 spl854_965),
% 92.33/13.69 inference(avatar_split_clause,[],[f18686,f83402])).
% 92.33/13.69 thf(f83402,plain,(
% 92.33/13.69 spl854_965 <=> ! [X0 : $tType,X1 : X0] : (vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_965])])).
% 92.33/13.69 thf(f18686,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14088,f17793])).
% 92.33/13.69 thf(f17793,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14043])).
% 92.33/13.69 thf(f14043,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9804,f9122])).
% 92.33/13.69 thf(f9804,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),c_2Enum_2E0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f2448])).
% 92.33/13.69 thf(f2448,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),c_2Enum_2E0)))),
% 92.33/13.69 inference(fool_elimination,[],[f2447])).
% 92.33/13.69 thf(f2447,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f1748])).
% 92.33/13.69 thf(f1748,axiom,(
% 92.33/13.69 ! [X35 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X35),c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__ZERO)).
% 92.33/13.69 thf(f14088,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9879,f13541,f13541])).
% 92.33/13.69 thf(f13541,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((c_2Epred__set_2EEMPTY(X0) = vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9355,f9976,f13520])).
% 92.33/13.69 thf(f13520,plain,(
% 92.33/13.69 (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9143,f13519,f9122])).
% 92.33/13.69 thf(f13519,plain,(
% 92.33/13.69 (c_2Earithmetic_2EODD = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9124,f9122])).
% 92.33/13.69 thf(f9124,plain,(
% 92.33/13.69 (c_2Earithmetic_2EODD = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,c_2Enum_2E0))),
% 92.33/13.69 inference(cnf_transformation,[],[f1789])).
% 92.33/13.69 thf(f1789,axiom,(
% 92.33/13.69 (c_2Earithmetic_2EODD = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT0__ODD)).
% 92.33/13.69 thf(f9143,plain,(
% 92.33/13.69 (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0))),
% 92.33/13.69 inference(cnf_transformation,[],[f2030])).
% 92.33/13.69 thf(f2030,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))) & (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0))),
% 92.33/13.69 inference(fool_elimination,[],[f2029])).
% 92.33/13.69 thf(f2029,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) <=> vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))) & (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f927])).
% 92.33/13.69 thf(f927,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) <=> vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X136))) & (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD)).
% 92.33/13.69 thf(f9976,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType] : ((kCOMB = c_2Ecombin_2EK(X0,X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f2546])).
% 92.33/13.69 thf(f2546,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType] : (kCOMB = c_2Ecombin_2EK(X0,X1))),
% 92.33/13.69 inference(fool_elimination,[],[f2545])).
% 92.33/13.69 thf(f2545,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType] : (c_2Ecombin_2EK(X0,X1) = (^[X2 : X0, X3 : X1] : (X2)))),
% 92.33/13.69 inference(rectify,[],[f314])).
% 92.33/13.69 thf(f314,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType] : (c_2Ecombin_2EK(X0,X5) = (^[X8 : X0, X18 : X5] : (X8)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EK__DEF)).
% 92.33/13.69 thf(f9355,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((c_2Epred__set_2EEMPTY(X0) = vAPP($o,sTfun(X0,$o),kCOMB,c_2Ebool_2EF))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f2082])).
% 92.33/13.69 thf(f2082,plain,(
% 92.33/13.69 ! [X0 : $tType] : (c_2Epred__set_2EEMPTY(X0) = vAPP($o,sTfun(X0,$o),kCOMB,c_2Ebool_2EF))),
% 92.33/13.69 inference(fool_elimination,[],[f2081])).
% 92.33/13.69 thf(f2081,plain,(
% 92.33/13.69 ! [X0 : $tType] : (c_2Epred__set_2EEMPTY(X0) = (^[X1 : X0] : (c_2Ebool_2EF)))),
% 92.33/13.69 inference(rectify,[],[f1842])).
% 92.33/13.69 thf(f1842,axiom,(
% 92.33/13.69 ! [X0 : $tType] : (c_2Epred__set_2EEMPTY(X0) = (^[X8 : X0] : (c_2Ebool_2EF)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__DEF)).
% 92.33/13.69 thf(f9879,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0] : ((c_2Epred__set_2EEMPTY(X0) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),c_2Epred__set_2EEMPTY(X0)),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4982])).
% 92.33/13.69 thf(f4982,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0] : (c_2Epred__set_2EEMPTY(X0) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),c_2Epred__set_2EEMPTY(X0)),X1))),
% 92.33/13.69 inference(rectify,[],[f1978])).
% 92.33/13.69 thf(f1978,axiom,(
% 92.33/13.69 ! [X0 : $tType,X8 : X0] : (c_2Epred__set_2EEMPTY(X0) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),c_2Epred__set_2EEMPTY(X0)),X8))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__DELETE)).
% 92.33/13.69 thf(f83400,plain,(
% 92.33/13.69 spl854_964),
% 92.33/13.69 inference(avatar_split_clause,[],[f18577,f83398])).
% 92.33/13.69 thf(f83398,plain,(
% 92.33/13.69 spl854_964 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X2) | (X0 = X2) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_964])])).
% 92.33/13.69 thf(f18577,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X2) | (X0 = X2) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14002,f18124])).
% 92.33/13.69 thf(f18124,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(forward_demodulation,[],[f18123,f13569])).
% 92.33/13.69 thf(f13569,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9170,f13512,f9122])).
% 92.33/13.69 thf(f9170,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,c_2Enum_2E0))),
% 92.33/13.69 inference(cnf_transformation,[],[f4842])).
% 92.33/13.69 thf(f4842,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f931])).
% 92.33/13.69 thf(f931,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EFACT)).
% 92.33/13.69 thf(f18123,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 inference(forward_demodulation,[],[f13629,f18122])).
% 92.33/13.69 thf(f18122,plain,(
% 92.33/13.69 ( ! [X26 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18121,f13563])).
% 92.33/13.69 thf(f13563,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9163,f13512,f13512])).
% 92.33/13.69 thf(f9163,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Earithmetic_2EZERO))),
% 92.33/13.69 inference(cnf_transformation,[],[f4841])).
% 92.33/13.69 thf(f4841,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Earithmetic_2EZERO))),
% 92.33/13.69 inference(rectify,[],[f1376])).
% 92.33/13.69 thf(f1376,axiom,(
% 92.33/13.69 ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137))) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Earithmetic_2EZERO))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__suc)).
% 92.33/13.69 thf(f18121,plain,(
% 92.33/13.69 ( ! [X26 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13613,f13548])).
% 92.33/13.69 thf(f13548,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9125,f9122,f13512])).
% 92.33/13.69 thf(f9125,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),
% 92.33/13.69 inference(cnf_transformation,[],[f940])).
% 92.33/13.69 thf(f940,axiom,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE)).
% 92.33/13.69 thf(f13613,plain,(
% 92.33/13.69 ( ! [X26 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9208,f13512,f9122])).
% 92.33/13.69 thf(f9208,plain,(
% 92.33/13.69 ( ! [X26 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),c_2Enum_2E0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6597])).
% 92.33/13.69 thf(f6597,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0) = $true) & (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0)) = $true) & ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1)) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X1)) & ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X3)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X3),X2)) & ! [X4 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),X4)) | (c_2Enum_2E0 != X4)) & ((c_2Enum_2E0 = X4) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),X4)))) & ! [X5 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X5),c_2Enum_2E0)) & ! [X6 : tyop_2Enum_2Enum,X7 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X6)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X7)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X6),X7)) & ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X8)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X8),c_2Earithmetic_2EZERO)) & ! [X9 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),X9)) & ! [X10 : tyop_2Enum_2Enum,X11 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X10)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X11)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X11),X10)) & ! [X12 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X12)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X12)) & ! [X13 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,c_2Enum_2E0),X13)) & ! [X14 : tyop_2Enum_2Enum,X15 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X14)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X15)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X14),X15)) & ! [X16 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X16)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X16)) & ! [X17 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X17),c_2Enum_2E0)) & ! [X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19)) | (X18 != X19)) & ((X18 = X19) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19)))) & ! [X20 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X20)) | (c_2Earithmetic_2EZERO != X20)) & ((c_2Earithmetic_2EZERO = X20) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X20)))) & ! [X21 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X21)) | (c_2Earithmetic_2EZERO != X21)) & ((c_2Earithmetic_2EZERO = X21) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X21)))) & ! [X22 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X22)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X22))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Enum_2E0)) & ! [X23 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X23)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X23))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & ! [X24 : tyop_2Enum_2Enum,X25 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X24)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X25)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X24),X25))) & ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),c_2Enum_2E0)) & ! [X27 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)))) & ! [X28 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28)))) & ! [X29 : tyop_2Enum_2Enum,X30 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X29)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X30)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X29),X30))) & ! [X31 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X31),c_2Enum_2E0) = X31) & ! [X32 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X32)) & ! [X33 : tyop_2Enum_2Enum,X34 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X33)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X34)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X33),X34))) & ! [X35 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X35),c_2Enum_2E0)) & ! [X36 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X36)) & ! [X37 : tyop_2Enum_2Enum,X38 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X37)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X38)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X37),X38)))) & ! [X39 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),c_2Enum_2E0) = X39) & ! [X40 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X40) = X40)),
% 92.33/13.69 inference(nnf_transformation,[],[f2038])).
% 92.33/13.69 thf(f2038,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0) = $true) & (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0)) = $true) & ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1)) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X1)) & ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X3)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X3),X2)) & ! [X4 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),X4)) <=> (c_2Enum_2E0 = X4)) & ! [X5 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X5),c_2Enum_2E0)) & ! [X6 : tyop_2Enum_2Enum,X7 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X6)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X7)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X6),X7)) & ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X8)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X8),c_2Earithmetic_2EZERO)) & ! [X9 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),X9)) & ! [X10 : tyop_2Enum_2Enum,X11 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X10)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X11)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X11),X10)) & ! [X12 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X12)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X12)) & ! [X13 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,c_2Enum_2E0),X13)) & ! [X14 : tyop_2Enum_2Enum,X15 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X14)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X15)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X14),X15)) & ! [X16 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X16)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X16)) & ! [X17 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X17),c_2Enum_2E0)) & ! [X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19)) <=> (X18 = X19)) & ! [X20 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X20)) <=> (c_2Earithmetic_2EZERO = X20)) & ! [X21 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X21)) <=> (c_2Earithmetic_2EZERO = X21)) & ! [X22 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X22)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X22))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Enum_2E0)) & ! [X23 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X23)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X23))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & ! [X24 : tyop_2Enum_2Enum,X25 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X24)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X25)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X24),X25))) & ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),c_2Enum_2E0)) & ! [X27 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)))) & ! [X28 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28)))) & ! [X29 : tyop_2Enum_2Enum,X30 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X29)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X30)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X29),X30))) & ! [X31 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X31),c_2Enum_2E0) = X31) & ! [X32 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X32)) & ! [X33 : tyop_2Enum_2Enum,X34 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X33)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X34)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X33),X34))) & ! [X35 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X35),c_2Enum_2E0)) & ! [X36 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X36)) & ! [X37 : tyop_2Enum_2Enum,X38 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X37)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X38)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X37),X38)))) & ! [X39 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),c_2Enum_2E0) = X39) & ! [X40 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X40) = X40)),
% 92.33/13.69 inference(fool_elimination,[],[f2037])).
% 92.33/13.69 thf(f2037,plain,(
% 92.33/13.69 vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0)) & ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1)) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X1)) & ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X3)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X3),X2)) & ! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),X4) <=> (c_2Enum_2E0 = X4)) & ! [X5 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X5),c_2Enum_2E0)) & ! [X6 : tyop_2Enum_2Enum,X7 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X6)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X7)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X6),X7)) & ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X8)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X8),c_2Earithmetic_2EZERO)) & ! [X9 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),X9)) & ! [X10 : tyop_2Enum_2Enum,X11 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X10)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X11)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X11),X10)) & ! [X12 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X12)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X12)) & ! [X13 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,c_2Enum_2E0),X13)) & ! [X14 : tyop_2Enum_2Enum,X15 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X14)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X15)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X14),X15)) & ! [X16 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X16)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X16)) & ! [X17 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X17),c_2Enum_2E0)) & ! [X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19)) <=> (X18 = X19)) & ! [X20 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X20)) <=> (c_2Earithmetic_2EZERO = X20)) & ! [X21 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X21)) <=> (c_2Earithmetic_2EZERO = X21)) & ! [X22 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X22)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X22))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Enum_2E0)) & ! [X23 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X23)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X23))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & ! [X24 : tyop_2Enum_2Enum,X25 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X24)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X25)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X24),X25))) & ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),c_2Enum_2E0)) & ! [X27 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)))) & ! [X28 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28)))) & ! [X29 : tyop_2Enum_2Enum,X30 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X29)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X30)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X29),X30))) & ! [X31 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X31),c_2Enum_2E0) = X31) & ! [X32 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X32)) & ! [X33 : tyop_2Enum_2Enum,X34 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X33)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X34)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X33),X34))) & ! [X35 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X35),c_2Enum_2E0)) & ! [X36 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X36)) & ! [X37 : tyop_2Enum_2Enum,X38 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X37)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X38)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X37),X38)))) & ! [X39 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),c_2Enum_2E0) = X39) & ! [X40 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X40) = X40)),
% 92.33/13.69 inference(rectify,[],[f1377])).
% 92.33/13.69 thf(f1377,axiom,(
% 92.33/13.69 vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0)) & ! [X391 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X391)) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X391)) & ! [X390 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X390)) = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X390)) & ! [X388 : tyop_2Enum_2Enum,X389 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X388)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X389)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X389),X388)) & ! [X387 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),X387) <=> (c_2Enum_2E0 = X387)) & ! [X386 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X386),c_2Enum_2E0)) & ! [X384 : tyop_2Enum_2Enum,X385 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X384)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X385)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X384),X385)) & ! [X383 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X383)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X383),c_2Earithmetic_2EZERO)) & ! [X382 : tyop_2Enum_2Enum] : (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),X382)) & ! [X380 : tyop_2Enum_2Enum,X381 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X380)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X381)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X381),X380)) & ! [X379 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X379)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X379)) & ! [X378 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,c_2Enum_2E0),X378)) & ! [X376 : tyop_2Enum_2Enum,X377 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X376)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X377)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X376),X377)) & ! [X375 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X375)) = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),X375)) & ! [X374 : tyop_2Enum_2Enum] : (c_2Ebool_2EF = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X374),c_2Enum_2E0)) & ! [X372 : tyop_2Enum_2Enum,X373 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X372) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X373)) <=> (X372 = X373)) & ! [X371 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X371)) <=> (c_2Earithmetic_2EZERO = X371)) & ! [X370 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X370)) <=> (c_2Earithmetic_2EZERO = X370)) & ! [X369 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X369)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X369))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Enum_2E0)) & ! [X368 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X368)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X368))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & ! [X366 : tyop_2Enum_2Enum,X367 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X366)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X367)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X366),X367))) & ! [X365 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X365),c_2Enum_2E0)) & ! [X364 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X364)))) & ! [X363 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X363)))) & ! [X352 : tyop_2Enum_2Enum,X362 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X352)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X362)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X352),X362))) & ! [X361 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X361),c_2Enum_2E0) = X361) & ! [X360 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X360)) & ! [X306 : tyop_2Enum_2Enum,X350 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X306)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X350)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X306),X350))) & ! [X359 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X359),c_2Enum_2E0)) & ! [X303 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X303)) & ! [X135 : tyop_2Enum_2Enum,X307 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X135),X307)))) & ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X137),c_2Enum_2E0) = X137) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X136) = X136)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__distrib)).
% 92.33/13.69 thf(f13629,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9244,f13512,f9122])).
% 92.33/13.69 thf(f9244,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X2),c_2Enum_2E0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4853])).
% 92.33/13.69 thf(f4853,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1))) & ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X2),c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f922])).
% 92.33/13.69 thf(f922,axiom,(
% 92.33/13.69 ! [X27 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X27),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X27),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X27),X135))) & ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X134),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEXP)).
% 92.33/13.69 thf(f14002,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X2) | (X0 = X2) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9750,f13512])).
% 92.33/13.69 thf(f9750,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X2) | (X0 = X2) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6794])).
% 92.33/13.69 thf(f6794,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) & ((! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X2) | (X0 = X2) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK185])],[f6792,f6793])).
% 92.33/13.69 thf(f6793,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) & (X0 != X1) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) => ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6792,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ? [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) & (X0 != X1) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) & ((! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X2) | (X0 = X2) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))))),
% 92.33/13.69 inference(rectify,[],[f6791])).
% 92.33/13.69 thf(f6791,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ? [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) & (X0 != X1) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) & ((! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))))),
% 92.33/13.69 inference(flattening,[],[f6790])).
% 92.33/13.69 thf(f6790,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (? [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) & (X0 != X1) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))))) & ((! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6384])).
% 92.33/13.69 thf(f6384,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) <=> (! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f83396,plain,(
% 92.33/13.69 spl854_963),
% 92.33/13.69 inference(avatar_split_clause,[],[f18374,f83394])).
% 92.33/13.69 thf(f83394,plain,(
% 92.33/13.69 spl854_963 <=> ! [X0 : $tType,X3 : X0 > tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_963])])).
% 92.33/13.69 thf(f18374,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : X0 > tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18373,f18297])).
% 92.33/13.69 thf(f18297,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true)))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18296,f18174])).
% 92.33/13.69 thf(f18174,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Eone_2Eone] : ((vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true)) = X0)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13662,f13591])).
% 92.33/13.69 thf(f13591,plain,(
% 92.33/13.69 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9236,f9122])).
% 92.33/13.69 thf(f9236,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0) = $true)),
% 92.33/13.69 inference(cnf_transformation,[],[f6597])).
% 92.33/13.69 thf(f13662,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Eone_2Eone] : ((vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0)) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9285,f13522])).
% 92.33/13.69 thf(f13522,plain,(
% 92.33/13.69 (c_2Eone_2Eone = vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.33/13.69 inference(definition_unfolding,[],[f9133,f9976,f13514])).
% 92.33/13.69 thf(f13514,plain,(
% 92.33/13.69 (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(definition_unfolding,[],[f9141,f9122])).
% 92.33/13.69 thf(f9141,plain,(
% 92.33/13.69 (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0))),
% 92.33/13.69 inference(cnf_transformation,[],[f2028])).
% 92.33/13.69 thf(f2028,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) & (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0))),
% 92.33/13.69 inference(fool_elimination,[],[f2027])).
% 92.33/13.69 thf(f2027,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) <=> vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) & (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f926])).
% 92.33/13.69 thf(f926,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) <=> vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X136))) & (c_2Ebool_2ET = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN)).
% 92.33/13.69 thf(f9133,plain,(
% 92.33/13.69 (c_2Eone_2Eone = vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),kCOMB,c_2Ebool_2ET)))),
% 92.33/13.69 inference(cnf_transformation,[],[f2012])).
% 92.33/13.69 thf(f2012,plain,(
% 92.33/13.69 (c_2Eone_2Eone = vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),kCOMB,c_2Ebool_2ET)))),
% 92.33/13.69 inference(fool_elimination,[],[f2011])).
% 92.33/13.69 thf(f2011,plain,(
% 92.33/13.69 (c_2Eone_2Eone = vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),(^[X0 : tyop_2Eone_2Eone] : (c_2Ebool_2ET))))),
% 92.33/13.69 inference(rectify,[],[f392])).
% 92.33/13.69 thf(f392,axiom,(
% 92.33/13.69 (c_2Eone_2Eone = vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),(^[X8 : tyop_2Eone_2Eone] : (c_2Ebool_2ET))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eone_2Eone__DEF)).
% 92.33/13.69 thf(f9285,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Eone_2Eone] : ((c_2Eone_2Eone = X0)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4860])).
% 92.33/13.69 thf(f4860,plain,(
% 92.33/13.69 ! [X0 : tyop_2Eone_2Eone] : (c_2Eone_2Eone = X0)),
% 92.33/13.69 inference(rectify,[],[f395])).
% 92.33/13.69 thf(f395,axiom,(
% 92.33/13.69 ! [X29 : tyop_2Eone_2Eone] : (c_2Eone_2Eone = X29)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eone_2Eone)).
% 92.33/13.69 thf(f18296,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13709,f18095])).
% 92.33/13.69 thf(f18095,plain,(
% 92.33/13.69 ($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 inference(not_proxy_clausification,[],[f13592])).
% 92.33/13.69 thf(f13592,plain,(
% 92.33/13.69 ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 inference(definition_unfolding,[],[f9235,f13519,f9122])).
% 92.33/13.69 thf(f9235,plain,(
% 92.33/13.69 (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Enum_2E0)) = $true)),
% 92.33/13.69 inference(cnf_transformation,[],[f6597])).
% 92.33/13.69 thf(f13709,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9368,f13523,f9976,f13520])).
% 92.33/13.69 thf(f13523,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((c_2Eoption_2ENONE(X0) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9314,f13522])).
% 92.33/13.69 thf(f9314,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((c_2Eoption_2ENONE(X0) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),c_2Eone_2Eone)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f706])).
% 92.33/13.69 thf(f706,axiom,(
% 92.33/13.69 ! [X0 : $tType] : (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),c_2Eone_2Eone)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2ENONE__DEF)).
% 92.33/13.69 thf(f9368,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : ((c_2Eoption_2ENONE(X0) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),kCOMB,c_2Ebool_2EF)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f2108])).
% 92.33/13.69 thf(f2108,plain,(
% 92.33/13.69 ! [X0 : $tType] : (c_2Eoption_2ENONE(X0) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),kCOMB,c_2Ebool_2EF)))),
% 92.33/13.69 inference(fool_elimination,[],[f2107])).
% 92.33/13.69 thf(f2107,plain,(
% 92.33/13.69 ! [X0 : $tType] : (vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),(^[X1 : X0] : (c_2Ebool_2EF))) = c_2Eoption_2ENONE(X0))),
% 92.33/13.69 inference(rectify,[],[f771])).
% 92.33/13.69 thf(f771,axiom,(
% 92.33/13.69 ! [X0 : $tType] : (vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),(^[X8 : X0] : (c_2Ebool_2EF))) = c_2Eoption_2ENONE(X0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Esome__F)).
% 92.33/13.69 thf(f18373,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : X0 > tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13793,f18174])).
% 92.33/13.69 thf(f13793,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : X0 > tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9482,f9122,f13523])).
% 92.33/13.69 thf(f9482,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : X0 > tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),c_2Eoption_2ENONE(X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4933])).
% 92.33/13.69 thf(f4933,plain,(
% 92.33/13.69 ! [X0 : $tType] : (! [X1 : X0 > tyop_2Enum_2Enum,X2 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(X0,tyop_2Enum_2Enum,X1,X2))) & ! [X3 : X0 > tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),c_2Eoption_2ENONE(X0))))),
% 92.33/13.69 inference(rectify,[],[f1452])).
% 92.33/13.69 thf(f1452,axiom,(
% 92.33/13.69 ! [X0 : $tType] : (! [X25 : X0 > tyop_2Enum_2Enum,X19 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X25),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X19)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(X0,tyop_2Enum_2Enum,X25,X19))) & ! [X3 : X0 > tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X3),c_2Eoption_2ENONE(X0))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Eoption__size__def)).
% 92.33/13.69 thf(f83392,plain,(
% 92.33/13.69 spl854_962),
% 92.33/13.69 inference(avatar_split_clause,[],[f17440,f83390])).
% 92.33/13.69 thf(f83390,plain,(
% 92.33/13.69 spl854_962 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_962])])).
% 92.33/13.69 thf(f17440,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14774])).
% 92.33/13.69 thf(f14774,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11071,f9122])).
% 92.33/13.69 thf(f11071,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7600])).
% 92.33/13.69 thf(f7600,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1))) & ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3384])).
% 92.33/13.69 thf(f3384,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)))),
% 92.33/13.69 inference(fool_elimination,[],[f3383])).
% 92.33/13.69 thf(f3383,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f1782])).
% 92.33/13.69 thf(f1782,axiom,(
% 92.33/13.69 ! [X35 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X35),X137)) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X35),X35),X137)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__SLICE__THM3)).
% 92.33/13.69 thf(f83388,plain,(
% 92.33/13.69 spl854_961),
% 92.33/13.69 inference(avatar_split_clause,[],[f17439,f83386])).
% 92.33/13.69 thf(f83386,plain,(
% 92.33/13.69 spl854_961 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_961])])).
% 92.33/13.69 thf(f17439,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14775])).
% 92.33/13.69 thf(f14775,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11070,f9122])).
% 92.33/13.69 thf(f11070,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X0),X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7600])).
% 92.33/13.69 thf(f83384,plain,(
% 92.33/13.69 spl854_960),
% 92.33/13.69 inference(avatar_split_clause,[],[f17438,f83382])).
% 92.33/13.69 thf(f83382,plain,(
% 92.33/13.69 spl854_960 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_960])])).
% 92.33/13.69 thf(f17438,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14776])).
% 92.33/13.69 thf(f14776,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11073,f9122])).
% 92.33/13.69 thf(f11073,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7601])).
% 92.33/13.69 thf(f7601,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1))) & ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3386])).
% 92.33/13.69 thf(f3386,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)))),
% 92.33/13.69 inference(fool_elimination,[],[f3385])).
% 92.33/13.69 thf(f3385,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f1775])).
% 92.33/13.69 thf(f1775,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum,X73 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X136),X73)) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X136),X136),X73)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ENOT__BIT)).
% 92.33/13.69 thf(f83380,plain,(
% 92.33/13.69 spl854_959),
% 92.33/13.69 inference(avatar_split_clause,[],[f17437,f83378])).
% 92.33/13.69 thf(f83378,plain,(
% 92.33/13.69 spl854_959 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_959])])).
% 92.33/13.69 thf(f17437,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14777])).
% 92.33/13.69 thf(f14777,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11072,f9122])).
% 92.33/13.69 thf(f11072,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7601])).
% 92.33/13.69 thf(f83376,plain,(
% 92.33/13.69 spl854_958),
% 92.33/13.69 inference(avatar_split_clause,[],[f15571,f83374])).
% 92.33/13.69 thf(f83374,plain,(
% 92.33/13.69 spl854_958 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : X0 > X1 > X2,X4 : X1,X5 : X0] : (vAPP(X1,X2,vAPP(X0,sTfun(X1,X2),X3,X5),X4) = vAPP(X0,X2,vAPP(X1,sTfun(X0,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(X1,sTfun(X0,X2)),cCOMB,X3),X4),X5))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_958])])).
% 92.33/13.69 thf(f15571,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X1 > X2,X4 : X1,X5 : X0] : ((vAPP(X1,X2,vAPP(X0,sTfun(X1,X2),X3,X5),X4) = vAPP(X0,X2,vAPP(X1,sTfun(X0,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(X1,sTfun(X0,X2)),cCOMB,X3),X4),X5))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f13275,f11318])).
% 92.33/13.69 thf(f11318,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((c_2Ecombin_2EC(X0,X1,X2) = cCOMB)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f3582])).
% 92.33/13.69 thf(f3582,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (c_2Ecombin_2EC(X0,X1,X2) = cCOMB)),
% 92.33/13.69 inference(fool_elimination,[],[f3581])).
% 92.33/13.69 thf(f3581,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (c_2Ecombin_2EC(X0,X1,X2) = (^[X3 : X0 > X1 > X2, X4 : X1, X5 : X0] : (vAPP(X1,X2,vAPP(X0,sTfun(X1,X2),X3,X5),X4))))),
% 92.33/13.69 inference(rectify,[],[f317])).
% 92.33/13.69 thf(f317,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X57 : $tType] : (c_2Ecombin_2EC(X0,X5,X57) = (^[X3 : X0 > X5 > X57, X4 : X5, X12 : X0] : (vAPP(X5,X57,vAPP(X0,sTfun(X5,X57),X3,X12),X4))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EC__DEF)).
% 92.33/13.69 thf(f13275,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X1 > X2,X4 : X1,X5 : X0] : ((vAPP(X1,X2,vAPP(X0,sTfun(X1,X2),X3,X5),X4) = vAPP(X0,X2,vAPP(X1,sTfun(X0,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(X1,sTfun(X0,X2)),c_2Ecombin_2EC(X0,X1,X2),X3),X4),X5))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5359])).
% 92.33/13.69 thf(f5359,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2,X4 : X1,X5 : X0] : (vAPP(X1,X2,vAPP(X0,sTfun(X1,X2),X3,X5),X4) = vAPP(X0,X2,vAPP(X1,sTfun(X0,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(X1,sTfun(X0,X2)),c_2Ecombin_2EC(X0,X1,X2),X3),X4),X5))),
% 92.33/13.69 inference(rectify,[],[f337])).
% 92.33/13.69 thf(f337,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X57 : $tType,X3 : X0 > X5 > X57,X4 : X5,X12 : X0] : (vAPP(X5,X57,vAPP(X0,sTfun(X5,X57),X3,X12),X4) = vAPP(X0,X57,vAPP(X5,sTfun(X0,X57),vAPP(sTfun(X0,sTfun(X5,X57)),sTfun(X5,sTfun(X0,X57)),c_2Ecombin_2EC(X0,X5,X57),X3),X4),X12))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EC__THM)).
% 92.33/13.69 thf(f83372,plain,(
% 92.33/13.69 spl854_957),
% 92.33/13.69 inference(avatar_split_clause,[],[f15506,f83370])).
% 92.33/13.69 thf(f83370,plain,(
% 92.33/13.69 spl854_957 <=> ! [X0 : $tType,X2 : X0,X4 : tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X2),X4),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X2)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_957])])).
% 92.33/13.69 thf(f15506,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X4 : tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X2),X4),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X2)) )),
% 92.33/13.69 inference(definition_unfolding,[],[f13070,f9122])).
% 92.33/13.69 thf(f13070,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X4 : tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X2),X4),c_2Enum_2E0) = X2)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5346])).
% 92.33/13.69 thf(f5346,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : X0,X3 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X2),X4),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X1)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),X4,X3),X1),vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X2),X4),X1))) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X2),X4),c_2Enum_2E0) = X2))),
% 92.33/13.69 inference(rectify,[],[f1686])).
% 92.33/13.69 thf(f1686,axiom,(
% 92.33/13.69 ! [X0 : $tType,X6 : tyop_2Enum_2Enum,X137 : X0,X119 : tyop_2Enum_2Enum,X75 : tyop_2Enum_2Enum > tyop_2Enum_2Enum > X0 > X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X137),X75),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X119),X6)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),X75,X119),X6),vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X137),X75),X6))) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,X0))),sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enlistrec(X0),X137),X75),c_2Enum_2E0) = X137))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlistrec__thm)).
% 92.33/13.69 thf(f83247,plain,(
% 92.33/13.69 spl854_956),
% 92.33/13.69 inference(avatar_split_clause,[],[f13276,f83245])).
% 92.33/13.69 thf(f83245,plain,(
% 92.33/13.69 spl854_956 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : X0 > X1,X4 : X2 > X0,X5 : X2] : (vAPP(X2,X1,vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),c_2Ecombin_2Eo(X2,X1,X0),X3),X4),X5) = vAPP(X0,X1,X3,vAPP(X2,X0,X4,X5)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_956])])).
% 92.33/13.69 thf(f13276,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X1,X4 : X2 > X0,X5 : X2] : ((vAPP(X2,X1,vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),c_2Ecombin_2Eo(X2,X1,X0),X3),X4),X5) = vAPP(X0,X1,X3,vAPP(X2,X0,X4,X5)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5360])).
% 92.33/13.69 thf(f5360,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1,X4 : X2 > X0,X5 : X2] : (vAPP(X2,X1,vAPP(sTfun(X2,X0),sTfun(X2,X1),vAPP(sTfun(X0,X1),sTfun(sTfun(X2,X0),sTfun(X2,X1)),c_2Ecombin_2Eo(X2,X1,X0),X3),X4),X5) = vAPP(X0,X1,X3,vAPP(X2,X0,X4,X5)))),
% 92.33/13.69 inference(rectify,[],[f329])).
% 92.33/13.69 thf(f329,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X57 : $tType,X3 : X0 > X5,X38 : X57 > X0,X19 : X57] : (vAPP(X57,X5,vAPP(sTfun(X57,X0),sTfun(X57,X5),vAPP(sTfun(X0,X5),sTfun(sTfun(X57,X0),sTfun(X57,X5)),c_2Ecombin_2Eo(X57,X5,X0),X3),X38),X19) = vAPP(X0,X5,X3,vAPP(X57,X0,X38,X19)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2Eo__THM)).
% 92.33/13.69 thf(f83243,plain,(
% 92.33/13.69 spl854_955),
% 92.33/13.69 inference(avatar_split_clause,[],[f13026,f83241])).
% 92.33/13.69 thf(f83241,plain,(
% 92.33/13.69 spl854_955 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X5 : X0,X2 : X1] : (vAPP(X0,X1,X3,X5) = vAPP(tyop_2Eoption_2Eoption(X0),X1,vAPP(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1),vAPP(sTfun(X0,X1),sTfun(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1)),sK750(X0,X1),X3),X2),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_955])])).
% 92.33/13.69 thf(f13026,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > X1,X5 : X0] : ((vAPP(X0,X1,X3,X5) = vAPP(tyop_2Eoption_2Eoption(X0),X1,vAPP(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1),vAPP(sTfun(X0,X1),sTfun(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1)),sK750(X0,X1),X3),X2),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8860])).
% 92.33/13.69 thf(f8860,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0 > X1] : (! [X5 : X0] : (vAPP(X0,X1,X3,X5) = vAPP(tyop_2Eoption_2Eoption(X0),X1,vAPP(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1),vAPP(sTfun(X0,X1),sTfun(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1)),sK750(X0,X1),X3),X2),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5))) & (vAPP(tyop_2Eoption_2Eoption(X0),X1,vAPP(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1),vAPP(sTfun(X0,X1),sTfun(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1)),sK750(X0,X1),X3),X2),c_2Eoption_2ENONE(X0)) = X2))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK750])],[f5332,f8859])).
% 92.33/13.69 thf(f8859,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0 > X1] : (? [X4 : tyop_2Eoption_2Eoption(X0) > X1] : (! [X5 : X0] : (vAPP(X0,X1,X3,X5) = vAPP(tyop_2Eoption_2Eoption(X0),X1,X4,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5))) & (vAPP(tyop_2Eoption_2Eoption(X0),X1,X4,c_2Eoption_2ENONE(X0)) = X2)) => (! [X5 : X0] : (vAPP(X0,X1,X3,X5) = vAPP(tyop_2Eoption_2Eoption(X0),X1,vAPP(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1),vAPP(sTfun(X0,X1),sTfun(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1)),sK750(X0,X1),X3),X2),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5))) & (vAPP(tyop_2Eoption_2Eoption(X0),X1,vAPP(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1),vAPP(sTfun(X0,X1),sTfun(X1,sTfun(tyop_2Eoption_2Eoption(X0),X1)),sK750(X0,X1),X3),X2),c_2Eoption_2ENONE(X0)) = X2)))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f5332,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0 > X1] : ? [X4 : tyop_2Eoption_2Eoption(X0) > X1] : (! [X5 : X0] : (vAPP(X0,X1,X3,X5) = vAPP(tyop_2Eoption_2Eoption(X0),X1,X4,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5))) & (vAPP(tyop_2Eoption_2Eoption(X0),X1,X4,c_2Eoption_2ENONE(X0)) = X2))),
% 92.33/13.69 inference(rectify,[],[f723])).
% 92.33/13.69 thf(f723,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X90 : X5,X25 : X0 > X5] : ? [X78 : tyop_2Eoption_2Eoption(X0) > X5] : (! [X15 : X0] : (vAPP(X0,X5,X25,X15) = vAPP(tyop_2Eoption_2Eoption(X0),X5,X78,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X15))) & (vAPP(tyop_2Eoption_2Eoption(X0),X5,X78,c_2Eoption_2ENONE(X0)) = X90))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__Axiom)).
% 92.33/13.69 thf(f83239,plain,(
% 92.33/13.69 spl854_954),
% 92.33/13.69 inference(avatar_split_clause,[],[f12325,f83237])).
% 92.33/13.69 thf(f83237,plain,(
% 92.33/13.69 spl854_954 <=> ! [X2 : $tType,X0 : X2 > X2 > $o,X1 : X2 > $o] : (($true = vAPP(X2,$o,X1,vAPP(sTfun(X2,$o),X2,sK624(X2),X1))) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP65(X2),X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_954])])).
% 92.33/13.69 thf(f12325,plain,(
% 92.33/13.69 ( ! [X2 : $tType,X0 : X2 > X2 > $o,X1 : X2 > $o] : (($true = vAPP(X2,$o,X1,vAPP(sTfun(X2,$o),X2,sK624(X2),X1))) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP65(X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8399])).
% 92.33/13.69 thf(f8399,plain,(
% 92.33/13.69 ! [X0 : X2 > X2 > $o,X1 : X2 > $o,X2 : $tType] : ((($true = vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP65(X2),X1),X0)) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP64(X2),X1),X0)) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP63(X2),X1),X0)) | (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),X0,vAPP(sTfun(X2,sTfun(X2,$o)),X2,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),X2),sK623(X2),X1),X0)),vAPP(sTfun(X2,sTfun(X2,$o)),X2,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),X2),sK623(X2),X1),X0))) & ($true = vAPP(X2,$o,X1,vAPP(sTfun(X2,sTfun(X2,$o)),X2,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),X2),sK623(X2),X1),X0)))) | ! [X4 : X2] : ($true != vAPP(X2,$o,X1,X4))) & ((($true = vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP64(X2),X1),X0)) & ($true = vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP63(X2),X1),X0)) & ! [X5 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),X0,X5),X5)) | ($true != vAPP(X2,$o,X1,X5))) & ($true = vAPP(X2,$o,X1,vAPP(sTfun(X2,$o),X2,sK624(X2),X1)))) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP65(X2),X1),X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK623,sK624])],[f8396,f8398,f8397])).
% 92.33/13.69 thf(f8397,plain,(
% 92.33/13.69 ! [X2 : $tType,X0 : X2 > X2 > $o,X1 : X2 > $o] : (? [X3 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),X0,X3),X3)) & ($true = vAPP(X2,$o,X1,X3))) => (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),X0,vAPP(sTfun(X2,sTfun(X2,$o)),X2,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),X2),sK623(X2),X1),X0)),vAPP(sTfun(X2,sTfun(X2,$o)),X2,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),X2),sK623(X2),X1),X0))) & ($true = vAPP(X2,$o,X1,vAPP(sTfun(X2,sTfun(X2,$o)),X2,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),X2),sK623(X2),X1),X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8398,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : X2 > $o] : (? [X6 : X2] : ($true = vAPP(X2,$o,X1,X6)) => ($true = vAPP(X2,$o,X1,vAPP(sTfun(X2,$o),X2,sK624(X2),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8396,plain,(
% 92.33/13.69 ! [X0 : X2 > X2 > $o,X1 : X2 > $o,X2 : $tType] : ((($true = vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP65(X2),X1),X0)) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP64(X2),X1),X0)) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP63(X2),X1),X0)) | ? [X3 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),X0,X3),X3)) & ($true = vAPP(X2,$o,X1,X3))) | ! [X4 : X2] : ($true != vAPP(X2,$o,X1,X4))) & ((($true = vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP64(X2),X1),X0)) & ($true = vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP63(X2),X1),X0)) & ! [X5 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),X0,X5),X5)) | ($true != vAPP(X2,$o,X1,X5))) & ? [X6 : X2] : ($true = vAPP(X2,$o,X1,X6))) | ($true != vAPP(sTfun(X2,sTfun(X2,$o)),$o,vAPP(sTfun(X2,$o),sTfun(sTfun(X2,sTfun(X2,$o)),$o),sP65(X2),X1),X0))))),
% 92.33/13.69 inference(rectify,[],[f8395])).
% 92.33/13.69 thf(f8395,plain,(
% 92.33/13.69 ! [X2 : X0 > X0 > $o,X1 : X0 > $o,X0 : $tType] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP65(X0),X1),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP64(X0),X1),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP63(X0),X1),X2)) | ? [X8 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X8),X8)) & ($true = vAPP(X0,$o,X1,X8))) | ! [X9 : X0] : ($true != vAPP(X0,$o,X1,X9))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP64(X0),X1),X2)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP63(X0),X1),X2)) & ! [X8 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X8),X8)) | ($true != vAPP(X0,$o,X1,X8))) & ? [X9 : X0] : ($true = vAPP(X0,$o,X1,X9))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP65(X0),X1),X2))))),
% 92.33/13.69 inference(flattening,[],[f8394])).
% 92.33/13.69 thf(f8394,plain,(
% 92.33/13.69 ! [X2 : X0 > X0 > $o,X1 : X0 > $o,X0 : $tType] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP65(X0),X1),X2)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP64(X0),X1),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP63(X0),X1),X2)) | ? [X8 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X8),X8)) & ($true = vAPP(X0,$o,X1,X8))) | ! [X9 : X0] : ($true != vAPP(X0,$o,X1,X9)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP64(X0),X1),X2)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP63(X0),X1),X2)) & ! [X8 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X8),X8)) | ($true != vAPP(X0,$o,X1,X8))) & ? [X9 : X0] : ($true = vAPP(X0,$o,X1,X9))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP65(X0),X1),X2))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6492])).
% 92.33/13.69 thf(f6492,plain,(
% 92.33/13.69 ! [X2 : X0 > X0 > $o,X1 : X0 > $o,X0 : $tType] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP65(X0),X1),X2)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP64(X0),X1),X2)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,sTfun(X0,$o)),$o),sP63(X0),X1),X2)) & ! [X8 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X8),X8)) | ($true != vAPP(X0,$o,X1,X8))) & ? [X9 : X0] : ($true = vAPP(X0,$o,X1,X9))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f83235,plain,(
% 92.33/13.69 spl854_953),
% 92.33/13.69 inference(avatar_split_clause,[],[f12070,f83233])).
% 92.33/13.69 thf(f83233,plain,(
% 92.33/13.69 spl854_953 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK581(X0,X1),X2))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_953])])).
% 92.33/13.69 thf(f12070,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o,X4 : X1] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK581(X0,X1),X2))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8194])).
% 92.33/13.69 thf(f8194,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK581(X0,X1),X2))) | (! [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))) & (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X1,sK582(X0,X1),X2)))) | ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X0,sK583(X0,X1),X2)))) | ! [X8 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X8))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK581,sK582,sK583])],[f8190,f8193,f8192,f8191])).
% 92.33/13.69 thf(f8191,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) => ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK581(X0,X1),X2))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8192,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X6 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X6))) => ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X1,sK582(X0,X1),X2)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8193,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X7 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X7))) => ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X0,sK583(X0,X1),X2)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8190,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | (! [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))) & (? [X6 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X6))) | ? [X7 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X7))) | ! [X8 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X8))))),
% 92.33/13.69 inference(rectify,[],[f8189])).
% 92.33/13.69 thf(f8189,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | (! [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))) & (? [X4 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) | ? [X5 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))) | ! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3))))),
% 92.33/13.69 inference(flattening,[],[f8188])).
% 92.33/13.69 thf(f8188,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | (! [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))) & ((? [X4 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) | ? [X5 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))) | ! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3))))),
% 92.33/13.69 inference(nnf_transformation,[],[f4022])).
% 92.33/13.69 thf(f4022,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) <=> (? [X4 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) | ? [X5 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))))),
% 92.33/13.69 inference(fool_elimination,[],[f4021])).
% 92.33/13.69 thf(f4021,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X3 : tyop_2Esum_2Esum(X0,X1)] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3) <=> (? [X4 : X1] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4)) | ? [X5 : X0] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))),
% 92.33/13.69 inference(rectify,[],[f678])).
% 92.33/13.69 thf(f678,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X7 : tyop_2Esum_2Esum(X0,X5) > $o] : (? [X157 : tyop_2Esum_2Esum(X0,X5)] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,X7,X157) <=> (? [X50 : X5] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,X7,vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X50)) | ? [X19 : X0] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,X7,vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X19))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EEXISTS__SUM)).
% 92.33/13.69 thf(f83231,plain,(
% 92.33/13.69 spl854_952),
% 92.33/13.69 inference(avatar_split_clause,[],[f12069,f83229])).
% 92.33/13.69 thf(f83229,plain,(
% 92.33/13.69 spl854_952 <=> ! [X1 : $tType,X0 : $tType,X5 : X0,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK581(X0,X1),X2))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_952])])).
% 92.33/13.69 thf(f12069,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o,X5 : X0] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK581(X0,X1),X2))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8194])).
% 92.33/13.69 thf(f83227,plain,(
% 92.33/13.69 spl854_951),
% 92.33/13.69 inference(avatar_split_clause,[],[f12024,f83225])).
% 92.33/13.69 thf(f83225,plain,(
% 92.33/13.69 spl854_951 <=> ! [X1 : $tType,X0 : $tType,X6 : X1,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X6))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK555(X0,X1),X2))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_951])])).
% 92.33/13.69 thf(f12024,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o,X6 : X1] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X6))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK555(X0,X1),X2)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8125])).
% 92.33/13.69 thf(f8125,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X1,sK553(X0,X1),X2)))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X0,sK554(X0,X1),X2))))) & ((! [X6 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X6))) & ! [X7 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X7)))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK555(X0,X1),X2)))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK553,sK554,sK555])],[f8121,f8124,f8123,f8122])).
% 92.33/13.69 thf(f8122,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) => ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X1,sK553(X0,X1),X2)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8123,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))) => ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),X0,sK554(X0,X1),X2)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8124,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (? [X8 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X8)) => ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK555(X0,X1),X2))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8121,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | ? [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) | ? [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))) & ((! [X6 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X6))) & ! [X7 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X7)))) | ? [X8 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X8))))),
% 92.33/13.69 inference(rectify,[],[f8120])).
% 92.33/13.69 thf(f8120,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | ? [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) | ? [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))) & ((! [X4 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))) | ? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3))))),
% 92.33/13.69 inference(flattening,[],[f8119])).
% 92.33/13.69 thf(f8119,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : ((! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) | (? [X4 : X1] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) | ? [X5 : X0] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))) & ((! [X4 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))) | ? [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3994])).
% 92.33/13.69 thf(f3994,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (! [X3 : tyop_2Esum_2Esum(X0,X1)] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3)) <=> (! [X4 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4))) & ! [X5 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))))),
% 92.33/13.69 inference(fool_elimination,[],[f3993])).
% 92.33/13.69 thf(f3993,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (! [X3 : tyop_2Esum_2Esum(X0,X1)] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,X3) <=> (! [X4 : X1] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X4)) & ! [X5 : X0] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))))),
% 92.33/13.69 inference(rectify,[],[f677])).
% 92.33/13.69 thf(f677,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X7 : tyop_2Esum_2Esum(X0,X5) > $o] : (! [X157 : tyop_2Esum_2Esum(X0,X5)] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,X7,X157) <=> (! [X50 : X5] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,X7,vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X50)) & ! [X19 : X0] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,X7,vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X19))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EFORALL__SUM)).
% 92.33/13.69 thf(f83223,plain,(
% 92.33/13.69 spl854_950),
% 92.33/13.69 inference(avatar_split_clause,[],[f12023,f83221])).
% 92.33/13.69 thf(f83221,plain,(
% 92.33/13.69 spl854_950 <=> ! [X1 : $tType,X0 : $tType,X7 : X0,X2 : tyop_2Esum_2Esum(X0,X1) > $o] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X7))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK555(X0,X1),X2))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_950])])).
% 92.33/13.69 thf(f12023,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1) > $o,X7 : X0] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X7))) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,X2,vAPP(sTfun(tyop_2Esum_2Esum(X0,X1),$o),tyop_2Esum_2Esum(X0,X1),sK555(X0,X1),X2)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8125])).
% 92.33/13.69 thf(f83219,plain,(
% 92.33/13.69 spl854_949),
% 92.33/13.69 inference(avatar_split_clause,[],[f11762,f83217])).
% 92.33/13.69 thf(f83217,plain,(
% 92.33/13.69 spl854_949 <=> ! [X0 : $tType,X2 : X0,X1 : tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0))] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = X1) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) != vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_949])])).
% 92.33/13.69 thf(f11762,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0))] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = X1) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) != vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7938])).
% 92.33/13.69 thf(f7938,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),X2 : X0] : (((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),X1)) | (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) != X1)) & ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = X1) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) != vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f5228])).
% 92.33/13.69 thf(f5228,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),X2 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),X1)) <=> (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = X1))),
% 92.33/13.69 inference(rectify,[],[f747])).
% 92.33/13.69 thf(f747,axiom,(
% 92.33/13.69 ! [X0 : $tType,X8 : tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),X18 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X18) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),X8)) <=> (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X18)) = X8))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__JOIN__EQ__SOME)).
% 92.33/13.69 thf(f83215,plain,(
% 92.33/13.69 spl854_948),
% 92.33/13.69 inference(avatar_split_clause,[],[f11476,f83213])).
% 92.33/13.69 thf(f83213,plain,(
% 92.33/13.69 spl854_948 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : ((c_2Erelation_2ERUNIV(X0,X1) = X2) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_948])])).
% 92.33/13.69 thf(f11476,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : ((c_2Erelation_2ERUNIV(X0,X1) = X2) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7724])).
% 92.33/13.69 thf(f7724,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),c_2Erelation_2ERUNIV(X0,X1))) & (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2)) | (c_2Erelation_2ERUNIV(X0,X1) != X2)) & ((c_2Erelation_2ERUNIV(X0,X1) = X2) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2))))),
% 92.33/13.69 inference(flattening,[],[f7723])).
% 92.33/13.69 thf(f7723,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),c_2Erelation_2ERUNIV(X0,X1))) & ((($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2)) | (c_2Erelation_2ERUNIV(X0,X1) != X2)) & ((c_2Erelation_2ERUNIV(X0,X1) = X2) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3642])).
% 92.33/13.69 thf(f3642,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),c_2Erelation_2ERUNIV(X0,X1))) & (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2)) <=> (c_2Erelation_2ERUNIV(X0,X1) = X2)))),
% 92.33/13.69 inference(fool_elimination,[],[f3641])).
% 92.33/13.69 thf(f3641,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o] : (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),c_2Erelation_2ERUNIV(X0,X1)) & (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),c_2Erelation_2ERUNIV(X0,X1)),X2) <=> (c_2Erelation_2ERUNIV(X0,X1) = X2)))),
% 92.33/13.69 inference(rectify,[],[f643])).
% 92.33/13.69 thf(f643,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X143 : X0 > X5 > $o] : (vAPP(sTfun(X0,sTfun(X5,$o)),$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o),c_2Erelation_2ERSUBSET(X0,X5),X143),c_2Erelation_2ERUNIV(X0,X5)) & (vAPP(sTfun(X0,sTfun(X5,$o)),$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o),c_2Erelation_2ERSUBSET(X0,X5),c_2Erelation_2ERUNIV(X0,X5)),X143) <=> (c_2Erelation_2ERUNIV(X0,X5) = X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERUNIV__SUBSET)).
% 92.33/13.69 thf(f83211,plain,(
% 92.33/13.69 spl854_947),
% 92.33/13.69 inference(avatar_split_clause,[],[f10749,f83209])).
% 92.33/13.69 thf(f83209,plain,(
% 92.33/13.69 spl854_947 <=> ! [X0 : $tType,X4 : X0,X5 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_947])])).
% 92.33/13.69 thf(f10749,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o,X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7349])).
% 92.33/13.69 thf(f7349,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK338(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK337(X0),X1))) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK337(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK338(X0),X1))))) & (! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK337,sK338])],[f7347,f7348])).
% 92.33/13.69 thf(f7348,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK338(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK337(X0),X1))) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK337(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK338(X0),X1)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f7347,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1)) | ? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & (! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1))))),
% 92.33/13.69 inference(rectify,[],[f7346])).
% 92.33/13.69 thf(f7346,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1)) | ? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & (! [X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3172])).
% 92.33/13.69 thf(f3172,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1)) <=> ! [X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.33/13.69 inference(fool_elimination,[],[f3171])).
% 92.33/13.69 thf(f3171,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X1) <=> ! [X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))),
% 92.33/13.69 inference(rectify,[],[f414])).
% 92.33/13.69 thf(f414,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etotal(X0),X143) <=> ! [X4 : X0,X12 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X12),X4) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Etotal__def)).
% 92.33/13.69 thf(f83207,plain,(
% 92.33/13.69 spl854_498 | spl854_946 | ~spl854_218),
% 92.33/13.69 inference(avatar_split_clause,[],[f24645,f23585,f83204,f48711])).
% 92.33/13.69 thf(f83204,plain,(
% 92.33/13.69 spl854_946 <=> ($true = vAPP(sTfun($o,$o),$o,sK401($o),vNOT))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_946])])).
% 92.33/13.69 thf(f23585,plain,(
% 92.33/13.69 spl854_218 <=> ! [X0 : $tType,X13 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X13)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK401(X0),X1))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_218])])).
% 92.33/13.69 thf(f24645,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK401($o),vNOT)) | ($false = X0)) ) | ~spl854_218),
% 92.33/13.69 inference(not_proxy_clausification,[],[f24644])).
% 92.33/13.69 thf(f24644,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK401($o),vNOT)) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_218),
% 92.33/13.69 inference(not_proxy_clausification,[],[f24584])).
% 92.33/13.69 thf(f24584,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK401($o),vNOT))) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_218),
% 92.33/13.69 inference(primitive_instantiation,[],[f23586])).
% 92.33/13.69 thf(f23586,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > $o,X13 : X0] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK401(X0),X1))) | ($true = vAPP(X0,$o,X1,X13))) ) | ~spl854_218),
% 92.33/13.69 inference(avatar_component_clause,[],[f23585])).
% 92.33/13.69 thf(f83202,plain,(
% 92.33/13.69 spl854_945),
% 92.33/13.69 inference(avatar_split_clause,[],[f10714,f83200])).
% 92.33/13.69 thf(f83200,plain,(
% 92.33/13.69 spl854_945 <=> ! [X0 : $tType,X4 : X0,X5 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_945])])).
% 92.33/13.69 thf(f10714,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o,X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7321])).
% 92.33/13.69 thf(f7321,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK326(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK325(X0),X1))) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK325(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK326(X0),X1)))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) & ((! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK325,sK326])],[f7319,f7320])).
% 92.33/13.69 thf(f7320,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK326(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK325(X0),X1))) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK325(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK326(X0),X1)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f7319,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | ? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) & ((! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))))),
% 92.33/13.69 inference(rectify,[],[f7318])).
% 92.33/13.69 thf(f7318,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | ? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) & ((! [X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7317])).
% 92.33/13.69 thf(f7317,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | (? [X2 : X0,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))) & ((! [X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3154])).
% 92.33/13.69 thf(f3154,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) <=> (! [X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3153])).
% 92.33/13.69 thf(f3153,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1) <=> (! [X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f633])).
% 92.33/13.69 thf(f633,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X143) <=> (! [X73 : X0,X79 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X79),X73) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X73),X79)) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWeakLinearOrder__dichotomy)).
% 92.33/13.69 thf(f83198,plain,(
% 92.33/13.69 spl854_944),
% 92.33/13.69 inference(avatar_split_clause,[],[f10689,f83196])).
% 92.33/13.69 thf(f83196,plain,(
% 92.33/13.69 spl854_944 <=> ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) | (vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) != X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_944])])).
% 92.33/13.69 thf(f10689,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) | (vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) != X1)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7295])).
% 92.33/13.69 thf(f7295,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) | (vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) != X1)) & ((vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) = X1) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3140])).
% 92.33/13.69 thf(f3140,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) <=> (vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) = X1))),
% 92.33/13.69 inference(fool_elimination,[],[f3139])).
% 92.33/13.69 thf(f3139,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : (vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1) <=> (vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) = X1))),
% 92.33/13.69 inference(rectify,[],[f433])).
% 92.33/13.69 thf(f433,axiom,(
% 92.33/13.69 ! [X139 : $tType,X3 : X139 > X139] : (vAPP(sTfun(X139,X139),$o,c_2Erelation_2EIDEM(X139),X3) <=> (vAPP(sTfun(X139,X139),sTfun(X139,X139),vAPP(sTfun(X139,X139),sTfun(sTfun(X139,X139),sTfun(X139,X139)),c_2Ecombin_2Eo(X139,X139,X139),X3),X3) = X3))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM__DEF)).
% 92.33/13.69 thf(f83194,plain,(
% 92.33/13.69 spl854_943),
% 92.33/13.69 inference(avatar_split_clause,[],[f10688,f83192])).
% 92.33/13.69 thf(f83192,plain,(
% 92.33/13.69 spl854_943 <=> ! [X0 : $tType,X1 : X0 > X0] : ((vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) = X1) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_943])])).
% 92.33/13.69 thf(f10688,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0] : ((vAPP(sTfun(X0,X0),sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0)),c_2Ecombin_2Eo(X0,X0,X0),X1),X1) = X1) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7295])).
% 92.33/13.69 thf(f83190,plain,(
% 92.33/13.69 spl854_942),
% 92.33/13.69 inference(avatar_split_clause,[],[f10347,f83188])).
% 92.33/13.69 thf(f83188,plain,(
% 92.33/13.69 spl854_942 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK241,X1),X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_942])])).
% 92.33/13.69 thf(f10347,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK241,X1),X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6943])).
% 92.33/13.69 thf(f6943,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0)) | ! [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK241,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK241,X1),X0)),X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK241])],[f6941,f6942])).
% 92.33/13.69 thf(f6942,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (? [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X1))) => (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK241,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK241,X1),X0)),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6941,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0)) | ! [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)))) & (? [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0))))),
% 92.33/13.69 inference(rectify,[],[f6940])).
% 92.33/13.69 thf(f6940,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0)) | ! [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)))) & (? [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6391])).
% 92.33/13.69 thf(f6391,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP7,X1),X0)) <=> ? [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f83186,plain,(
% 92.33/13.69 spl854_941),
% 92.33/13.69 inference(avatar_split_clause,[],[f10340,f83184])).
% 92.33/13.69 thf(f83184,plain,(
% 92.33/13.69 spl854_941 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK239,X1),X0))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_941])])).
% 92.33/13.69 thf(f10340,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK239,X1),X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6934])).
% 92.33/13.69 thf(f6934,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK239,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK239,X1),X0)),X1)))) & (! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK239])],[f6932,f6933])).
% 92.33/13.69 thf(f6933,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))) => (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK239,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK239,X1),X0)),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6932,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)))) & (! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0))))),
% 92.33/13.69 inference(rectify,[],[f6931])).
% 92.33/13.69 thf(f6931,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)))) & (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6388])).
% 92.33/13.69 thf(f6388,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP5,X1),X0)) <=> ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f83182,plain,(
% 92.33/13.69 spl854_940),
% 92.33/13.69 inference(avatar_split_clause,[],[f10149,f83180])).
% 92.33/13.69 thf(f83180,plain,(
% 92.33/13.69 spl854_940 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X0 > X1] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X3),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X3,X4)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_940])])).
% 92.33/13.69 thf(f10149,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X4 : X0] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X3),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X3,X4)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5095])).
% 92.33/13.69 thf(f5095,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0 > X1] : (c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X2),c_2Eoption_2ENONE(X0))) & ! [X3 : X0 > X1,X4 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X3),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X3,X4))))),
% 92.33/13.69 inference(rectify,[],[f708])).
% 92.33/13.69 thf(f708,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType] : (! [X114 : X0 > X5] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5),vAPP(sTfun(X0,X5),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5)),c_2Eoption_2EOPTION__MAP(X0,X5),X114),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X5)) & ! [X3 : X0 > X5,X4 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5),vAPP(sTfun(X0,X5),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5)),c_2Eoption_2EOPTION__MAP(X0,X5),X3),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4)) = vAPP(X5,tyop_2Eoption_2Eoption(X5),c_2Eoption_2ESOME(X5),vAPP(X0,X5,X3,X4))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__MAP__DEF)).
% 92.33/13.69 thf(f83178,plain,(
% 92.33/13.69 spl854_939),
% 92.33/13.69 inference(avatar_split_clause,[],[f9924,f83176])).
% 92.33/13.69 thf(f9924,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5027])).
% 92.33/13.69 thf(f5027,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f1853])).
% 92.33/13.69 thf(f1853,axiom,(
% 92.33/13.69 ! [X0 : $tType,X111 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X111) = vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X111),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X111)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF)).
% 92.33/13.69 thf(f83174,plain,(
% 92.33/13.69 spl854_938),
% 92.33/13.69 inference(avatar_split_clause,[],[f9717,f83172])).
% 92.33/13.69 thf(f83172,plain,(
% 92.33/13.69 spl854_938 <=> ! [X0 : tyop_2Emin_2Eind,X3 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X3,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3)))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,c_2Enum_2EZERO__REP)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_938])])).
% 92.33/13.69 thf(f9717,plain,(
% 92.33/13.69 ( ! [X3 : tyop_2Emin_2Eind > $o,X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,X3,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3)))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,c_2Enum_2EZERO__REP)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6788])).
% 92.33/13.69 thf(f6788,plain,(
% 92.33/13.69 ! [X0 : tyop_2Emin_2Eind] : ((($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | (($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X0)) & ! [X2 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),c_2Enum_2EZERO__REP)))) & (! [X3 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X3,X0)) | (($true != vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3)))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3)))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK183,sK184])],[f6785,f6787,f6786])).
% 92.33/13.69 thf(f6786,plain,(
% 92.33/13.69 ! [X0 : tyop_2Emin_2Eind] : (? [X1 : tyop_2Emin_2Eind > $o] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,X0)) & ! [X2 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP))) => (($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X0)) & ! [X2 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),c_2Enum_2EZERO__REP))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6787,plain,(
% 92.33/13.69 ! [X3 : tyop_2Emin_2Eind > $o] : (? [X4 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X4))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X3,X4))) => (($true != vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3)))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6785,plain,(
% 92.33/13.69 ! [X0 : tyop_2Emin_2Eind] : ((($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ? [X1 : tyop_2Emin_2Eind > $o] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,X0)) & ! [X2 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP)))) & (! [X3 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X3,X0)) | ? [X4 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X4))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X3,X4))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))))),
% 92.33/13.69 inference(rectify,[],[f6784])).
% 92.33/13.69 thf(f6784,plain,(
% 92.33/13.69 ! [X0 : tyop_2Emin_2Eind] : ((($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ? [X1 : tyop_2Emin_2Eind > $o] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,X0)) & ! [X2 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP)))) & (! [X1 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,X0)) | ? [X2 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6382])).
% 92.33/13.69 thf(f6382,plain,(
% 92.33/13.69 ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) <=> ! [X1 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,X0)) | ? [X2 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f82022,plain,(
% 92.33/13.69 spl854_937 | ~spl854_44 | ~spl854_911),
% 92.33/13.69 inference(avatar_split_clause,[],[f81855,f81034,f22112,f82020])).
% 92.33/13.69 thf(f22112,plain,(
% 92.33/13.69 spl854_44 <=> ($false = vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_44])])).
% 92.33/13.69 thf(f81034,plain,(
% 92.33/13.69 spl854_911 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X2),X1)),X2))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_911])])).
% 92.33/13.69 thf(f81855,plain,(
% 92.33/13.69 ( ! [X0 : sK123] : ((vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP(sK123,sTfun(sK123,$o),vAPP(sTfun(sK123,$o),sTfun(sK123,sTfun(sK123,$o)),c_2Epred__set_2EDELETE(sK123),sK124),X0))) ) | (~spl854_44 | ~spl854_911)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f81784])).
% 92.33/13.69 thf(f81784,plain,(
% 92.33/13.69 ( ! [X0 : sK123] : (($true = $false) | (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP(sK123,sTfun(sK123,$o),vAPP(sTfun(sK123,$o),sTfun(sK123,sTfun(sK123,$o)),c_2Epred__set_2EDELETE(sK123),sK124),X0))) ) | (~spl854_44 | ~spl854_911)),
% 92.33/13.69 inference(constrained_superposition,[],[f81035,f22114])).
% 92.33/13.69 thf(f22114,plain,(
% 92.33/13.69 ($false = vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124)) | ~spl854_44),
% 92.33/13.69 inference(avatar_component_clause,[],[f22112])).
% 92.33/13.69 thf(f81035,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X2),X1)),X2))) ) | ~spl854_911),
% 92.33/13.69 inference(avatar_component_clause,[],[f81034])).
% 92.33/13.69 thf(f81370,plain,(
% 92.33/13.69 spl854_936 | ~spl854_9),
% 92.33/13.69 inference(avatar_split_clause,[],[f30271,f21928,f81368])).
% 92.33/13.69 thf(f81368,plain,(
% 92.33/13.69 spl854_936 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_936])])).
% 92.33/13.69 thf(f30271,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))))) ) | ~spl854_9),
% 92.33/13.69 inference(forward_demodulation,[],[f13571,f21929])).
% 92.33/13.69 thf(f13571,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9173,f9121])).
% 92.33/13.69 thf(f9173,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4843])).
% 92.33/13.69 thf(f4843,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f1392])).
% 92.33/13.69 thf(f1392,axiom,(
% 92.33/13.69 ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X137))))) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__fact)).
% 92.33/13.69 thf(f81366,plain,(
% 92.33/13.69 spl854_935 | ~spl854_9 | ~spl854_168),
% 92.33/13.69 inference(avatar_split_clause,[],[f30268,f22983,f21928,f81364])).
% 92.33/13.69 thf(f81364,plain,(
% 92.33/13.69 spl854_935 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_935])])).
% 92.33/13.69 thf(f22983,plain,(
% 92.33/13.69 spl854_168 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_168])])).
% 92.33/13.69 thf(f30268,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))))) ) | (~spl854_9 | ~spl854_168)),
% 92.33/13.69 inference(forward_demodulation,[],[f30267,f21929])).
% 92.33/13.69 thf(f30267,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))))))) ) | (~spl854_9 | ~spl854_168)),
% 92.33/13.69 inference(forward_demodulation,[],[f30266,f18201])).
% 92.33/13.69 thf(f18201,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18200,f18124])).
% 92.33/13.69 thf(f18200,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18199,f13563])).
% 92.33/13.69 thf(f18199,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13681,f13548])).
% 92.33/13.69 thf(f13681,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9322,f13512])).
% 92.33/13.69 thf(f9322,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4894])).
% 92.33/13.69 thf(f4894,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.33/13.69 inference(rectify,[],[f991])).
% 92.33/13.69 thf(f991,axiom,(
% 92.33/13.69 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X134),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EPRE__SUB1)).
% 92.33/13.69 thf(f30266,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) ) | (~spl854_9 | ~spl854_168)),
% 92.33/13.69 inference(forward_demodulation,[],[f30265,f22985])).
% 92.33/13.69 thf(f22985,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_168),
% 92.33/13.69 inference(avatar_component_clause,[],[f22983])).
% 92.33/13.69 thf(f30265,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) ) | ~spl854_9),
% 92.33/13.69 inference(forward_demodulation,[],[f18105,f29751])).
% 92.33/13.69 thf(f29751,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_9),
% 92.33/13.69 inference(forward_demodulation,[],[f13548,f21929])).
% 92.33/13.69 thf(f18105,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13560,f13548])).
% 92.33/13.69 thf(f13560,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9159,f13512])).
% 92.33/13.69 thf(f9159,plain,(
% 92.33/13.69 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4839])).
% 92.33/13.69 thf(f4839,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,c_2Enum_2E0))),
% 92.33/13.69 inference(rectify,[],[f1656])).
% 92.33/13.69 thf(f1656,axiom,(
% 92.33/13.69 ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X137))))) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Etri__def__compute)).
% 92.33/13.69 thf(f81362,plain,(
% 92.33/13.69 spl854_934),
% 92.33/13.69 inference(avatar_split_clause,[],[f18572,f81360])).
% 92.33/13.69 thf(f81360,plain,(
% 92.33/13.69 spl854_934 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_934])])).
% 92.33/13.69 thf(f18572,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18571,f18124])).
% 92.33/13.69 thf(f18571,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18570,f9293])).
% 92.33/13.69 thf(f18570,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f17827,f18124])).
% 92.33/13.69 thf(f17827,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.33/13.69 inference(equality_proxy_clausification,[],[f17826])).
% 92.33/13.69 thf(f17826,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f13999])).
% 92.33/13.69 thf(f13999,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9753,f13512,f13512])).
% 92.33/13.69 thf(f9753,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6794])).
% 92.33/13.69 thf(f81280,plain,(
% 92.33/13.69 spl854_933),
% 92.33/13.69 inference(avatar_split_clause,[],[f17950,f81278])).
% 92.33/13.69 thf(f81278,plain,(
% 92.33/13.69 spl854_933 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_933])])).
% 92.33/13.69 thf(f17950,plain,(
% 92.33/13.69 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f9631])).
% 92.33/13.69 thf(f9631,plain,(
% 92.33/13.69 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6698])).
% 92.33/13.69 thf(f6698,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ! [X1 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0)),X1))) | ! [X3 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) & ((! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK164,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK165,X0)))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK163,sK164,sK165])],[f6694,f6697,f6696,f6695])).
% 92.33/13.69 thf(f6695,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) => (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK163,X1),X0)),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6696,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X4 : tyop_2Enum_2Enum] : ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4))) => ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK164,X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6697,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X6 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X6)) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK165,X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6694,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ! [X1 : tyop_2Enum_2Enum] : ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) | ! [X3 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) & ((? [X4 : tyop_2Enum_2Enum] : ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4))) & ? [X6 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X6))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(rectify,[],[f6693])).
% 92.33/13.69 thf(f6693,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ! [X1 : tyop_2Enum_2Enum] : ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) | ! [X3 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) & ((? [X1 : tyop_2Enum_2Enum] : ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) & ? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(flattening,[],[f6692])).
% 92.33/13.69 thf(f6692,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | (! [X1 : tyop_2Enum_2Enum] : ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) | ! [X3 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)))) & ((? [X1 : tyop_2Enum_2Enum] : ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) & ? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6380])).
% 92.33/13.69 thf(f6380,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) <=> (? [X1 : tyop_2Enum_2Enum] : ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) & ? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f81276,plain,(
% 92.33/13.69 spl854_932),
% 92.33/13.69 inference(avatar_split_clause,[],[f17948,f81274])).
% 92.33/13.69 thf(f81274,plain,(
% 92.33/13.69 spl854_932 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_932])])).
% 92.33/13.69 thf(f17948,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f9635])).
% 92.33/13.69 thf(f9635,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6703])).
% 92.33/13.69 thf(f6703,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ! [X1 : tyop_2Enum_2Enum] : ((($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0)),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))) & ((! [X4 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X4))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0)))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK166,sK167])],[f6700,f6702,f6701])).
% 92.33/13.69 thf(f6701,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) => (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK166,X1),X0)),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6702,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X3 : tyop_2Enum_2Enum] : (! [X4 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X4))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) => (! [X4 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X4))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6700,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ! [X1 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))) & (? [X3 : tyop_2Enum_2Enum] : (! [X4 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X4))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(rectify,[],[f6699])).
% 92.33/13.69 thf(f6699,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) | ! [X4 : tyop_2Enum_2Enum] : (? [X5 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4)))) & (? [X4 : tyop_2Enum_2Enum] : (! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X4))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6381])).
% 92.33/13.69 thf(f6381,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)) <=> ? [X4 : tyop_2Enum_2Enum] : (! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(definition_folding,[],[f5499,f6380])).
% 92.33/13.69 thf(f5499,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((? [X1 : tyop_2Enum_2Enum] : ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1))) & ? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) <=> ? [X4 : tyop_2Enum_2Enum] : (! [X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2278])).
% 92.33/13.69 thf(f2278,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((? [X1 : tyop_2Enum_2Enum] : ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1)) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2)))) & ? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) <=> ? [X4 : tyop_2Enum_2Enum] : (! [X5 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4)) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(fool_elimination,[],[f2277])).
% 92.33/13.69 thf(f2277,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((? [X1 : tyop_2Enum_2Enum] : ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X2),X1) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ? [X3 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X3)) <=> ? [X4 : tyop_2Enum_2Enum] : (! [X5 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),X4) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) & vAPP(tyop_2Enum_2Enum,$o,X0,X4)))),
% 92.33/13.69 inference(rectify,[],[f1238])).
% 92.33/13.69 thf(f1238,axiom,(
% 92.33/13.69 ! [X7 : tyop_2Enum_2Enum > $o] : ((? [X19 : tyop_2Enum_2Enum] : ! [X50 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X50),X19) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X7,X50))) & ? [X4 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X4)) <=> ? [X23 : tyop_2Enum_2Enum] : (! [X85 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X85),X23) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X7,X85))) & vAPP(tyop_2Enum_2Enum,$o,X7,X23)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEXISTS__GREATEST)).
% 92.33/13.69 thf(f81272,plain,(
% 92.33/13.69 spl854_931),
% 92.33/13.69 inference(avatar_split_clause,[],[f17074,f81270])).
% 92.33/13.69 thf(f81270,plain,(
% 92.33/13.69 spl854_931 <=> ! [X0 : $o,X3 : $o,X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | ($false = X1) | ($false = X2))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_931])])).
% 92.33/13.69 thf(f17074,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | ($false = X1) | ($false = X2)) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f17073])).
% 92.33/13.69 thf(f17073,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | ($false = X1) | ($true = vAPP($o,$o,vNOT,X2))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f12601])).
% 92.33/13.69 thf(f12601,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6527])).
% 92.33/13.69 thf(f6527,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | ((X2 != X3) & (vAPP($o,$o,vNOT,X1) = $true)) | ((X0 != X1) & ($true = vAPP($o,$o,vNOT,X2))))),
% 92.33/13.69 inference(definition_folding,[],[f6107,f6526])).
% 92.33/13.69 thf(f6526,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f6107,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))) | ((X2 != X3) & (vAPP($o,$o,vNOT,X1) = $true)) | ((X0 != X1) & ($true = vAPP($o,$o,vNOT,X2))))),
% 92.33/13.69 inference(flattening,[],[f6106])).
% 92.33/13.69 thf(f6106,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))) | (((X2 != X3) & (vAPP($o,$o,vNOT,X1) = $true)) | ((X0 != X1) & ($true = vAPP($o,$o,vNOT,X2)))))),
% 92.33/13.69 inference(ennf_transformation,[],[f4306])).
% 92.33/13.69 thf(f4306,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : ((((vAPP($o,$o,vNOT,X1) = $true) => (X2 = X3)) & (($true = vAPP($o,$o,vNOT,X2)) => (X0 = X1))) => ((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f4305])).
% 92.33/13.69 thf(f4305,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((vAPP($o,$o,vNOT,X1) => (X2 = X3)) & (vAPP($o,$o,vNOT,X2) => (X0 = X1))) => ((X2 | X0) <=> (X3 | X1)))),
% 92.33/13.69 inference(rectify,[],[f144])).
% 92.33/13.69 thf(f144,axiom,(
% 92.33/13.69 ! [X7 : $o,X61 : $o,X62 : $o,X63 : $o] : (((vAPP($o,$o,vNOT,X61) => (X62 = X63)) & (vAPP($o,$o,vNOT,X62) => (X7 = X61))) => ((X62 | X7) <=> (X63 | X61)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CONG)).
% 92.33/13.69 thf(f81268,plain,(
% 92.33/13.69 spl854_930),
% 92.33/13.69 inference(avatar_split_clause,[],[f16618,f81266])).
% 92.33/13.69 thf(f81266,plain,(
% 92.33/13.69 spl854_930 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,$true),X2),X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_930])])).
% 92.33/13.69 thf(f16618,plain,(
% 92.33/13.69 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,$true),X2),X1),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12597])).
% 92.33/13.69 thf(f12597,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8487])).
% 92.33/13.69 thf(f8487,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true = X3) | (($true != X0) & ($true != X1))) & (($true = X0) | ($true = X1) | (($true != X2) & ($true != X3)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),X0)))),
% 92.33/13.69 inference(rectify,[],[f8486])).
% 92.33/13.69 thf(f8486,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) | ($true = X0) | (($true != X3) & ($true != X1))) & (($true = X3) | ($true = X1) | (($true != X2) & ($true != X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)))),
% 92.33/13.69 inference(flattening,[],[f8485])).
% 92.33/13.69 thf(f8485,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) | ($true = X0)) | (($true != X3) & ($true != X1))) & ((($true = X3) | ($true = X1)) | (($true != X2) & ($true != X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)))),
% 92.33/13.69 inference(nnf_transformation,[],[f6526])).
% 92.33/13.69 thf(f81264,plain,(
% 92.33/13.69 spl854_929),
% 92.33/13.69 inference(avatar_split_clause,[],[f16617,f81262])).
% 92.33/13.69 thf(f81262,plain,(
% 92.33/13.69 spl854_929 <=> ! [X0 : $o,X1 : $o,X3 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),$true),X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_929])])).
% 92.33/13.69 thf(f16617,plain,(
% 92.33/13.69 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),$true),X1),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12598])).
% 92.33/13.69 thf(f12598,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8487])).
% 92.33/13.69 thf(f81260,plain,(
% 92.33/13.69 spl854_928),
% 92.33/13.69 inference(avatar_split_clause,[],[f16616,f81258])).
% 92.33/13.69 thf(f81258,plain,(
% 92.33/13.69 spl854_928 <=> ! [X2 : $o,X0 : $o,X3 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),$true),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_928])])).
% 92.33/13.69 thf(f16616,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),$true),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12599])).
% 92.33/13.69 thf(f12599,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X3) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8487])).
% 92.33/13.69 thf(f81256,plain,(
% 92.33/13.69 spl854_927),
% 92.33/13.69 inference(avatar_split_clause,[],[f16615,f81254])).
% 92.33/13.69 thf(f81254,plain,(
% 92.33/13.69 spl854_927 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),$true)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_927])])).
% 92.33/13.69 thf(f16615,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),$true))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12600])).
% 92.33/13.69 thf(f12600,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X3) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8487])).
% 92.33/13.69 thf(f81252,plain,(
% 92.33/13.69 spl854_926),
% 92.33/13.69 inference(avatar_split_clause,[],[f16532,f81250])).
% 92.33/13.69 thf(f81250,plain,(
% 92.33/13.69 spl854_926 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,$true),X2),X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_926])])).
% 92.33/13.69 thf(f16532,plain,(
% 92.33/13.69 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,$true),X2),X1),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12519])).
% 92.33/13.69 thf(f12519,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8456])).
% 92.33/13.69 thf(f8456,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true = X3) | (($true != X0) & ($true != X1))) & (($true = X0) | ($true = X1) | (($true != X2) & ($true != X3)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),X0)))),
% 92.33/13.69 inference(rectify,[],[f8455])).
% 92.33/13.69 thf(f8455,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) | ($true = X0) | (($true != X3) & ($true != X1))) & (($true = X3) | ($true = X1) | (($true != X2) & ($true != X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X2),X1),X3)))),
% 92.33/13.69 inference(flattening,[],[f8454])).
% 92.33/13.69 thf(f8454,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) | ($true = X0)) | (($true != X3) & ($true != X1))) & ((($true = X3) | ($true = X1)) | (($true != X2) & ($true != X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X2),X1),X3)))),
% 92.33/13.69 inference(nnf_transformation,[],[f6500])).
% 92.33/13.69 thf(f6500,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X2),X1),X3)))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f81248,plain,(
% 92.33/13.69 spl854_925),
% 92.33/13.69 inference(avatar_split_clause,[],[f16531,f81246])).
% 92.33/13.69 thf(f81246,plain,(
% 92.33/13.69 spl854_925 <=> ! [X0 : $o,X1 : $o,X3 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),$true),X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_925])])).
% 92.33/13.69 thf(f16531,plain,(
% 92.33/13.69 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),$true),X1),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12520])).
% 92.33/13.69 thf(f12520,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8456])).
% 92.33/13.69 thf(f81244,plain,(
% 92.33/13.69 spl854_924),
% 92.33/13.69 inference(avatar_split_clause,[],[f16530,f81242])).
% 92.33/13.69 thf(f81242,plain,(
% 92.33/13.69 spl854_924 <=> ! [X2 : $o,X0 : $o,X3 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),$true),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_924])])).
% 92.33/13.69 thf(f16530,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),$true),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12521])).
% 92.33/13.69 thf(f12521,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X3) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8456])).
% 92.33/13.69 thf(f81162,plain,(
% 92.33/13.69 spl854_923),
% 92.33/13.69 inference(avatar_split_clause,[],[f16529,f81160])).
% 92.33/13.69 thf(f81160,plain,(
% 92.33/13.69 spl854_923 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),$true)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_923])])).
% 92.33/13.69 thf(f16529,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),$true))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12522])).
% 92.33/13.69 thf(f12522,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X3) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8456])).
% 92.33/13.69 thf(f81158,plain,(
% 92.33/13.69 spl854_922),
% 92.33/13.69 inference(avatar_split_clause,[],[f16525,f81156])).
% 92.33/13.69 thf(f81156,plain,(
% 92.33/13.69 spl854_922 <=> ! [X2 : $o,X0 : $o,X3 : $o] : (($true = X0) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),$true),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_922])])).
% 92.33/13.69 thf(f16525,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o] : (($true = X0) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),$true),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12513])).
% 92.33/13.69 thf(f12513,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8453])).
% 92.33/13.69 thf(f8453,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true != X3) | (($true != X0) & ($true = X1))) & (($true = X0) | ($true != X1) | (($true != X2) & ($true = X3)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),X1),X0)))),
% 92.33/13.69 inference(rectify,[],[f8452])).
% 92.33/13.69 thf(f8452,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) | ($true != X0) | (($true != X3) & ($true = X1))) & (($true = X3) | ($true != X1) | (($true != X2) & ($true = X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X2),X1),X3)))),
% 92.33/13.69 inference(flattening,[],[f8451])).
% 92.33/13.69 thf(f8451,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) | ($true != X0)) | (($true != X3) & ($true = X1))) & ((($true = X3) | ($true != X1)) | (($true != X2) & ($true = X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X2),X1),X3)))),
% 92.33/13.69 inference(nnf_transformation,[],[f6498])).
% 92.33/13.69 thf(f6498,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) | ($true != X0)) <=> (($true = X3) | ($true != X1))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X2),X1),X3)))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f81154,plain,(
% 92.33/13.69 spl854_921),
% 92.33/13.69 inference(avatar_split_clause,[],[f16522,f81152])).
% 92.33/13.69 thf(f81152,plain,(
% 92.33/13.69 spl854_921 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,$true),X2),X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_921])])).
% 92.33/13.69 thf(f16522,plain,(
% 92.33/13.69 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,$true),X2),X1),X0))) )),
% 92.33/13.69 inference(equality_resolution,[],[f12515])).
% 92.33/13.69 thf(f12515,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X3) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8453])).
% 92.33/13.69 thf(f81150,plain,(
% 92.33/13.69 spl854_920),
% 92.33/13.69 inference(avatar_split_clause,[],[f14103,f81148])).
% 92.33/13.69 thf(f81148,plain,(
% 92.33/13.69 spl854_920 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_920])])).
% 92.33/13.69 thf(f14103,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9923,f9121,f9121])).
% 92.33/13.69 thf(f9923,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5026])).
% 92.33/13.69 thf(f5026,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f993])).
% 92.33/13.69 thf(f993,axiom,(
% 92.33/13.69 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X137)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__SUC)).
% 92.33/13.69 thf(f81146,plain,(
% 92.33/13.69 spl854_919),
% 92.33/13.69 inference(avatar_split_clause,[],[f14102,f81144])).
% 92.33/13.69 thf(f81144,plain,(
% 92.33/13.69 spl854_919 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_919])])).
% 92.33/13.69 thf(f14102,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9902,f9122])).
% 92.33/13.69 thf(f9902,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5005])).
% 92.33/13.69 thf(f5005,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X1),X0))),
% 92.33/13.69 inference(rectify,[],[f1790])).
% 92.33/13.69 thf(f1790,axiom,(
% 92.33/13.69 ! [X35 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X137),X35) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X35),X137)),c_2Enum_2E0))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBITV__THM)).
% 92.33/13.69 thf(f81142,plain,(
% 92.33/13.69 spl854_918),
% 92.33/13.69 inference(avatar_split_clause,[],[f13640,f81140])).
% 92.33/13.69 thf(f81140,plain,(
% 92.33/13.69 spl854_918 <=> ! [X4 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum > $o > $o] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X3),X4))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_918])])).
% 92.33/13.69 thf(f13640,plain,(
% 92.33/13.69 ( ! [X3 : tyop_2Enum_2Enum > $o > $o,X4 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X3),X4))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9257,f9122,f9122])).
% 92.33/13.69 thf(f9257,plain,(
% 92.33/13.69 ( ! [X3 : tyop_2Enum_2Enum > $o > $o,X4 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,c_2Enum_2E0),X3),X4))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4855])).
% 92.33/13.69 thf(f4855,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o > $o,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,X0),X1),X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP($o,$o,vAPP(tyop_2Enum_2Enum,sTfun($o,$o),X1,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X2))),X0))) & ! [X3 : tyop_2Enum_2Enum > $o > $o,X4 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,c_2Enum_2E0),X3),X4))),
% 92.33/13.69 inference(rectify,[],[f1713])).
% 92.33/13.69 thf(f1713,axiom,(
% 92.33/13.69 ! [X135 : tyop_2Enum_2Enum,X75 : tyop_2Enum_2Enum > $o > $o,X23 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135)),X75),X23) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,X135),X75),X23)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP($o,$o,vAPP(tyop_2Enum_2Enum,sTfun($o,$o),X75,X135),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X135),X23))),X135))) & ! [X3 : tyop_2Enum_2Enum > $o > $o,X4 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,sTfun($o,$o)),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__MODIFY,c_2Enum_2E0),X3),X4))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__MODIFY__def)).
% 92.33/13.69 thf(f81138,plain,(
% 92.33/13.69 spl854_917),
% 92.33/13.69 inference(avatar_split_clause,[],[f13628,f81136])).
% 92.33/13.69 thf(f81136,plain,(
% 92.33/13.69 spl854_917 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_917])])).
% 92.33/13.69 thf(f13628,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9245,f9121])).
% 92.33/13.69 thf(f9245,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4853])).
% 92.33/13.69 thf(f81134,plain,(
% 92.33/13.69 spl854_916),
% 92.33/13.69 inference(avatar_split_clause,[],[f13577,f81132])).
% 92.33/13.69 thf(f81132,plain,(
% 92.33/13.69 spl854_916 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_916])])).
% 92.33/13.69 thf(f13577,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9183,f9121,f9121])).
% 92.33/13.69 thf(f9183,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4846])).
% 92.33/13.69 thf(f4846,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)),X1)) & ! [X2 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X2))),
% 92.33/13.69 inference(rectify,[],[f921])).
% 92.33/13.69 thf(f921,axiom,(
% 92.33/13.69 ! [X27 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X27)),X135) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X27),X135)),X135)) & ! [X136 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X136))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT)).
% 92.33/13.69 thf(f81130,plain,(
% 92.33/13.69 spl854_915),
% 92.33/13.69 inference(avatar_split_clause,[],[f13076,f81128])).
% 92.33/13.69 thf(f81128,plain,(
% 92.33/13.69 spl854_915 <=> ! [X1 : $tType,X0 : $tType,X4 : tyop_2Eoption_2Eoption(X0),X3 : tyop_2Eoption_2Eoption(X1),X2 : X1] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) | (vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_915])])).
% 92.33/13.69 thf(f13076,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) | (vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8871])).
% 92.33/13.69 thf(f8871,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : (((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ! [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != X3) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) != X4))) & (((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(X1,X0,vAPP(tyop_2Eoption_2Eoption(X1),sTfun(X1,X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),sTfun(X1,X0)),sK754(X0,X1),X4),X3),X2)) = X4)) | (vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))) & ((c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ((c_2Eoption_2ENONE(X1) != X3) & (c_2Eoption_2ENONE(X0) != X4))) & ((c_2Eoption_2ENONE(X1) = X3) | (c_2Eoption_2ENONE(X0) = X4) | (c_2Eoption_2ENONE(X1) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK754])],[f8869,f8870])).
% 92.33/13.69 thf(f8870,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : (? [X6 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X6) = X4)) => ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(X1,X0,vAPP(tyop_2Eoption_2Eoption(X1),sTfun(X1,X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),sTfun(X1,X0)),sK754(X0,X1),X4),X3),X2)) = X4)))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8869,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : (((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ! [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != X3) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) != X4))) & (? [X6 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X6) = X4)) | (vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))) & ((c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ((c_2Eoption_2ENONE(X1) != X3) & (c_2Eoption_2ENONE(X0) != X4))) & ((c_2Eoption_2ENONE(X1) = X3) | (c_2Eoption_2ENONE(X0) = X4) | (c_2Eoption_2ENONE(X1) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))))),
% 92.33/13.69 inference(rectify,[],[f8868])).
% 92.33/13.69 thf(f8868,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : (((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ! [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != X3) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) != X4))) & (? [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) = X4)) | (vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))) & ((c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ((c_2Eoption_2ENONE(X1) != X3) & (c_2Eoption_2ENONE(X0) != X4))) & ((c_2Eoption_2ENONE(X1) = X3) | (c_2Eoption_2ENONE(X0) = X4) | (c_2Eoption_2ENONE(X1) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3))))),
% 92.33/13.69 inference(flattening,[],[f8867])).
% 92.33/13.69 thf(f8867,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : ((((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ! [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != X3) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) != X4))) & (? [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) = X4)) | (vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)))) & (((c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) | ((c_2Eoption_2ENONE(X1) != X3) & (c_2Eoption_2ENONE(X0) != X4))) & (((c_2Eoption_2ENONE(X1) = X3) | (c_2Eoption_2ENONE(X0) = X4)) | (c_2Eoption_2ENONE(X1) != vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f5347])).
% 92.33/13.69 thf(f5347,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : tyop_2Eoption_2Eoption(X1),X4 : tyop_2Eoption_2Eoption(X0)] : (((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) <=> ? [X5 : X0] : ((vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2) = X3) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X5) = X4))) & ((c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X1),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__IGNORE__BIND(X1,X0),X4),X3)) <=> ((c_2Eoption_2ENONE(X1) = X3) | (c_2Eoption_2ENONE(X0) = X4))))),
% 92.33/13.69 inference(rectify,[],[f756])).
% 92.33/13.69 thf(f756,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X70 : X5,X210 : tyop_2Eoption_2Eoption(X5),X252 : tyop_2Eoption_2Eoption(X0)] : (((vAPP(X5,tyop_2Eoption_2Eoption(X5),c_2Eoption_2ESOME(X5),X70) = vAPP(tyop_2Eoption_2Eoption(X5),tyop_2Eoption_2Eoption(X5),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X5),tyop_2Eoption_2Eoption(X5)),c_2Eoption_2EOPTION__IGNORE__BIND(X5,X0),X252),X210)) <=> ? [X15 : X0] : ((vAPP(X5,tyop_2Eoption_2Eoption(X5),c_2Eoption_2ESOME(X5),X70) = X210) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X15) = X252))) & ((c_2Eoption_2ENONE(X5) = vAPP(tyop_2Eoption_2Eoption(X5),tyop_2Eoption_2Eoption(X5),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X5),tyop_2Eoption_2Eoption(X5)),c_2Eoption_2EOPTION__IGNORE__BIND(X5,X0),X252),X210)) <=> ((c_2Eoption_2ENONE(X5) = X210) | (c_2Eoption_2ENONE(X0) = X252))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION)).
% 92.33/13.69 thf(f81126,plain,(
% 92.33/13.69 spl854_914),
% 92.33/13.69 inference(avatar_split_clause,[],[f12529,f81124])).
% 92.33/13.69 thf(f81124,plain,(
% 92.33/13.69 spl854_914 <=> ! [X0 : $o,X3 : $o,X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)) | ($true = X1) | ($true = X2))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_914])])).
% 92.33/13.69 thf(f12529,plain,(
% 92.33/13.69 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)) | ($true = X1) | ($true = X2)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6503])).
% 92.33/13.69 thf(f6503,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)) | ((X2 != X3) & ($true = X1)) | ((X0 != X1) & ($true = X2)))),
% 92.33/13.69 inference(definition_folding,[],[f6087,f6502])).
% 92.33/13.69 thf(f6502,plain,(
% 92.33/13.69 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f6087,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))) | ((X2 != X3) & ($true = X1)) | ((X0 != X1) & ($true = X2)))),
% 92.33/13.69 inference(flattening,[],[f6086])).
% 92.33/13.69 thf(f6086,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))) | (((X2 != X3) & ($true = X1)) | ((X0 != X1) & ($true = X2))))),
% 92.33/13.69 inference(ennf_transformation,[],[f4286])).
% 92.33/13.69 thf(f4286,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X1) => (X2 = X3)) & (($true = X2) => (X0 = X1))) => ((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f4285])).
% 92.33/13.69 thf(f4285,plain,(
% 92.33/13.69 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X1 => (X2 = X3)) & (X2 => (X0 = X1))) => ((X2 & X0) <=> (X3 & X1)))),
% 92.33/13.69 inference(rectify,[],[f142])).
% 92.33/13.69 thf(f142,axiom,(
% 92.33/13.69 ! [X7 : $o,X61 : $o,X62 : $o,X63 : $o] : (((X61 => (X62 = X63)) & (X62 => (X7 = X61))) => ((X62 & X7) <=> (X63 & X61)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CONG)).
% 92.33/13.69 thf(f81044,plain,(
% 92.33/13.69 spl854_913),
% 92.33/13.69 inference(avatar_split_clause,[],[f12397,f81042])).
% 92.33/13.69 thf(f81042,plain,(
% 92.33/13.69 spl854_913 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : X0 > X1 > X2] : (vAPP(sTfun(tyop_2Epair_2Eprod(X0,X1),X2),sTfun(X0,sTfun(X1,X2)),c_2Epair_2ECURRY(X0,X1,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY(X0,X1,X2),X3)) = X3)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_913])])).
% 92.33/13.69 thf(f12397,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X1 > X2] : ((vAPP(sTfun(tyop_2Epair_2Eprod(X0,X1),X2),sTfun(X0,sTfun(X1,X2)),c_2Epair_2ECURRY(X0,X1,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY(X0,X1,X2),X3)) = X3)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5269])).
% 92.33/13.69 thf(f5269,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X1 > X2] : (vAPP(sTfun(tyop_2Epair_2Eprod(X0,X1),X2),sTfun(X0,sTfun(X1,X2)),c_2Epair_2ECURRY(X0,X1,X2),vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY(X0,X1,X2),X3)) = X3)),
% 92.33/13.69 inference(rectify,[],[f809])).
% 92.33/13.69 thf(f809,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X57 : $tType,X3 : X0 > X5 > X57] : (vAPP(sTfun(tyop_2Epair_2Eprod(X0,X5),X57),sTfun(X0,sTfun(X5,X57)),c_2Epair_2ECURRY(X0,X5,X57),vAPP(sTfun(X0,sTfun(X5,X57)),sTfun(tyop_2Epair_2Eprod(X0,X5),X57),c_2Epair_2EUNCURRY(X0,X5,X57),X3)) = X3)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2ECURRY__UNCURRY__THM)).
% 92.33/13.69 thf(f81040,plain,(
% 92.33/13.69 spl854_912),
% 92.33/13.69 inference(avatar_split_clause,[],[f12396,f81038])).
% 92.33/13.69 thf(f81038,plain,(
% 92.33/13.69 spl854_912 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : tyop_2Epair_2Eprod(X0,X1) > X2] : (vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY(X0,X1,X2),vAPP(sTfun(tyop_2Epair_2Eprod(X0,X1),X2),sTfun(X0,sTfun(X1,X2)),c_2Epair_2ECURRY(X0,X1,X2),X3)) = X3)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_912])])).
% 92.33/13.69 thf(f12396,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : tyop_2Epair_2Eprod(X0,X1) > X2] : ((vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY(X0,X1,X2),vAPP(sTfun(tyop_2Epair_2Eprod(X0,X1),X2),sTfun(X0,sTfun(X1,X2)),c_2Epair_2ECURRY(X0,X1,X2),X3)) = X3)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5268])).
% 92.33/13.69 thf(f5268,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : tyop_2Epair_2Eprod(X0,X1) > X2] : (vAPP(sTfun(X0,sTfun(X1,X2)),sTfun(tyop_2Epair_2Eprod(X0,X1),X2),c_2Epair_2EUNCURRY(X0,X1,X2),vAPP(sTfun(tyop_2Epair_2Eprod(X0,X1),X2),sTfun(X0,sTfun(X1,X2)),c_2Epair_2ECURRY(X0,X1,X2),X3)) = X3)),
% 92.33/13.69 inference(rectify,[],[f810])).
% 92.33/13.69 thf(f810,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X57 : $tType,X3 : tyop_2Epair_2Eprod(X0,X5) > X57] : (vAPP(sTfun(X0,sTfun(X5,X57)),sTfun(tyop_2Epair_2Eprod(X0,X5),X57),c_2Epair_2EUNCURRY(X0,X5,X57),vAPP(sTfun(tyop_2Epair_2Eprod(X0,X5),X57),sTfun(X0,sTfun(X5,X57)),c_2Epair_2ECURRY(X0,X5,X57),X3)) = X3)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2EUNCURRY__CURRY__THM)).
% 92.33/13.69 thf(f81036,plain,(
% 92.33/13.69 spl854_911),
% 92.33/13.69 inference(avatar_split_clause,[],[f12374,f81034])).
% 92.33/13.69 thf(f12374,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X2),X1)),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4214])).
% 92.33/13.69 thf(f4214,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X2),X1)),X2))),
% 92.33/13.69 inference(fool_elimination,[],[f4213])).
% 92.33/13.69 thf(f4213,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X2),X1)),X2)),
% 92.33/13.69 inference(rectify,[],[f1982])).
% 92.33/13.69 thf(f1982,axiom,(
% 92.33/13.69 ! [X0 : $tType,X8 : X0,X157 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X157),X8)),X157)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__SUBSET)).
% 92.33/13.69 thf(f81032,plain,(
% 92.33/13.69 spl854_910),
% 92.33/13.69 inference(avatar_split_clause,[],[f12368,f81030])).
% 92.33/13.69 thf(f81030,plain,(
% 92.33/13.69 spl854_910 <=> ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK640(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK641(X0,X1),X2)) = X2)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_910])])).
% 92.33/13.69 thf(f12368,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : ((vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK640(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK641(X0,X1),X2)) = X2)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8439])).
% 92.33/13.69 thf(f8439,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK640(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK641(X0,X1),X2)) = X2)),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK640,sK641])],[f5257,f8438])).
% 92.33/13.69 thf(f8438,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (? [X3 : X0,X4 : X1] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X3),X4) = X2) => (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK640(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK641(X0,X1),X2)) = X2))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f5257,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : ? [X3 : X0,X4 : X1] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X3),X4) = X2)),
% 92.33/13.69 inference(rectify,[],[f802])).
% 92.33/13.69 thf(f802,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X8 : tyop_2Epair_2Eprod(X0,X5)] : ? [X103 : X0,X263 : X5] : (vAPP(X5,tyop_2Epair_2Eprod(X0,X5),vAPP(X0,sTfun(X5,tyop_2Epair_2Eprod(X0,X5)),c_2Epair_2E_2C(X0,X5),X103),X263) = X8)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2Epair__CASES)).
% 92.33/13.69 thf(f81028,plain,(
% 92.33/13.69 spl854_909),
% 92.33/13.69 inference(avatar_split_clause,[],[f12367,f81026])).
% 92.33/13.69 thf(f81026,plain,(
% 92.33/13.69 spl854_909 <=> ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK638(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK639(X0,X1),X2)) = X2)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_909])])).
% 92.33/13.69 thf(f12367,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : ((vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK638(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK639(X0,X1),X2)) = X2)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8437])).
% 92.33/13.69 thf(f8437,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK638(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK639(X0,X1),X2)) = X2)),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK638,sK639])],[f5256,f8436])).
% 92.33/13.69 thf(f8436,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (? [X3 : X0,X4 : X1] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X3),X4) = X2) => (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,sK638(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,sK639(X0,X1),X2)) = X2))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f5256,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : ? [X3 : X0,X4 : X1] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X3),X4) = X2)),
% 92.33/13.69 inference(rectify,[],[f801])).
% 92.33/13.69 thf(f801,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X8 : tyop_2Epair_2Eprod(X0,X5)] : ? [X103 : X0,X263 : X5] : (vAPP(X5,tyop_2Epair_2Eprod(X0,X5),vAPP(X0,sTfun(X5,tyop_2Epair_2Eprod(X0,X5)),c_2Epair_2E_2C(X0,X5),X103),X263) = X8)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2EABS__PAIR__THM)).
% 92.33/13.69 thf(f81024,plain,(
% 92.33/13.69 spl854_908),
% 92.33/13.69 inference(avatar_split_clause,[],[f12175,f81022])).
% 92.33/13.69 thf(f81022,plain,(
% 92.33/13.69 spl854_908 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_908])])).
% 92.33/13.69 thf(f12175,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8287])).
% 92.33/13.69 thf(f8287,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1))) & ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) & ($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2))))),
% 92.33/13.69 inference(flattening,[],[f8286])).
% 92.33/13.69 thf(f8286,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2)) | (($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1)))) & ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) & ($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2))))),
% 92.33/13.69 inference(nnf_transformation,[],[f4110])).
% 92.33/13.69 thf(f4110,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2)) <=> (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) & ($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f4109])).
% 92.33/13.69 thf(f4109,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > X0,X2 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2) <=> (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X1),X2) & vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2) & vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f327])).
% 92.33/13.69 thf(f327,axiom,(
% 92.33/13.69 ! [X0 : $tType,X3 : X0 > X0 > X0,X117 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X3),X117) <=> (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X0),X3),X117) & vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X3),X117) & vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X3)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EMONOID__DEF)).
% 92.33/13.69 thf(f81020,plain,(
% 92.33/13.69 spl854_907),
% 92.33/13.69 inference(avatar_split_clause,[],[f12174,f81018])).
% 92.33/13.69 thf(f81018,plain,(
% 92.33/13.69 spl854_907 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_907])])).
% 92.33/13.69 thf(f12174,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2ERIGHT__ID(X0,X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8287])).
% 92.33/13.69 thf(f81016,plain,(
% 92.33/13.69 spl854_906),
% 92.33/13.69 inference(avatar_split_clause,[],[f11251,f81014])).
% 92.33/13.69 thf(f81014,plain,(
% 92.33/13.69 spl854_906 <=> ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,c_2Epair_2EFST(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,c_2Epair_2ESND(X0,X1),X2)) = X2)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_906])])).
% 92.33/13.69 thf(f11251,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : ((vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,c_2Epair_2EFST(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,c_2Epair_2ESND(X0,X1),X2)) = X2)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5147])).
% 92.33/13.69 thf(f5147,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),X0,c_2Epair_2EFST(X0,X1),X2)),vAPP(tyop_2Epair_2Eprod(X0,X1),X1,c_2Epair_2ESND(X0,X1),X2)) = X2)),
% 92.33/13.69 inference(rectify,[],[f790])).
% 92.33/13.69 thf(f790,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X8 : tyop_2Epair_2Eprod(X0,X5)] : (vAPP(X5,tyop_2Epair_2Eprod(X0,X5),vAPP(X0,sTfun(X5,tyop_2Epair_2Eprod(X0,X5)),c_2Epair_2E_2C(X0,X5),vAPP(tyop_2Epair_2Eprod(X0,X5),X0,c_2Epair_2EFST(X0,X5),X8)),vAPP(tyop_2Epair_2Eprod(X0,X5),X5,c_2Epair_2ESND(X0,X5),X8)) = X8)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2EPAIR)).
% 92.33/13.69 thf(f81012,plain,(
% 92.33/13.69 spl854_905),
% 92.33/13.69 inference(avatar_split_clause,[],[f10315,f81010])).
% 92.33/13.69 thf(f81010,plain,(
% 92.33/13.69 spl854_905 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_905])])).
% 92.33/13.69 thf(f10315,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5689])).
% 92.33/13.69 thf(f5689,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f2816])).
% 92.33/13.69 thf(f2816,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f2815])).
% 92.33/13.69 thf(f2815,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f559])).
% 92.33/13.69 thf(f559,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__TC)).
% 92.33/13.69 thf(f81008,plain,(
% 92.33/13.69 spl854_904),
% 92.33/13.69 inference(avatar_split_clause,[],[f10310,f81006])).
% 92.33/13.69 thf(f81006,plain,(
% 92.33/13.69 spl854_904 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_904])])).
% 92.33/13.69 thf(f10310,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5685])).
% 92.33/13.69 thf(f5685,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f2808])).
% 92.33/13.69 thf(f2808,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f2807])).
% 92.33/13.69 thf(f2807,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f483])).
% 92.33/13.69 thf(f483,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Etransitive__RC)).
% 92.33/13.69 thf(f80926,plain,(
% 92.33/13.69 spl854_903),
% 92.33/13.69 inference(avatar_split_clause,[],[f10308,f80924])).
% 92.33/13.69 thf(f80924,plain,(
% 92.33/13.69 spl854_903 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_903])])).
% 92.33/13.69 thf(f10308,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5683])).
% 92.33/13.69 thf(f5683,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f2804])).
% 92.33/13.69 thf(f2804,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f2803])).
% 92.33/13.69 thf(f2803,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f521])).
% 92.33/13.69 thf(f521,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ereflexive__TC)).
% 92.33/13.69 thf(f80922,plain,(
% 92.33/13.69 spl854_902),
% 92.33/13.69 inference(avatar_split_clause,[],[f10306,f80920])).
% 92.33/13.69 thf(f80920,plain,(
% 92.33/13.69 spl854_902 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_902])])).
% 92.33/13.69 thf(f10306,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5681])).
% 92.33/13.69 thf(f5681,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f2800])).
% 92.33/13.69 thf(f2800,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f2799])).
% 92.33/13.69 thf(f2799,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f520])).
% 92.33/13.69 thf(f520,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Esymmetric__TC)).
% 92.33/13.69 thf(f80918,plain,(
% 92.33/13.69 spl854_901),
% 92.33/13.69 inference(avatar_split_clause,[],[f10303,f80916])).
% 92.33/13.69 thf(f80916,plain,(
% 92.33/13.69 spl854_901 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_901])])).
% 92.33/13.69 thf(f10303,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5678])).
% 92.33/13.69 thf(f5678,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f2794])).
% 92.33/13.69 thf(f2794,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f2793])).
% 92.33/13.69 thf(f2793,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f649])).
% 92.33/13.69 thf(f649,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ediamond__TC__diamond)).
% 92.33/13.69 thf(f80914,plain,(
% 92.33/13.69 spl854_900),
% 92.33/13.69 inference(avatar_split_clause,[],[f10302,f80912])).
% 92.33/13.69 thf(f80912,plain,(
% 92.33/13.69 spl854_900 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_900])])).
% 92.33/13.69 thf(f10302,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5677])).
% 92.33/13.69 thf(f5677,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f2792])).
% 92.33/13.69 thf(f2792,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f2791])).
% 92.33/13.69 thf(f2791,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f648])).
% 92.33/13.69 thf(f648,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ediamond__RC__diamond)).
% 92.33/13.69 thf(f80910,plain,(
% 92.33/13.69 spl854_899),
% 92.33/13.69 inference(avatar_split_clause,[],[f9922,f80908])).
% 92.33/13.69 thf(f80908,plain,(
% 92.33/13.69 spl854_899 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))),X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_899])])).
% 92.33/13.69 thf(f9922,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5025])).
% 92.33/13.69 thf(f5025,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))),X1))),
% 92.33/13.69 inference(rectify,[],[f1648])).
% 92.33/13.69 thf(f1648,axiom,(
% 92.33/13.69 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137))),X137))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enpair__def)).
% 92.33/13.69 thf(f80906,plain,(
% 92.33/13.69 spl854_898),
% 92.33/13.69 inference(avatar_split_clause,[],[f9719,f80904])).
% 92.33/13.69 thf(f80904,plain,(
% 92.33/13.69 spl854_898 <=> ! [X2 : tyop_2Emin_2Eind,X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_898])])).
% 92.33/13.69 thf(f9719,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Emin_2Eind,X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6788])).
% 92.33/13.69 thf(f80798,plain,(
% 92.33/13.69 spl854_897 | ~spl854_308 | ~spl854_892),
% 92.33/13.69 inference(avatar_split_clause,[],[f80054,f80051,f35574,f80796])).
% 92.33/13.69 thf(f80796,plain,(
% 92.33/13.69 spl854_897 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_897])])).
% 92.33/13.69 thf(f35574,plain,(
% 92.33/13.69 spl854_308 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_308])])).
% 92.33/13.69 thf(f80051,plain,(
% 92.33/13.69 spl854_892 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_892])])).
% 92.33/13.69 thf(f80054,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) ) | (~spl854_308 | ~spl854_892)),
% 92.33/13.69 inference(forward_demodulation,[],[f80052,f35576])).
% 92.33/13.69 thf(f35576,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_308),
% 92.33/13.69 inference(avatar_component_clause,[],[f35574])).
% 92.33/13.69 thf(f80052,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) ) | ~spl854_892),
% 92.33/13.69 inference(avatar_component_clause,[],[f80051])).
% 92.33/13.69 thf(f80791,plain,(
% 92.33/13.69 spl854_896 | ~spl854_5 | spl854_712),
% 92.33/13.69 inference(avatar_split_clause,[],[f74611,f68675,f21881,f80788])).
% 92.33/13.69 thf(f80788,plain,(
% 92.33/13.69 spl854_896 <=> ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_896])])).
% 92.33/13.69 thf(f21881,plain,(
% 92.33/13.69 spl854_5 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_5])])).
% 92.33/13.69 thf(f68675,plain,(
% 92.33/13.69 spl854_712 <=> ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_712])])).
% 92.33/13.69 thf(f74611,plain,(
% 92.33/13.69 ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9)) | (~spl854_5 | spl854_712)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f74610])).
% 92.33/13.69 thf(f74610,plain,(
% 92.33/13.69 ($true != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9)) | (~spl854_5 | spl854_712)),
% 92.33/13.69 inference(superposition,[],[f68677,f21882])).
% 92.33/13.69 thf(f21882,plain,(
% 92.33/13.69 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl854_5),
% 92.33/13.69 inference(avatar_component_clause,[],[f21881])).
% 92.33/13.69 thf(f68677,plain,(
% 92.33/13.69 ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9)) | spl854_712),
% 92.33/13.69 inference(avatar_component_clause,[],[f68675])).
% 92.33/13.69 thf(f80267,plain,(
% 92.33/13.69 spl854_895 | ~spl854_5 | spl854_701),
% 92.33/13.69 inference(avatar_split_clause,[],[f74340,f68630,f21881,f80264])).
% 92.33/13.69 thf(f80264,plain,(
% 92.33/13.69 spl854_895 <=> ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_895])])).
% 92.33/13.69 thf(f68630,plain,(
% 92.33/13.69 spl854_701 <=> ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_701])])).
% 92.33/13.69 thf(f74340,plain,(
% 92.33/13.69 ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10)) | (~spl854_5 | spl854_701)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f74339])).
% 92.33/13.69 thf(f74339,plain,(
% 92.33/13.69 ($true != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10)) | (~spl854_5 | spl854_701)),
% 92.33/13.69 inference(superposition,[],[f68632,f21882])).
% 92.33/13.69 thf(f68632,plain,(
% 92.33/13.69 ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10)) | spl854_701),
% 92.33/13.69 inference(avatar_component_clause,[],[f68630])).
% 92.33/13.69 thf(f80063,plain,(
% 92.33/13.69 spl854_894),
% 92.33/13.69 inference(avatar_split_clause,[],[f19602,f80061])).
% 92.33/13.69 thf(f80061,plain,(
% 92.33/13.69 spl854_894 <=> ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : (vAPP(X0,X0,X2,X1) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_894])])).
% 92.33/13.69 thf(f19602,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(X0,X0,X2,X1) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19601,f18124])).
% 92.33/13.69 thf(f19601,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(X0,X0,X2,X1) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19600,f13563])).
% 92.33/13.69 thf(f19600,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(X0,X0,X2,X1) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14910,f13548])).
% 92.33/13.69 thf(f14910,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(X0,X0,X2,X1) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11249,f13512])).
% 92.33/13.69 thf(f11249,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X1) = vAPP(X0,X0,X2,X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5145])).
% 92.33/13.69 thf(f5145,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0,X2 : X0 > X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X1) = vAPP(X0,X0,X2,X1))),
% 92.33/13.69 inference(rectify,[],[f1270])).
% 92.33/13.69 thf(f1270,axiom,(
% 92.33/13.69 ! [X0 : $tType,X8 : X0,X25 : X0 > X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X25),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X8) = vAPP(X0,X0,X25,X8))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EFUNPOW__1)).
% 92.33/13.69 thf(f80059,plain,(
% 92.33/13.69 spl854_893 | ~spl854_5 | spl854_694),
% 92.33/13.69 inference(avatar_split_clause,[],[f74015,f68537,f21881,f80056])).
% 92.33/13.69 thf(f80056,plain,(
% 92.33/13.69 spl854_893 <=> ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_893])])).
% 92.33/13.69 thf(f68537,plain,(
% 92.33/13.69 spl854_694 <=> ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_694])])).
% 92.33/13.69 thf(f74015,plain,(
% 92.33/13.69 ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC)) | (~spl854_5 | spl854_694)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f74014])).
% 92.33/13.69 thf(f74014,plain,(
% 92.33/13.69 ($true != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC)) | (~spl854_5 | spl854_694)),
% 92.33/13.69 inference(superposition,[],[f68539,f21882])).
% 92.33/13.69 thf(f68539,plain,(
% 92.33/13.69 ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC)) | spl854_694),
% 92.33/13.69 inference(avatar_component_clause,[],[f68537])).
% 92.33/13.69 thf(f80053,plain,(
% 92.33/13.69 spl854_892),
% 92.33/13.69 inference(avatar_split_clause,[],[f18957,f80051])).
% 92.33/13.69 thf(f18957,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18956,f13567])).
% 92.33/13.69 thf(f18956,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18955,f13621])).
% 92.33/13.69 thf(f13621,plain,(
% 92.33/13.69 ( ! [X39 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X39)) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9198,f9122])).
% 92.33/13.69 thf(f9198,plain,(
% 92.33/13.69 ( ! [X39 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),c_2Enum_2E0) = X39)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6597])).
% 92.33/13.69 thf(f18955,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18954,f9898])).
% 92.33/13.69 thf(f9898,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5001])).
% 92.33/13.69 thf(f5001,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f946])).
% 92.33/13.69 thf(f946,axiom,(
% 92.33/13.69 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__SUC)).
% 92.33/13.69 thf(f18954,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14245,f13548])).
% 92.33/13.69 thf(f14245,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f10188,f13512,f13512])).
% 92.33/13.69 thf(f10188,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5536])).
% 92.33/13.69 thf(f5536,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0)))),
% 92.33/13.69 inference(ennf_transformation,[],[f5103])).
% 92.33/13.69 thf(f5103,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X0)) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = X0))),
% 92.33/13.69 inference(rectify,[],[f1404])).
% 92.33/13.69 thf(f1404,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X27) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,X136)) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X27),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = X136))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Eexactlog__characterisation)).
% 92.33/13.69 thf(f80049,plain,(
% 92.33/13.69 spl854_891),
% 92.33/13.69 inference(avatar_split_clause,[],[f18685,f80047])).
% 92.33/13.69 thf(f80047,plain,(
% 92.33/13.69 spl854_891 <=> ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X1),vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))) = X1)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_891])])).
% 92.33/13.69 thf(f18685,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X1),vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))) = X1)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18684,f18297])).
% 92.33/13.69 thf(f18684,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X1),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))))) = X1)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14083,f18174])).
% 92.33/13.69 thf(f14083,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X1),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) = X1)) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9865,f13523])).
% 92.33/13.69 thf(f9865,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X1),c_2Eoption_2ENONE(X0)) = X1)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4968])).
% 92.33/13.69 thf(f4968,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X1),c_2Eoption_2ENONE(X0)) = X1)),
% 92.33/13.69 inference(rectify,[],[f760])).
% 92.33/13.69 thf(f760,axiom,(
% 92.33/13.69 ! [X0 : $tType,X209 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),X209),c_2Eoption_2ENONE(X0)) = X209)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__CHOICE__NONE)).
% 92.33/13.69 thf(f80045,plain,(
% 92.33/13.69 spl854_890),
% 92.33/13.69 inference(avatar_split_clause,[],[f18378,f80043])).
% 92.33/13.69 thf(f80043,plain,(
% 92.33/13.69 spl854_890 <=> ! [X0 : $tType,X3 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))),X3) = X3)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_890])])).
% 92.33/13.69 thf(f18378,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))),X3) = X3)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18377,f18297])).
% 92.33/13.69 thf(f18377,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))))),X3) = X3)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13796,f18174])).
% 92.33/13.69 thf(f13796,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eone_2Eone,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINR(X0,tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))),X3) = X3)) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9487,f13523])).
% 92.33/13.69 thf(f9487,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X3 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),c_2Eoption_2ENONE(X0)),X3) = X3)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4935])).
% 92.33/13.69 thf(f4935,plain,(
% 92.33/13.69 ! [X0 : $tType] : (! [X1 : X0,X2 : tyop_2Eoption_2Eoption(X0)] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)),X2)) & ! [X3 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),c_2Eoption_2ENONE(X0)),X3) = X3))),
% 92.33/13.69 inference(rectify,[],[f717])).
% 92.33/13.69 thf(f717,axiom,(
% 92.33/13.69 ! [X0 : $tType] : (! [X4 : X0,X212 : tyop_2Eoption_2Eoption(X0)] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4)),X212)) & ! [X211 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),c_2Eoption_2ENONE(X0)),X211) = X211))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__CHOICE__def)).
% 92.33/13.69 thf(f80041,plain,(
% 92.33/13.69 spl854_889),
% 92.33/13.69 inference(avatar_split_clause,[],[f15099,f80039])).
% 92.33/13.69 thf(f80039,plain,(
% 92.33/13.69 spl854_889 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_889])])).
% 92.33/13.69 thf(f15099,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11707,f9121])).
% 92.33/13.69 thf(f11707,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6007])).
% 92.33/13.69 thf(f6007,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)))),
% 92.33/13.69 inference(ennf_transformation,[],[f3860])).
% 92.33/13.69 thf(f3860,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) => ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X2))))),
% 92.33/13.69 inference(fool_elimination,[],[f3859])).
% 92.33/13.69 thf(f3859,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X2)))),
% 92.33/13.69 inference(rectify,[],[f1476])).
% 92.33/13.69 thf(f1476,axiom,(
% 92.33/13.69 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum,X315 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X72),X49) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X72),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X49),X315)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EDIVIDES__MULT)).
% 92.33/13.69 thf(f80037,plain,(
% 92.33/13.69 spl854_888),
% 92.33/13.69 inference(avatar_split_clause,[],[f14758,f80035])).
% 92.33/13.69 thf(f80035,plain,(
% 92.33/13.69 spl854_888 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK369,X1),X0)),X0) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_888])])).
% 92.33/13.69 thf(f14758,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK369,X1),X0)),X0) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f11043,f9121])).
% 92.33/13.69 thf(f11043,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK369,X1),X0)),X0) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7574])).
% 92.33/13.69 thf(f7574,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) != X1)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK369,X1),X0)),X0) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK369])],[f7572,f7573])).
% 92.33/13.69 thf(f7573,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (? [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X3),X0) = X1) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK369,X1),X0)),X0) = X1))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f7572,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) != X1)) & (? [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X3),X0) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))))),
% 92.33/13.69 inference(rectify,[],[f7571])).
% 92.33/13.69 thf(f7571,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) != X1)) & (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3362])).
% 92.33/13.69 thf(f3362,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) <=> ? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) = X1))),
% 92.33/13.69 inference(fool_elimination,[],[f3361])).
% 92.33/13.69 thf(f3361,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1) <=> ? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) = X1))),
% 92.33/13.69 inference(rectify,[],[f1460])).
% 92.33/13.69 thf(f1460,axiom,(
% 92.33/13.69 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X72),X49) <=> ? [X113 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X113),X72) = X49))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2Edivides__def)).
% 92.33/13.69 thf(f80033,plain,(
% 92.33/13.69 spl854_887),
% 92.33/13.69 inference(avatar_split_clause,[],[f12709,f80031])).
% 92.33/13.69 thf(f80031,plain,(
% 92.33/13.69 spl854_887 <=> ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X0 : X2 > X1,X6 : X2] : (($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X6))) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK680(X1),X3))) | ($true != vAPP(sTfun(X2,X1),$o,sP94(X1,X2),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_887])])).
% 92.33/13.69 thf(f12709,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X0 : X2 > X1,X6 : X2] : (($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X6))) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK680(X1),X3))) | ($true != vAPP(sTfun(X2,X1),$o,sP94(X1,X2),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8570])).
% 92.33/13.69 thf(f8570,plain,(
% 92.33/13.69 ! [X0 : X2 > X1,X1 : $tType,X2 : $tType] : (! [X3 : X1 > $o] : ((! [X4 : X1] : ($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X2),sK679(X1,X2),X3),X0))))) & (! [X6 : X2] : ($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X6))) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK680(X1),X3))))) | ($true != vAPP(sTfun(X2,X1),$o,sP94(X1,X2),X0)))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK679,sK680])],[f8567,f8569,f8568])).
% 92.33/13.69 thf(f8568,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : $tType,X0 : X2 > X1,X3 : X1 > $o] : (? [X5 : X2] : ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,X5))) => ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X2),sK679(X1,X2),X3),X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8569,plain,(
% 92.33/13.69 ! [X1 : $tType,X3 : X1 > $o] : (? [X7 : X1] : ($true != vAPP(X1,$o,X3,X7)) => ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK680(X1),X3))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8567,plain,(
% 92.33/13.69 ! [X0 : X2 > X1,X1 : $tType,X2 : $tType] : (! [X3 : X1 > $o] : ((! [X4 : X1] : ($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X2] : ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,X5)))) & (! [X6 : X2] : ($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X6))) | ? [X7 : X1] : ($true != vAPP(X1,$o,X3,X7)))) | ($true != vAPP(sTfun(X2,X1),$o,sP94(X1,X2),X0)))),
% 92.33/13.69 inference(rectify,[],[f8566])).
% 92.33/13.69 thf(f8566,plain,(
% 92.33/13.69 ! [X2 : X1 > X0,X0 : $tType,X1 : $tType] : (! [X9 : X0 > $o] : ((! [X10 : X0] : ($true = vAPP(X0,$o,X9,X10)) | ? [X11 : X1] : ($true != vAPP(X0,$o,X9,vAPP(X1,X0,X2,X11)))) & (! [X11 : X1] : ($true = vAPP(X0,$o,X9,vAPP(X1,X0,X2,X11))) | ? [X10 : X0] : ($true != vAPP(X0,$o,X9,X10)))) | ($true != vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2)))),
% 92.33/13.69 inference(nnf_transformation,[],[f6544])).
% 92.33/13.69 thf(f6544,plain,(
% 92.33/13.69 ! [X2 : X1 > X0,X0 : $tType,X1 : $tType] : (! [X9 : X0 > $o] : (! [X10 : X0] : ($true = vAPP(X0,$o,X9,X10)) <=> ! [X11 : X1] : ($true = vAPP(X0,$o,X9,vAPP(X1,X0,X2,X11)))) | ~($true = vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2)))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f80029,plain,(
% 92.33/13.69 spl854_886),
% 92.33/13.69 inference(avatar_split_clause,[],[f12708,f80027])).
% 92.33/13.69 thf(f80027,plain,(
% 92.33/13.69 spl854_886 <=> ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X0 : X2 > X1,X5 : X2] : (($true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK677(X1),X3))) | ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,X5))) | ($true != vAPP(sTfun(X2,X1),$o,sP95(X1,X2),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_886])])).
% 92.33/13.69 thf(f12708,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X0 : X2 > X1,X5 : X2] : (($true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK677(X1),X3))) | ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,X5))) | ($true != vAPP(sTfun(X2,X1),$o,sP95(X1,X2),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8565])).
% 92.33/13.69 thf(f8565,plain,(
% 92.33/13.69 ! [X0 : X2 > X1,X1 : $tType,X2 : $tType] : (! [X3 : X1 > $o] : ((($true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK677(X1),X3))) | ! [X5 : X2] : ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,X5)))) & (($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X2),sK678(X1,X2),X3),X0)))) | ! [X7 : X1] : ($true != vAPP(X1,$o,X3,X7)))) | ($true != vAPP(sTfun(X2,X1),$o,sP95(X1,X2),X0)))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK677,sK678])],[f8562,f8564,f8563])).
% 92.33/13.69 thf(f8563,plain,(
% 92.33/13.69 ! [X1 : $tType,X3 : X1 > $o] : (? [X4 : X1] : ($true = vAPP(X1,$o,X3,X4)) => ($true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,sK677(X1),X3))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8564,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : $tType,X0 : X2 > X1,X3 : X1 > $o] : (? [X6 : X2] : ($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X6))) => ($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X2),sK678(X1,X2),X3),X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8562,plain,(
% 92.33/13.69 ! [X0 : X2 > X1,X1 : $tType,X2 : $tType] : (! [X3 : X1 > $o] : ((? [X4 : X1] : ($true = vAPP(X1,$o,X3,X4)) | ! [X5 : X2] : ($true != vAPP(X1,$o,X3,vAPP(X2,X1,X0,X5)))) & (? [X6 : X2] : ($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X6))) | ! [X7 : X1] : ($true != vAPP(X1,$o,X3,X7)))) | ($true != vAPP(sTfun(X2,X1),$o,sP95(X1,X2),X0)))),
% 92.33/13.69 inference(rectify,[],[f8561])).
% 92.33/13.69 thf(f8561,plain,(
% 92.33/13.69 ! [X2 : X1 > X0,X0 : $tType,X1 : $tType] : (! [X6 : X0 > $o] : ((? [X7 : X0] : ($true = vAPP(X0,$o,X6,X7)) | ! [X8 : X1] : ($true != vAPP(X0,$o,X6,vAPP(X1,X0,X2,X8)))) & (? [X8 : X1] : ($true = vAPP(X0,$o,X6,vAPP(X1,X0,X2,X8))) | ! [X7 : X0] : ($true != vAPP(X0,$o,X6,X7)))) | ($true != vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2)))),
% 92.33/13.69 inference(nnf_transformation,[],[f6545])).
% 92.33/13.69 thf(f6545,plain,(
% 92.33/13.69 ! [X2 : X1 > X0,X0 : $tType,X1 : $tType] : (! [X6 : X0 > $o] : (? [X7 : X0] : ($true = vAPP(X0,$o,X6,X7)) <=> ? [X8 : X1] : ($true = vAPP(X0,$o,X6,vAPP(X1,X0,X2,X8)))) | ~($true = vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2)))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f80025,plain,(
% 92.33/13.69 spl854_885),
% 92.33/13.69 inference(avatar_split_clause,[],[f12169,f80023])).
% 92.33/13.69 thf(f80023,plain,(
% 92.33/13.69 spl854_885 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_885])])).
% 92.33/13.69 thf(f12169,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8281])).
% 92.33/13.69 thf(f8281,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2))) & (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6476])).
% 92.33/13.69 thf(f6476,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) <=> ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2)))),
% 92.33/13.69 inference(definition_folding,[],[f6063,f6475])).
% 92.33/13.69 thf(f6475,plain,(
% 92.33/13.69 ! [X2 : X0,X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2)) <=> ! [X3 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ? [X4 : X0] : ((vAPP(X0,$o,X3,X4) != $true) & ! [X5 : X0] : (($true = vAPP(X0,$o,X3,X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f6063,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) <=> ! [X3 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ? [X4 : X0] : ((vAPP(X0,$o,X3,X4) != $true) & ! [X5 : X0] : (($true = vAPP(X0,$o,X3,X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))))))),
% 92.33/13.69 inference(ennf_transformation,[],[f4106])).
% 92.33/13.69 thf(f4106,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) <=> ! [X3 : X0 > $o] : (! [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) => ($true = vAPP(X0,$o,X3,X5))) => (vAPP(X0,$o,X3,X4) = $true)) => ($true = vAPP(X0,$o,X3,X2))))),
% 92.33/13.69 inference(fool_elimination,[],[f4105])).
% 92.33/13.69 thf(f4105,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2) <=> ! [X3 : X0 > $o] : (! [X4 : X0] : (! [X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4) => vAPP(X0,$o,X3,X5)) => vAPP(X0,$o,X3,X4)) => vAPP(X0,$o,X3,X2)))),
% 92.33/13.69 inference(rectify,[],[f428])).
% 92.33/13.69 thf(f428,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o,X73 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X143),X73) <=> ! [X133 : X0 > $o] : (! [X15 : X0] : (! [X28 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X28),X15) => vAPP(X0,$o,X133,X28)) => vAPP(X0,$o,X133,X15)) => vAPP(X0,$o,X133,X73)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWFP__DEF)).
% 92.33/13.69 thf(f80021,plain,(
% 92.33/13.69 spl854_884),
% 92.33/13.69 inference(avatar_split_clause,[],[f12168,f80019])).
% 92.33/13.69 thf(f80019,plain,(
% 92.33/13.69 spl854_884 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_884])])).
% 92.33/13.69 thf(f12168,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),sP55(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8281])).
% 92.33/13.69 thf(f80017,plain,(
% 92.33/13.69 spl854_883),
% 92.33/13.69 inference(avatar_split_clause,[],[f12088,f80015])).
% 92.33/13.69 thf(f80015,plain,(
% 92.33/13.69 spl854_883 <=> ! [X1 : $tType,X0 : $tType,X5 : X0,X6 : X0,X2 : X0 > X0 > X1] : ((vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X5),X6) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X6),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_883])])).
% 92.33/13.69 thf(f12088,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X0 > X1,X6 : X0,X5 : X0] : ((vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X5),X6) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X6),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8232])).
% 92.33/13.69 thf(f8232,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X1] : ((($true = vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2)) | (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK603(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK604(X0,X1),X2)) != vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK604(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK603(X0,X1),X2)))) & (! [X5 : X0,X6 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X5),X6) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X6),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK603,sK604])],[f8230,f8231])).
% 92.33/13.69 thf(f8231,plain,(
% 92.33/13.69 ! [X1 : $tType,X0 : $tType,X2 : X0 > X0 > X1] : (? [X3 : X0,X4 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X3),X4) != vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X4),X3)) => (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK603(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK604(X0,X1),X2)) != vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK604(X0,X1),X2)),vAPP(sTfun(X0,sTfun(X0,X1)),X0,sK603(X0,X1),X2))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8230,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X1] : ((($true = vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2)) | ? [X3 : X0,X4 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X3),X4) != vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X4),X3))) & (! [X5 : X0,X6 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X5),X6) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X6),X5)) | ($true != vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2))))),
% 92.33/13.69 inference(rectify,[],[f8229])).
% 92.33/13.69 thf(f8229,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X1] : ((($true = vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2)) | ? [X3 : X0,X4 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X3),X4) != vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X4),X3))) & (! [X3 : X0,X4 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X3),X4) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X4),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2))))),
% 92.33/13.69 inference(nnf_transformation,[],[f4038])).
% 92.33/13.69 thf(f4038,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X1] : (($true = vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2)) <=> ! [X3 : X0,X4 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X3),X4) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X4),X3)))),
% 92.33/13.69 inference(fool_elimination,[],[f4037])).
% 92.33/13.69 thf(f4037,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X0 > X1] : (vAPP(sTfun(X0,sTfun(X0,X1)),$o,c_2Ecombin_2ECOMM(X0,X1),X2) <=> ! [X3 : X0,X4 : X0] : (vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X3),X4) = vAPP(X0,X1,vAPP(X0,sTfun(X0,X1),X2,X4),X3)))),
% 92.33/13.69 inference(rectify,[],[f323])).
% 92.33/13.69 thf(f323,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X3 : X0 > X0 > X5] : (vAPP(sTfun(X0,sTfun(X0,X5)),$o,c_2Ecombin_2ECOMM(X0,X5),X3) <=> ! [X4 : X0,X12 : X0] : (vAPP(X0,X5,vAPP(X0,sTfun(X0,X5),X3,X4),X12) = vAPP(X0,X5,vAPP(X0,sTfun(X0,X5),X3,X12),X4)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2ECOMM__DEF)).
% 92.33/13.69 thf(f80013,plain,(
% 92.33/13.69 spl854_882 | ~spl854_5 | spl854_693),
% 92.33/13.69 inference(avatar_split_clause,[],[f71306,f68269,f21881,f80010])).
% 92.33/13.69 thf(f80010,plain,(
% 92.33/13.69 spl854_882 <=> ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_882])])).
% 92.33/13.69 thf(f68269,plain,(
% 92.33/13.69 spl854_693 <=> ($true = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_693])])).
% 92.33/13.69 thf(f71306,plain,(
% 92.33/13.69 ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61)) | (~spl854_5 | spl854_693)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f71305])).
% 92.33/13.69 thf(f71305,plain,(
% 92.33/13.69 ($true != $true) | ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61)) | (~spl854_5 | spl854_693)),
% 92.33/13.69 inference(superposition,[],[f68271,f21882])).
% 92.33/13.69 thf(f68271,plain,(
% 92.33/13.69 ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61)) | spl854_693),
% 92.33/13.69 inference(avatar_component_clause,[],[f68269])).
% 92.33/13.69 thf(f80008,plain,(
% 92.33/13.69 spl854_881),
% 92.33/13.69 inference(avatar_split_clause,[],[f10748,f80006])).
% 92.33/13.69 thf(f80006,plain,(
% 92.33/13.69 spl854_881 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_881])])).
% 92.33/13.69 thf(f10748,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7345])).
% 92.33/13.69 thf(f7345,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7344])).
% 92.33/13.69 thf(f7344,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3170])).
% 92.33/13.69 thf(f3170,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3169])).
% 92.33/13.69 thf(f3169,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f440])).
% 92.33/13.69 thf(f440,axiom,(
% 92.33/13.69 ! [X140 : $tType,X156 : X140 > X140 > $o] : (vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2EOrder(X140),X156) <=> (vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Etransitive(X140),X156) & vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Eantisymmetric(X140),X156)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EOrder)).
% 92.33/13.69 thf(f80004,plain,(
% 92.33/13.69 spl854_880),
% 92.33/13.69 inference(avatar_split_clause,[],[f10745,f80002])).
% 92.33/13.69 thf(f80002,plain,(
% 92.33/13.69 spl854_880 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_880])])).
% 92.33/13.69 thf(f10745,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7343])).
% 92.33/13.69 thf(f7343,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7342])).
% 92.33/13.69 thf(f7342,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3168])).
% 92.33/13.69 thf(f3168,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3167])).
% 92.33/13.69 thf(f3167,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f442])).
% 92.33/13.69 thf(f442,axiom,(
% 92.33/13.69 ! [X140 : $tType,X156 : X140 > X140 > $o] : (vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2EStrongOrder(X140),X156) <=> (vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Etransitive(X140),X156) & vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Eirreflexive(X140),X156)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EStrongOrder)).
% 92.33/13.69 thf(f80000,plain,(
% 92.33/13.69 spl854_879),
% 92.33/13.69 inference(avatar_split_clause,[],[f10719,f79998])).
% 92.33/13.69 thf(f79998,plain,(
% 92.33/13.69 spl854_879 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_879])])).
% 92.33/13.69 thf(f10719,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7323])).
% 92.33/13.69 thf(f7323,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7322])).
% 92.33/13.69 thf(f7322,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3156])).
% 92.33/13.69 thf(f3156,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3155])).
% 92.33/13.69 thf(f3155,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f446])).
% 92.33/13.69 thf(f446,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X143) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWeakLinearOrder)).
% 92.33/13.69 thf(f79996,plain,(
% 92.33/13.69 spl854_878),
% 92.33/13.69 inference(avatar_split_clause,[],[f10712,f79994])).
% 92.33/13.69 thf(f79994,plain,(
% 92.33/13.69 spl854_878 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_878])])).
% 92.33/13.69 thf(f10712,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7316])).
% 92.33/13.69 thf(f7316,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7315])).
% 92.33/13.69 thf(f7315,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3152])).
% 92.33/13.69 thf(f3152,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3151])).
% 92.33/13.69 thf(f3151,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f439])).
% 92.33/13.69 thf(f439,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X143) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EPreOrder)).
% 92.33/13.69 thf(f79992,plain,(
% 92.33/13.69 spl854_877),
% 92.33/13.69 inference(avatar_split_clause,[],[f10709,f79990])).
% 92.33/13.69 thf(f79990,plain,(
% 92.33/13.69 spl854_877 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_877])])).
% 92.33/13.69 thf(f10709,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7314])).
% 92.33/13.69 thf(f7314,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7313])).
% 92.33/13.69 thf(f7313,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3150])).
% 92.33/13.69 thf(f3150,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3149])).
% 92.33/13.69 thf(f3149,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f444])).
% 92.33/13.69 thf(f444,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X143) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ELinearOrder)).
% 92.33/13.69 thf(f79988,plain,(
% 92.33/13.69 spl854_876),
% 92.33/13.69 inference(avatar_split_clause,[],[f10706,f79986])).
% 92.33/13.69 thf(f79986,plain,(
% 92.33/13.69 spl854_876 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_876])])).
% 92.33/13.69 thf(f10706,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7312])).
% 92.33/13.69 thf(f7312,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7311])).
% 92.33/13.69 thf(f7311,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3148])).
% 92.33/13.69 thf(f3148,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))))),
% 92.33/13.69 inference(fool_elimination,[],[f3147])).
% 92.33/13.69 thf(f3147,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))),
% 92.33/13.69 inference(rectify,[],[f445])).
% 92.33/13.69 thf(f445,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X143) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X143)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EStrongLinearOrder)).
% 92.33/13.69 thf(f79984,plain,(
% 92.33/13.69 spl854_875),
% 92.33/13.69 inference(avatar_split_clause,[],[f10215,f79982])).
% 92.33/13.69 thf(f79982,plain,(
% 92.33/13.69 spl854_875 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_875])])).
% 92.33/13.69 thf(f10215,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5567])).
% 92.33/13.69 thf(f5567,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))),
% 92.33/13.69 inference(flattening,[],[f5566])).
% 92.33/13.69 thf(f5566,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2666])).
% 92.33/13.69 thf(f2666,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)))),
% 92.33/13.69 inference(fool_elimination,[],[f2665])).
% 92.33/13.69 thf(f2665,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))),
% 92.33/13.69 inference(rectify,[],[f612])).
% 92.33/13.69 thf(f612,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X143)) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X143))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Eirrefl__trans__implies__antisym)).
% 92.33/13.69 thf(f79980,plain,(
% 92.33/13.69 spl854_874),
% 92.33/13.69 inference(avatar_split_clause,[],[f10214,f79978])).
% 92.33/13.69 thf(f79978,plain,(
% 92.33/13.69 spl854_874 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_874])])).
% 92.33/13.69 thf(f10214,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5565])).
% 92.33/13.69 thf(f5565,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)))),
% 92.33/13.69 inference(flattening,[],[f5564])).
% 92.33/13.69 thf(f5564,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2664])).
% 92.33/13.69 thf(f2664,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1))) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)))),
% 92.33/13.69 inference(fool_elimination,[],[f2663])).
% 92.33/13.69 thf(f2663,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1))),
% 92.33/13.69 inference(rectify,[],[f651])).
% 92.33/13.69 thf(f651,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ESN(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X143)) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X143))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ENewmans__lemma)).
% 92.33/13.69 thf(f79976,plain,(
% 92.33/13.69 spl854_873),
% 92.33/13.69 inference(avatar_split_clause,[],[f10173,f79974])).
% 92.33/13.69 thf(f79974,plain,(
% 92.33/13.69 spl854_873 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ((c_2Erelation_2EEMPTY__REL(X0) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_873])])).
% 92.33/13.69 thf(f10173,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((c_2Erelation_2EEMPTY__REL(X0) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6853])).
% 92.33/13.69 thf(f6853,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0))) | (c_2Erelation_2EEMPTY__REL(X0) != X1)) & ((c_2Erelation_2EEMPTY__REL(X0) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0)))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X1)))),
% 92.33/13.69 inference(flattening,[],[f6852])).
% 92.33/13.69 thf(f6852,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0))) | (c_2Erelation_2EEMPTY__REL(X0) != X1)) & ((c_2Erelation_2EEMPTY__REL(X0) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0))))) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X1)))),
% 92.33/13.69 inference(nnf_transformation,[],[f2620])).
% 92.33/13.69 thf(f2620,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0))) <=> (c_2Erelation_2EEMPTY__REL(X0) = X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X1)))),
% 92.33/13.69 inference(fool_elimination,[],[f2619])).
% 92.33/13.69 thf(f2619,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X1),c_2Erelation_2EEMPTY__REL(X0)) <=> (c_2Erelation_2EEMPTY__REL(X0) = X1)) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X1))),
% 92.33/13.69 inference(rectify,[],[f644])).
% 92.33/13.69 thf(f644,axiom,(
% 92.33/13.69 ! [X0 : $tType,X143 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),X143),c_2Erelation_2EEMPTY__REL(X0)) <=> (c_2Erelation_2EEMPTY__REL(X0) = X143)) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X143))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EREMPTY__SUBSET)).
% 92.33/13.69 thf(f79972,plain,(
% 92.33/13.69 spl854_872),
% 92.33/13.69 inference(avatar_split_clause,[],[f10132,f79970])).
% 92.33/13.69 thf(f79970,plain,(
% 92.33/13.69 spl854_872 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > tyop_2Eoption_2Eoption(X0),X2 : X1] : (vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X1),sTfun(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__BIND(X0,X1),vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2)),X3) = vAPP(X1,tyop_2Eoption_2Eoption(X0),X3,X2))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_872])])).
% 92.33/13.69 thf(f10132,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1 > tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X1),sTfun(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__BIND(X0,X1),vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2)),X3) = vAPP(X1,tyop_2Eoption_2Eoption(X0),X3,X2))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5092])).
% 92.33/13.69 thf(f5092,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1,X3 : X1 > tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X1),sTfun(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__BIND(X0,X1),vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),X2)),X3) = vAPP(X1,tyop_2Eoption_2Eoption(X0),X3,X2)) & ! [X4 : X1 > tyop_2Eoption_2Eoption(X0)] : (c_2Eoption_2ENONE(X0) = vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X1),sTfun(sTfun(X1,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__BIND(X0,X1),c_2Eoption_2ENONE(X1)),X4)))),
% 92.33/13.69 inference(rectify,[],[f714])).
% 92.33/13.69 thf(f714,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType] : (! [X4 : X5,X114 : X5 > tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X5,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X5),sTfun(sTfun(X5,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__BIND(X0,X5),vAPP(X5,tyop_2Eoption_2Eoption(X5),c_2Eoption_2ESOME(X5),X4)),X114) = vAPP(X5,tyop_2Eoption_2Eoption(X0),X114,X4)) & ! [X3 : X5 > tyop_2Eoption_2Eoption(X0)] : (c_2Eoption_2ENONE(X0) = vAPP(sTfun(X5,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X5),sTfun(sTfun(X5,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__BIND(X0,X5),c_2Eoption_2ENONE(X5)),X3)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__BIND__def)).
% 92.33/13.69 thf(f79968,plain,(
% 92.33/13.69 spl854_871 | ~spl854_5 | spl854_691),
% 92.33/13.69 inference(avatar_split_clause,[],[f70438,f66975,f21881,f79965])).
% 92.33/13.69 thf(f79965,plain,(
% 92.33/13.69 spl854_871 <=> ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_871])])).
% 92.33/13.69 thf(f66975,plain,(
% 92.33/13.69 spl854_691 <=> ($true = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_691])])).
% 92.33/13.69 thf(f70438,plain,(
% 92.33/13.69 ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides)) | (~spl854_5 | spl854_691)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f70437])).
% 92.33/13.69 thf(f70437,plain,(
% 92.33/13.69 ($true != $true) | ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides)) | (~spl854_5 | spl854_691)),
% 92.33/13.69 inference(superposition,[],[f66977,f21882])).
% 92.33/13.69 thf(f66977,plain,(
% 92.33/13.69 ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides)) | spl854_691),
% 92.33/13.69 inference(avatar_component_clause,[],[f66975])).
% 92.33/13.69 thf(f79963,plain,(
% 92.33/13.69 spl854_870),
% 92.33/13.69 inference(avatar_split_clause,[],[f9507,f79961])).
% 92.33/13.69 thf(f79961,plain,(
% 92.33/13.69 spl854_870 <=> ! [X0 : $tType,X3 : tyop_2Enum_2Enum > X0,X2 : X0,X1 : tyop_2Enum_2Enum] : (vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X2),X3) = vAPP(tyop_2Enum_2Enum,X0,X3,X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_870])])).
% 92.33/13.69 thf(f9507,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X3 : tyop_2Enum_2Enum > X0,X1 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X2),X3) = vAPP(tyop_2Enum_2Enum,X0,X3,X1))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4943])).
% 92.33/13.69 thf(f4943,plain,(
% 92.33/13.69 ! [X0 : $tType] : (! [X1 : tyop_2Enum_2Enum,X2 : X0,X3 : tyop_2Enum_2Enum > X0] : (vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X2),X3) = vAPP(tyop_2Enum_2Enum,X0,X3,X1)) & ! [X4 : X0,X5 : tyop_2Enum_2Enum > X0] : (vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),c_2Enum_2E0),X4),X5) = X4))),
% 92.33/13.69 inference(rectify,[],[f928])).
% 92.33/13.69 thf(f928,axiom,(
% 92.33/13.69 ! [X0 : $tType] : (! [X135 : tyop_2Enum_2Enum,X122 : X0,X153 : tyop_2Enum_2Enum > X0] : (vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135)),X122),X153) = vAPP(tyop_2Enum_2Enum,X0,X153,X135)) & ! [X29 : X0,X25 : tyop_2Enum_2Enum > X0] : (vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),c_2Enum_2E0),X29),X25) = X29))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2Enum__case__def)).
% 92.33/13.69 thf(f79747,plain,(
% 92.33/13.69 spl854_869 | ~spl854_308 | ~spl854_858),
% 92.33/13.69 inference(avatar_split_clause,[],[f76700,f76697,f35574,f79745])).
% 92.33/13.69 thf(f79745,plain,(
% 92.33/13.69 spl854_869 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_869])])).
% 92.33/13.69 thf(f76697,plain,(
% 92.33/13.69 spl854_858 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_858])])).
% 92.33/13.69 thf(f76700,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) ) | (~spl854_308 | ~spl854_858)),
% 92.33/13.69 inference(forward_demodulation,[],[f76698,f35576])).
% 92.33/13.69 thf(f76698,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) ) | ~spl854_858),
% 92.33/13.69 inference(avatar_component_clause,[],[f76697])).
% 92.33/13.69 thf(f79735,plain,(
% 92.33/13.69 spl854_868 | ~spl854_5 | spl854_680),
% 92.33/13.69 inference(avatar_split_clause,[],[f68729,f66930,f21881,f79732])).
% 92.33/13.69 thf(f79732,plain,(
% 92.33/13.69 spl854_868 <=> ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_868])])).
% 92.33/13.69 thf(f66930,plain,(
% 92.33/13.69 spl854_680 <=> ($true = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_680])])).
% 92.33/13.69 thf(f68729,plain,(
% 92.33/13.69 ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D)) | (~spl854_5 | spl854_680)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f68728])).
% 92.33/13.69 thf(f68728,plain,(
% 92.33/13.69 ($true != $true) | ($false = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D)) | (~spl854_5 | spl854_680)),
% 92.33/13.69 inference(superposition,[],[f66932,f21882])).
% 92.33/13.69 thf(f66932,plain,(
% 92.33/13.69 ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D)) | spl854_680),
% 92.33/13.69 inference(avatar_component_clause,[],[f66930])).
% 92.33/13.69 thf(f76738,plain,(
% 92.33/13.69 spl854_867 | ~spl854_71 | ~spl854_115 | ~spl854_705 | ~spl854_866),
% 92.33/13.69 inference(avatar_split_clause,[],[f76734,f76730,f68647,f22649,f22298,f76736])).
% 92.33/13.69 thf(f76736,plain,(
% 92.33/13.69 spl854_867 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_867])])).
% 92.33/13.69 thf(f22298,plain,(
% 92.33/13.69 spl854_71 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_71])])).
% 92.33/13.69 thf(f22649,plain,(
% 92.33/13.69 spl854_115 <=> ! [X39 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X39)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_115])])).
% 92.33/13.69 thf(f68647,plain,(
% 92.33/13.69 spl854_705 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_705])])).
% 92.33/13.69 thf(f76730,plain,(
% 92.33/13.69 spl854_866 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_866])])).
% 92.33/13.69 thf(f76734,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0)))) ) | (~spl854_71 | ~spl854_115 | ~spl854_705 | ~spl854_866)),
% 92.33/13.69 inference(forward_demodulation,[],[f76733,f22650])).
% 92.33/13.69 thf(f22650,plain,(
% 92.33/13.69 ( ! [X39 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X39),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X39)) ) | ~spl854_115),
% 92.33/13.69 inference(avatar_component_clause,[],[f22649])).
% 92.33/13.69 thf(f76733,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) ) | (~spl854_71 | ~spl854_705 | ~spl854_866)),
% 92.33/13.69 inference(forward_demodulation,[],[f76731,f68952])).
% 92.33/13.69 thf(f68952,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0)))) ) | (~spl854_71 | ~spl854_705)),
% 92.33/13.69 inference(forward_demodulation,[],[f68951,f22299])).
% 92.33/13.69 thf(f22299,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))) ) | ~spl854_71),
% 92.33/13.69 inference(avatar_component_clause,[],[f22298])).
% 92.33/13.69 thf(f68951,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0))))) ) | (~spl854_71 | ~spl854_705)),
% 92.33/13.69 inference(forward_demodulation,[],[f68920,f68648])).
% 92.33/13.69 thf(f68648,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)))) ) | ~spl854_705),
% 92.33/13.69 inference(avatar_component_clause,[],[f68647])).
% 92.33/13.69 thf(f68920,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))))) ) | (~spl854_71 | ~spl854_705)),
% 92.33/13.69 inference(superposition,[],[f68648,f22299])).
% 92.33/13.69 thf(f76731,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) ) | ~spl854_866),
% 92.33/13.69 inference(avatar_component_clause,[],[f76730])).
% 92.33/13.69 thf(f76732,plain,(
% 92.33/13.69 spl854_866 | ~spl854_9 | ~spl854_160),
% 92.33/13.69 inference(avatar_split_clause,[],[f29756,f22950,f21928,f76730])).
% 92.33/13.69 thf(f29756,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) ) | (~spl854_9 | ~spl854_160)),
% 92.33/13.69 inference(forward_demodulation,[],[f18224,f29755])).
% 92.33/13.69 thf(f18224,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18223,f13567])).
% 92.33/13.69 thf(f18223,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13691,f18104])).
% 92.33/13.69 thf(f18104,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 inference(forward_demodulation,[],[f13549,f13548])).
% 92.33/13.69 thf(f13549,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.33/13.69 inference(definition_unfolding,[],[f9127,f13512,f13512])).
% 92.33/13.69 thf(f9127,plain,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.33/13.69 inference(cnf_transformation,[],[f941])).
% 92.33/13.69 thf(f941,axiom,(
% 92.33/13.69 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO)).
% 92.33/13.69 thf(f13691,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9333,f9122])).
% 92.33/13.69 thf(f9333,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4904])).
% 92.33/13.69 thf(f4904,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)))))),
% 92.33/13.69 inference(rectify,[],[f918])).
% 92.33/13.69 thf(f918,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EBIT2)).
% 92.33/13.69 thf(f76728,plain,(
% 92.33/13.69 spl854_865),
% 92.33/13.69 inference(avatar_split_clause,[],[f19776,f76726])).
% 92.33/13.69 thf(f76726,plain,(
% 92.33/13.69 spl854_865 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) != X2) | ($true != vAPP(X0,$o,X1,X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_865])])).
% 92.33/13.69 thf(f19776,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) != X2) | ($true != vAPP(X0,$o,X1,X2))) )),
% 92.33/13.69 inference(inner_rewriting,[],[f11640])).
% 92.33/13.69 thf(f11640,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7867])).
% 92.33/13.69 thf(f7867,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2) | (((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1)))) & ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1))))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK493])],[f7865,f7866])).
% 92.33/13.69 thf(f7866,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (((X2 != X3) | ($true != vAPP(X0,$o,X1,X3))) & ((X2 = X3) | ($true = vAPP(X0,$o,X1,X3)))) => (((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1)))) & ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1) = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK493(X0),X2),X1))))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f7865,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2) | ? [X3 : X0] : (((X2 != X3) | ($true != vAPP(X0,$o,X1,X3))) & ((X2 = X3) | ($true = vAPP(X0,$o,X1,X3)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f5964])).
% 92.33/13.69 thf(f5964,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2) | ? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) <~> (X2 = X3)))),
% 92.33/13.69 inference(ennf_transformation,[],[f3788])).
% 92.33/13.69 thf(f3788,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) <=> (X2 = X3)) => (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2))),
% 92.33/13.69 inference(fool_elimination,[],[f3787])).
% 92.33/13.69 thf(f3787,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) <=> (X2 = X3)) => (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1) = X2))),
% 92.33/13.69 inference(rectify,[],[f86])).
% 92.33/13.69 thf(f86,axiom,(
% 92.33/13.69 ! [X0 : $tType,X7 : X0 > $o,X4 : X0] : (! [X12 : X0] : (vAPP(X0,$o,X7,X12) <=> (X4 = X12)) => (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X7) = X4))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESELECT__UNIQUE)).
% 92.33/13.69 thf(f76724,plain,(
% 92.33/13.69 spl854_864 | ~spl854_4 | ~spl854_838),
% 92.33/13.69 inference(avatar_split_clause,[],[f76568,f75109,f21876,f76722])).
% 92.33/13.69 thf(f76722,plain,(
% 92.33/13.69 spl854_864 <=> ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone] : ($true = vAPP(sTfun(tyop_2Eone_2Eone,tyop_2Eone_2Eone),$o,sP95(tyop_2Eone_2Eone,tyop_2Eone_2Eone),X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_864])])).
% 92.33/13.69 thf(f21876,plain,(
% 92.33/13.69 spl854_4 <=> ! [X0 : $tType,X2 : X0 > tyop_2Eone_2Eone,X1 : X0 > tyop_2Eone_2Eone] : (X1 = X2)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_4])])).
% 92.33/13.69 thf(f75109,plain,(
% 92.33/13.69 spl854_838 <=> ! [X0 : $tType] : ($true = vAPP(sTfun(X0,X0),$o,sP95(X0,X0),iCOMB))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_838])])).
% 92.33/13.69 thf(f76568,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone] : (($true = vAPP(sTfun(tyop_2Eone_2Eone,tyop_2Eone_2Eone),$o,sP95(tyop_2Eone_2Eone,tyop_2Eone_2Eone),X0))) ) | (~spl854_4 | ~spl854_838)),
% 92.33/13.69 inference(superposition,[],[f75110,f21877])).
% 92.33/13.69 thf(f21877,plain,(
% 92.33/13.69 ( ! [X2 : X0 > tyop_2Eone_2Eone,X1 : X0 > tyop_2Eone_2Eone] : ((X1 = X2)) ) | ~spl854_4),
% 92.33/13.69 inference(avatar_component_clause,[],[f21876])).
% 92.33/13.69 thf(f75110,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true = vAPP(sTfun(X0,X0),$o,sP95(X0,X0),iCOMB))) ) | ~spl854_838),
% 92.33/13.69 inference(avatar_component_clause,[],[f75109])).
% 92.33/13.69 thf(f76720,plain,(
% 92.33/13.69 spl854_863),
% 92.33/13.69 inference(avatar_split_clause,[],[f19180,f76718])).
% 92.33/13.69 thf(f76718,plain,(
% 92.33/13.69 spl854_863 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_863])])).
% 92.33/13.69 thf(f19180,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14451,f18124])).
% 92.33/13.69 thf(f14451,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f10481,f9122,f13512])).
% 92.33/13.69 thf(f10481,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7007])).
% 92.33/13.69 thf(f7007,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)) | (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0) | (c_2Enum_2E0 != X1)) & ((c_2Enum_2E0 != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) & (c_2Enum_2E0 = X1)) | ((c_2Enum_2E0 = X0) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))))),
% 92.33/13.69 inference(rectify,[],[f7006])).
% 92.33/13.69 thf(f7006,plain,(
% 92.33/13.69 ! [X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)) | (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 != X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (c_2Enum_2E0 = X0)) | ((c_2Enum_2E0 = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))))),
% 92.33/13.69 inference(flattening,[],[f7005])).
% 92.33/13.69 thf(f7005,plain,(
% 92.33/13.69 ! [X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)) | (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 != X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0)))) & ((((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (c_2Enum_2E0 = X0)) | ((c_2Enum_2E0 = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6398])).
% 92.33/13.69 thf(f6398,plain,(
% 92.33/13.69 ! [X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)) <=> (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (c_2Enum_2E0 = X0)) | ((c_2Enum_2E0 = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f76716,plain,(
% 92.33/13.69 spl854_862),
% 92.33/13.69 inference(avatar_split_clause,[],[f19176,f76714])).
% 92.33/13.69 thf(f76714,plain,(
% 92.33/13.69 spl854_862 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_862])])).
% 92.33/13.69 thf(f19176,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14448,f18124])).
% 92.33/13.69 thf(f14448,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f10484,f13512,f9122])).
% 92.33/13.69 thf(f10484,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) | (c_2Enum_2E0 = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7007])).
% 92.33/13.69 thf(f76712,plain,(
% 92.33/13.69 spl854_861),
% 92.33/13.69 inference(avatar_split_clause,[],[f19144,f76710])).
% 92.33/13.69 thf(f76710,plain,(
% 92.33/13.69 spl854_861 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_861])])).
% 92.33/13.69 thf(f19144,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != X1)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14435,f18124])).
% 92.33/13.69 thf(f14435,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != X1)) )),
% 92.33/13.69 inference(definition_unfolding,[],[f10466,f9122,f13512,f9121])).
% 92.33/13.69 thf(f10466,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) != X1)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6994])).
% 92.33/13.69 thf(f6994,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) = X1) | ((c_2Enum_2E0 != X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0))) & ((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) != X1)))),
% 92.33/13.69 inference(flattening,[],[f6993])).
% 92.33/13.69 thf(f6993,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) = X1) | ((c_2Enum_2E0 != X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0))) & (((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) != X1)))),
% 92.33/13.69 inference(nnf_transformation,[],[f5115])).
% 92.33/13.69 thf(f5115,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) = X1) <=> ((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)))),
% 92.33/13.69 inference(rectify,[],[f1078])).
% 92.33/13.69 thf(f1078,axiom,(
% 92.33/13.69 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X137) = X137) <=> ((c_2Enum_2E0 = X137) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X134)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__ID)).
% 92.33/13.69 thf(f76708,plain,(
% 92.33/13.69 spl854_860),
% 92.33/13.69 inference(avatar_split_clause,[],[f18838,f76706])).
% 92.33/13.69 thf(f76706,plain,(
% 92.33/13.69 spl854_860 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_860])])).
% 92.33/13.69 thf(f18838,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18837,f13577])).
% 92.33/13.69 thf(f18837,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)),X1)))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f10002,f9292])).
% 92.33/13.69 thf(f9292,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,X0) = X0)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4867])).
% 92.33/13.69 thf(f4867,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,X0) = X0)),
% 92.33/13.69 inference(rectify,[],[f1366])).
% 92.33/13.69 thf(f1366,axiom,(
% 92.33/13.69 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,X8) = X8)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiZ)).
% 92.33/13.69 thf(f10002,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)),X1))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5075])).
% 92.33/13.69 thf(f5075,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)),X1)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))),X1))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),c_2Earithmetic_2EZERO)) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,c_2Earithmetic_2EZERO),X0)))),
% 92.33/13.69 inference(rectify,[],[f1407])).
% 92.33/13.69 thf(f1407,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)),X27) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X136),X27)),X27)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)),X27) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X136),X27))),X27))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X136),c_2Earithmetic_2EZERO)) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,c_2Earithmetic_2EZERO),X136)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Einternal__mult__characterisation)).
% 92.33/13.69 thf(f76704,plain,(
% 92.33/13.69 spl854_859),
% 92.33/13.69 inference(avatar_split_clause,[],[f18576,f76702])).
% 92.33/13.69 thf(f76702,plain,(
% 92.33/13.69 spl854_859 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_859])])).
% 92.33/13.69 thf(f18576,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18575,f18124])).
% 92.33/13.69 thf(f18575,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18574,f13563])).
% 92.33/13.69 thf(f18574,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f17823,f13548])).
% 92.33/13.69 thf(f17823,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.33/13.69 inference(equality_proxy_clausification,[],[f17822])).
% 92.33/13.69 thf(f17822,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14001])).
% 92.33/13.69 thf(f14001,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9751,f13512])).
% 92.33/13.69 thf(f9751,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6794])).
% 92.33/13.69 thf(f76699,plain,(
% 92.33/13.69 spl854_858),
% 92.33/13.69 inference(avatar_split_clause,[],[f18226,f76697])).
% 92.33/13.69 thf(f18226,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f18225,f13567])).
% 92.33/13.69 thf(f18225,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f13692,f9293])).
% 92.33/13.69 thf(f13692,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9335,f13512])).
% 92.33/13.69 thf(f9335,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f4906])).
% 92.33/13.69 thf(f4906,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X0)))),
% 92.33/13.69 inference(rectify,[],[f1638])).
% 92.33/13.69 thf(f1638,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EROOT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X136)) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,X136)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Elogroot_2Enumeral__root2)).
% 92.33/13.69 thf(f76695,plain,(
% 92.33/13.69 spl854_857),
% 92.33/13.69 inference(avatar_split_clause,[],[f17949,f76693])).
% 92.33/13.69 thf(f76693,plain,(
% 92.33/13.69 spl854_857 <=> ! [X5 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($false = vAPP(tyop_2Enum_2Enum,$o,X0,X5)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK164,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_857])])).
% 92.33/13.69 thf(f17949,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X5 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,X0,X5)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK164,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f9629])).
% 92.33/13.69 thf(f9629,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X5 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X5))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X5),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK164,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6698])).
% 92.33/13.69 thf(f76691,plain,(
% 92.33/13.69 spl854_856),
% 92.33/13.69 inference(avatar_split_clause,[],[f17947,f76689])).
% 92.33/13.69 thf(f76689,plain,(
% 92.33/13.69 spl854_856 <=> ! [X4 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($false = vAPP(tyop_2Enum_2Enum,$o,X0,X4)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_856])])).
% 92.33/13.69 thf(f17947,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X4 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,X0,X4)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f9633])).
% 92.33/13.69 thf(f9633,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X4 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X4))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X4),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6703])).
% 92.33/13.69 thf(f76687,plain,(
% 92.33/13.69 spl854_855),
% 92.33/13.69 inference(avatar_split_clause,[],[f17615,f76685])).
% 92.33/13.69 thf(f76685,plain,(
% 92.33/13.69 spl854_855 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_855])])).
% 92.33/13.69 thf(f17615,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0)))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f10196])).
% 92.33/13.69 thf(f10196,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6867])).
% 92.33/13.69 thf(f6867,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0)),X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK205])],[f5541,f6866])).
% 92.33/13.69 thf(f6866,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) => (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK205,X1),X0)),X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f5541,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))))),
% 92.33/13.69 inference(flattening,[],[f5540])).
% 92.33/13.69 thf(f5540,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0) | (($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0)))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2640])).
% 92.33/13.69 thf(f2640,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0)) & ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0)) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))))) => (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0))),
% 92.33/13.69 inference(fool_elimination,[],[f2639])).
% 92.33/13.69 thf(f2639,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(tyop_2Enum_2Enum,$o,X1,X0) & ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2)))) => (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X1) = X0))),
% 92.33/13.69 inference(rectify,[],[f1833])).
% 92.33/13.69 thf(f1833,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum,X43 : tyop_2Enum_2Enum > $o] : ((vAPP(tyop_2Enum_2Enum,$o,X43,X136) & ! [X104 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X104),X136) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X43,X104)))) => (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X43) = X136))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ELEAST__THM)).
% 92.33/13.69 thf(f76683,plain,(
% 92.33/13.69 spl854_854),
% 92.33/13.69 inference(avatar_split_clause,[],[f13968,f76681])).
% 92.33/13.69 thf(f76681,plain,(
% 92.33/13.69 spl854_854 <=> ! [X4 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK179,X0)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_854])])).
% 92.33/13.69 thf(f13968,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X4 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK179,X0)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9709,f9122])).
% 92.33/13.69 thf(f9709,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X4 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK179,X0)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6777])).
% 92.33/13.69 thf(f6777,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))) | (! [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))) & (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK179,X0)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | ! [X4 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK178,sK179])],[f6774,f6776,f6775])).
% 92.33/13.69 thf(f6775,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6776,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK179,X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6774,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (! [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))) & (? [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | ! [X4 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(rectify,[],[f6773])).
% 92.33/13.69 thf(f6773,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (! [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))) & (? [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | ! [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.33/13.69 inference(flattening,[],[f6772])).
% 92.33/13.69 thf(f6772,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (! [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))) & ((? [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ! [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f2328])).
% 92.33/13.69 thf(f2328,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) <=> (? [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))))),
% 92.33/13.69 inference(fool_elimination,[],[f2327])).
% 92.33/13.69 thf(f2327,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X1) <=> (? [X2 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)) | vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.33/13.69 inference(rectify,[],[f1239])).
% 92.33/13.69 thf(f1239,axiom,(
% 92.33/13.69 ! [X7 : tyop_2Enum_2Enum > $o] : (? [X137 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X137) <=> (? [X104 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X104)) | vAPP(tyop_2Enum_2Enum,$o,X7,c_2Enum_2E0)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEXISTS__NUM)).
% 92.33/13.69 thf(f76567,plain,(
% 92.33/13.69 spl854_853),
% 92.33/13.69 inference(avatar_split_clause,[],[f13960,f76565])).
% 92.33/13.69 thf(f76565,plain,(
% 92.33/13.69 spl854_853 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK172,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_853])])).
% 92.33/13.69 thf(f13960,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK172,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9701,f9122])).
% 92.33/13.69 thf(f9701,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK172,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6760])).
% 92.33/13.69 thf(f6760,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK172,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) & ((! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0)))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK172,sK173])],[f6757,f6759,f6758])).
% 92.33/13.69 thf(f6758,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) => ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK172,X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6759,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X4 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4)) => ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6757,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) & ((! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ? [X4 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(rectify,[],[f6756])).
% 92.33/13.69 thf(f6756,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) & ((! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ? [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.33/13.69 inference(flattening,[],[f6755])).
% 92.33/13.69 thf(f6755,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (? [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))) & ((! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ? [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f2322])).
% 92.33/13.69 thf(f2322,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) <=> (! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))))),
% 92.33/13.69 inference(fool_elimination,[],[f2321])).
% 92.33/13.69 thf(f2321,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X1) <=> (! [X2 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)) & vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.33/13.69 inference(rectify,[],[f1240])).
% 92.33/13.69 thf(f1240,axiom,(
% 92.33/13.69 ! [X7 : tyop_2Enum_2Enum > $o] : (! [X137 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X137) <=> (! [X135 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135)) & vAPP(tyop_2Enum_2Enum,$o,X7,c_2Enum_2E0)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EFORALL__NUM)).
% 92.33/13.69 thf(f76563,plain,(
% 92.33/13.69 spl854_852),
% 92.33/13.69 inference(avatar_split_clause,[],[f13957,f76561])).
% 92.33/13.69 thf(f76561,plain,(
% 92.33/13.69 spl854_852 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_852])])).
% 92.33/13.69 thf(f13957,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9698,f9122])).
% 92.33/13.69 thf(f9698,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6754])).
% 92.33/13.69 thf(f6754,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) & ((! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0)))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK170,sK171])],[f6751,f6753,f6752])).
% 92.33/13.69 thf(f6752,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) => (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6753,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X4 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4)) => ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6751,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) & ((! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ? [X4 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X4))))),
% 92.33/13.69 inference(rectify,[],[f6750])).
% 92.33/13.69 thf(f6750,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) & ((! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ? [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.33/13.69 inference(flattening,[],[f6749])).
% 92.33/13.69 thf(f6749,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))) & ((! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) | ? [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f5507])).
% 92.33/13.69 thf(f5507,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) <=> (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2320])).
% 92.33/13.69 thf(f2320,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) <=> (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))))),
% 92.33/13.69 inference(fool_elimination,[],[f2319])).
% 92.33/13.69 thf(f2319,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X1) <=> (! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,X0,X2) => vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.33/13.69 inference(rectify,[],[f1036])).
% 92.33/13.69 thf(f1036,axiom,(
% 92.33/13.69 ! [X7 : tyop_2Enum_2Enum > $o] : (! [X137 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X137) <=> (! [X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,X7,X135) => vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135))) & vAPP(tyop_2Enum_2Enum,$o,X7,c_2Enum_2E0)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EFORALL__NUM__THM)).
% 92.33/13.69 thf(f76559,plain,(
% 92.33/13.69 spl854_851),
% 92.33/13.69 inference(avatar_split_clause,[],[f13841,f76557])).
% 92.33/13.69 thf(f76557,plain,(
% 92.33/13.69 spl854_851 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_851])])).
% 92.33/13.69 thf(f13841,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f9552,f9122])).
% 92.33/13.69 thf(f9552,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f6651])).
% 92.33/13.69 thf(f6651,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK145])],[f6649,f6650])).
% 92.33/13.69 thf(f6650,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) => (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f6649,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.33/13.69 inference(rectify,[],[f5435])).
% 92.33/13.69 thf(f5435,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ? [X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.33/13.69 inference(flattening,[],[f5434])).
% 92.33/13.69 thf(f5434,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | (? [X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2158])).
% 92.33/13.69 thf(f2158,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) => ! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)))),
% 92.33/13.69 inference(fool_elimination,[],[f2157])).
% 92.33/13.69 thf(f2157,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,X0,X1) => vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1))) & vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) => ! [X2 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X2))),
% 92.33/13.69 inference(rectify,[],[f383])).
% 92.33/13.69 thf(f383,axiom,(
% 92.33/13.69 ! [X7 : tyop_2Enum_2Enum > $o] : ((! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,X7,X137) => vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137))) & vAPP(tyop_2Enum_2Enum,$o,X7,c_2Enum_2E0)) => ! [X135 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X135))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EINDUCTION)).
% 92.33/13.69 thf(f76555,plain,(
% 92.33/13.69 spl854_850),
% 92.33/13.69 inference(avatar_split_clause,[],[f13303,f76553])).
% 92.33/13.69 thf(f76553,plain,(
% 92.33/13.69 spl854_850 <=> ! [X0 : $tType,X1 : $tType,X5 : X0 > tyop_2Eoption_2Eoption(X1)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X1)),sTfun(X0,tyop_2Eoption_2Eoption(X1)),vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X1)),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X1)),sTfun(X0,tyop_2Eoption_2Eoption(X1))),c_2Eoption_2EOPTION__MCOMP(X1,X1,X0),c_2Eoption_2ESOME(X1)),X5) = X5)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_850])])).
% 92.33/13.69 thf(f13303,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X5 : X0 > tyop_2Eoption_2Eoption(X1)] : ((vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X1)),sTfun(X0,tyop_2Eoption_2Eoption(X1)),vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X1)),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X1)),sTfun(X0,tyop_2Eoption_2Eoption(X1))),c_2Eoption_2EOPTION__MCOMP(X1,X1,X0),c_2Eoption_2ESOME(X1)),X5) = X5)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5383])).
% 92.33/13.69 thf(f5383,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X2 > tyop_2Eoption_2Eoption(X3),X5 : X0 > tyop_2Eoption_2Eoption(X1)] : ((vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X1)),sTfun(X0,tyop_2Eoption_2Eoption(X1)),vAPP(sTfun(X1,tyop_2Eoption_2Eoption(X1)),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X1)),sTfun(X0,tyop_2Eoption_2Eoption(X1))),c_2Eoption_2EOPTION__MCOMP(X1,X1,X0),c_2Eoption_2ESOME(X1)),X5) = X5) & (vAPP(sTfun(X2,tyop_2Eoption_2Eoption(X2)),sTfun(X2,tyop_2Eoption_2Eoption(X3)),vAPP(sTfun(X2,tyop_2Eoption_2Eoption(X3)),sTfun(sTfun(X2,tyop_2Eoption_2Eoption(X2)),sTfun(X2,tyop_2Eoption_2Eoption(X3))),c_2Eoption_2EOPTION__MCOMP(X3,X2,X2),X4),c_2Eoption_2ESOME(X2)) = X4))),
% 92.33/13.69 inference(rectify,[],[f762])).
% 92.33/13.69 thf(f762,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X57 : $tType,X118 : $tType,X66 : X57 > tyop_2Eoption_2Eoption(X118),X25 : X0 > tyop_2Eoption_2Eoption(X5)] : ((vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X5)),sTfun(X0,tyop_2Eoption_2Eoption(X5)),vAPP(sTfun(X5,tyop_2Eoption_2Eoption(X5)),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X5)),sTfun(X0,tyop_2Eoption_2Eoption(X5))),c_2Eoption_2EOPTION__MCOMP(X5,X5,X0),c_2Eoption_2ESOME(X5)),X25) = X25) & (vAPP(sTfun(X57,tyop_2Eoption_2Eoption(X57)),sTfun(X57,tyop_2Eoption_2Eoption(X118)),vAPP(sTfun(X57,tyop_2Eoption_2Eoption(X118)),sTfun(sTfun(X57,tyop_2Eoption_2Eoption(X57)),sTfun(X57,tyop_2Eoption_2Eoption(X118))),c_2Eoption_2EOPTION__MCOMP(X118,X57,X57),X66),c_2Eoption_2ESOME(X57)) = X66))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__MCOMP__ID)).
% 92.33/13.69 thf(f76551,plain,(
% 92.33/13.69 spl854_849),
% 92.33/13.69 inference(avatar_split_clause,[],[f13302,f76549])).
% 92.33/13.69 thf(f76549,plain,(
% 92.33/13.69 spl854_849 <=> ! [X3 : $tType,X2 : $tType,X4 : X2 > tyop_2Eoption_2Eoption(X3)] : (vAPP(sTfun(X2,tyop_2Eoption_2Eoption(X2)),sTfun(X2,tyop_2Eoption_2Eoption(X3)),vAPP(sTfun(X2,tyop_2Eoption_2Eoption(X3)),sTfun(sTfun(X2,tyop_2Eoption_2Eoption(X2)),sTfun(X2,tyop_2Eoption_2Eoption(X3))),c_2Eoption_2EOPTION__MCOMP(X3,X2,X2),X4),c_2Eoption_2ESOME(X2)) = X4)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_849])])).
% 92.33/13.69 thf(f13302,plain,(
% 92.33/13.69 ( ! [X3 : $tType,X2 : $tType,X4 : X2 > tyop_2Eoption_2Eoption(X3)] : ((vAPP(sTfun(X2,tyop_2Eoption_2Eoption(X2)),sTfun(X2,tyop_2Eoption_2Eoption(X3)),vAPP(sTfun(X2,tyop_2Eoption_2Eoption(X3)),sTfun(sTfun(X2,tyop_2Eoption_2Eoption(X2)),sTfun(X2,tyop_2Eoption_2Eoption(X3))),c_2Eoption_2EOPTION__MCOMP(X3,X2,X2),X4),c_2Eoption_2ESOME(X2)) = X4)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5383])).
% 92.33/13.69 thf(f76547,plain,(
% 92.33/13.69 spl854_848),
% 92.33/13.69 inference(avatar_split_clause,[],[f12834,f76545])).
% 92.33/13.69 thf(f76545,plain,(
% 92.33/13.69 spl854_848 <=> ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X13 : X2,X0 : X2 > X1,X12 : X2] : ((X12 = X13) | (vAPP(X2,X1,X0,X13) != vAPP(X2,X1,X0,X12)) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_848])])).
% 92.33/13.69 thf(f12834,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X0 : X2 > X1,X12 : X2,X13 : X2] : ((X12 = X13) | (vAPP(X2,X1,X0,X13) != vAPP(X2,X1,X0,X12)) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8691])).
% 92.33/13.69 thf(f8691,plain,(
% 92.33/13.69 ! [X0 : X2 > X1,X1 : $tType,X2 : $tType,X3 : X1 > $o] : ((($true = vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0)) | ((! [X5 : X2] : (vAPP(X2,X1,X0,X5) != vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0)))) & ((vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0) = vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X2),sK703(X1,X2),X3),X0))) | ($true = vAPP(X1,$o,X3,vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0))))) | ((vAPP(sTfun(X2,X1),X2,sK704(X1,X2),X0) != vAPP(sTfun(X2,X1),X2,sK705(X1,X2),X0)) & (vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,sK705(X1,X2),X0)) = vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,sK704(X1,X2),X0))))) & ((! [X9 : X1] : ((($true = vAPP(X1,$o,X3,X9)) | ! [X10 : X2] : (vAPP(X2,X1,X0,X10) != X9)) & ((vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(X1,sTfun(sTfun(X2,X1),X2),sK706(X1,X2),X9),X0)) = X9) | ($true != vAPP(X1,$o,X3,X9)))) & ! [X12 : X2,X13 : X2] : ((X12 = X13) | (vAPP(X2,X1,X0,X13) != vAPP(X2,X1,X0,X12)))) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK702,sK703,sK704,sK705,sK706])],[f8686,f8690,f8689,f8688,f8687])).
% 92.33/13.69 thf(f8687,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : $tType,X0 : X2 > X1,X3 : X1 > $o] : (? [X4 : X1] : ((! [X5 : X2] : (vAPP(X2,X1,X0,X5) != X4) | ($true != vAPP(X1,$o,X3,X4))) & (? [X6 : X2] : (vAPP(X2,X1,X0,X6) = X4) | ($true = vAPP(X1,$o,X3,X4)))) => ((! [X5 : X2] : (vAPP(X2,X1,X0,X5) != vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0)))) & (? [X6 : X2] : (vAPP(X2,X1,X0,X6) = vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0)) | ($true = vAPP(X1,$o,X3,vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0))))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8688,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : $tType,X0 : X2 > X1,X3 : X1 > $o] : (? [X6 : X2] : (vAPP(X2,X1,X0,X6) = vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0)) => (vAPP(sTfun(X2,X1),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X1),sK702(X1,X2),X3),X0) = vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),X2),sK703(X1,X2),X3),X0))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8689,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : $tType,X0 : X2 > X1] : (? [X7 : X2,X8 : X2] : ((X7 != X8) & (vAPP(X2,X1,X0,X8) = vAPP(X2,X1,X0,X7))) => ((vAPP(sTfun(X2,X1),X2,sK704(X1,X2),X0) != vAPP(sTfun(X2,X1),X2,sK705(X1,X2),X0)) & (vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,sK705(X1,X2),X0)) = vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,sK704(X1,X2),X0)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8690,plain,(
% 92.33/13.69 ! [X2 : $tType,X1 : $tType,X0 : X2 > X1,X9 : X1] : (? [X11 : X2] : (vAPP(X2,X1,X0,X11) = X9) => (vAPP(X2,X1,X0,vAPP(sTfun(X2,X1),X2,vAPP(X1,sTfun(sTfun(X2,X1),X2),sK706(X1,X2),X9),X0)) = X9))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8686,plain,(
% 92.33/13.69 ! [X0 : X2 > X1,X1 : $tType,X2 : $tType,X3 : X1 > $o] : ((($true = vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0)) | ? [X4 : X1] : ((! [X5 : X2] : (vAPP(X2,X1,X0,X5) != X4) | ($true != vAPP(X1,$o,X3,X4))) & (? [X6 : X2] : (vAPP(X2,X1,X0,X6) = X4) | ($true = vAPP(X1,$o,X3,X4)))) | ? [X7 : X2,X8 : X2] : ((X7 != X8) & (vAPP(X2,X1,X0,X8) = vAPP(X2,X1,X0,X7)))) & ((! [X9 : X1] : ((($true = vAPP(X1,$o,X3,X9)) | ! [X10 : X2] : (vAPP(X2,X1,X0,X10) != X9)) & (? [X11 : X2] : (vAPP(X2,X1,X0,X11) = X9) | ($true != vAPP(X1,$o,X3,X9)))) & ! [X12 : X2,X13 : X2] : ((X12 = X13) | (vAPP(X2,X1,X0,X13) != vAPP(X2,X1,X0,X12)))) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0))))),
% 92.33/13.69 inference(rectify,[],[f8685])).
% 92.33/13.69 thf(f8685,plain,(
% 92.33/13.69 ! [X3 : X1 > X0,X0 : $tType,X1 : $tType,X2 : X0 > $o] : ((($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,X0),$o),sP104(X0,X1),X2),X3)) | ? [X4 : X0] : ((! [X5 : X1] : (vAPP(X1,X0,X3,X5) != X4) | ($true != vAPP(X0,$o,X2,X4))) & (? [X5 : X1] : (vAPP(X1,X0,X3,X5) = X4) | ($true = vAPP(X0,$o,X2,X4)))) | ? [X6 : X1,X7 : X1] : ((X6 != X7) & (vAPP(X1,X0,X3,X7) = vAPP(X1,X0,X3,X6)))) & ((! [X4 : X0] : ((($true = vAPP(X0,$o,X2,X4)) | ! [X5 : X1] : (vAPP(X1,X0,X3,X5) != X4)) & (? [X5 : X1] : (vAPP(X1,X0,X3,X5) = X4) | ($true != vAPP(X0,$o,X2,X4)))) & ! [X6 : X1,X7 : X1] : ((X6 = X7) | (vAPP(X1,X0,X3,X7) != vAPP(X1,X0,X3,X6)))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,X0),$o),sP104(X0,X1),X2),X3))))),
% 92.33/13.69 inference(flattening,[],[f8684])).
% 92.33/13.69 thf(f8684,plain,(
% 92.33/13.69 ! [X3 : X1 > X0,X0 : $tType,X1 : $tType,X2 : X0 > $o] : ((($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,X0),$o),sP104(X0,X1),X2),X3)) | (? [X4 : X0] : ((! [X5 : X1] : (vAPP(X1,X0,X3,X5) != X4) | ($true != vAPP(X0,$o,X2,X4))) & (? [X5 : X1] : (vAPP(X1,X0,X3,X5) = X4) | ($true = vAPP(X0,$o,X2,X4)))) | ? [X6 : X1,X7 : X1] : ((X6 != X7) & (vAPP(X1,X0,X3,X7) = vAPP(X1,X0,X3,X6))))) & ((! [X4 : X0] : ((($true = vAPP(X0,$o,X2,X4)) | ! [X5 : X1] : (vAPP(X1,X0,X3,X5) != X4)) & (? [X5 : X1] : (vAPP(X1,X0,X3,X5) = X4) | ($true != vAPP(X0,$o,X2,X4)))) & ! [X6 : X1,X7 : X1] : ((X6 = X7) | (vAPP(X1,X0,X3,X7) != vAPP(X1,X0,X3,X6)))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,X0),$o),sP104(X0,X1),X2),X3))))),
% 92.33/13.69 inference(nnf_transformation,[],[f6559])).
% 92.33/13.69 thf(f6559,plain,(
% 92.33/13.69 ! [X3 : X1 > X0,X0 : $tType,X1 : $tType,X2 : X0 > $o] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,X0),$o),sP104(X0,X1),X2),X3)) <=> (! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) <=> ? [X5 : X1] : (vAPP(X1,X0,X3,X5) = X4)) & ! [X6 : X1,X7 : X1] : ((X6 = X7) | (vAPP(X1,X0,X3,X7) != vAPP(X1,X0,X3,X6)))))),
% 92.33/13.69 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.69 thf(f76543,plain,(
% 92.33/13.69 spl854_847),
% 92.33/13.69 inference(avatar_split_clause,[],[f12053,f76541])).
% 92.33/13.69 thf(f76541,plain,(
% 92.33/13.69 spl854_847 <=> ! [X0 : $tType,X8 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK575(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK576(X0),X1))) | ($true != vAPP(X0,$o,X2,X8)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_847])])).
% 92.33/13.69 thf(f12053,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X8 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK575(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK576(X0),X1))) | ($true != vAPP(X0,$o,X2,X8))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8173])).
% 92.33/13.69 thf(f8173,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK574(X0),X2),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK574(X0),X2),X1)))) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)))) & (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK575(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK576(X0),X1))) | ! [X8 : X0] : (($true != vAPP(X0,$o,X2,X8)) & ($true != vAPP(X0,$o,X1,X8)))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK574,sK575,sK576])],[f8169,f8172,f8171,f8170])).
% 92.33/13.69 thf(f8170,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X1,X3))) => (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK574(X0),X2),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK574(X0),X2),X1)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8171,plain,(
% 92.33/13.69 ! [X0 : $tType,X2 : X0 > $o] : (? [X6 : X0] : ($true = vAPP(X0,$o,X2,X6)) => ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK575(X0),X2))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8172,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o] : (? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK576(X0),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8169,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X1,X3))) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)))) & (? [X6 : X0] : ($true = vAPP(X0,$o,X2,X6)) | ? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) | ! [X8 : X0] : (($true != vAPP(X0,$o,X2,X8)) & ($true != vAPP(X0,$o,X1,X8)))))),
% 92.33/13.69 inference(rectify,[],[f8168])).
% 92.33/13.69 thf(f8168,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X1,X3))) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)))) & (? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5)) | ! [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true != vAPP(X0,$o,X1,X3)))))),
% 92.33/13.69 inference(flattening,[],[f8167])).
% 92.33/13.69 thf(f8167,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X1,X3))) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)))) & ((? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ! [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true != vAPP(X0,$o,X1,X3)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f4014])).
% 92.33/13.69 thf(f4014,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X1,X3))) <=> (? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))))),
% 92.33/13.69 inference(fool_elimination,[],[f4013])).
% 92.33/13.69 thf(f4013,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (vAPP(X0,$o,X2,X3) | vAPP(X0,$o,X1,X3)) <=> (? [X4 : X0] : vAPP(X0,$o,X2,X4) | ? [X5 : X0] : vAPP(X0,$o,X1,X5)))),
% 92.33/13.69 inference(rectify,[],[f93])).
% 92.33/13.69 thf(f93,axiom,(
% 92.33/13.69 ! [X0 : $tType,X7 : X0 > $o,X41 : X0 > $o] : (? [X19 : X0] : (vAPP(X0,$o,X41,X19) | vAPP(X0,$o,X7,X19)) <=> (? [X23 : X0] : vAPP(X0,$o,X41,X23) | ? [X15 : X0] : vAPP(X0,$o,X7,X15)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__OR__THM)).
% 92.33/13.69 thf(f76539,plain,(
% 92.33/13.69 spl854_846),
% 92.33/13.69 inference(avatar_split_clause,[],[f12052,f76537])).
% 92.33/13.69 thf(f76537,plain,(
% 92.33/13.69 spl854_846 <=> ! [X0 : $tType,X8 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK575(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK576(X0),X1))) | ($true != vAPP(X0,$o,X1,X8)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_846])])).
% 92.33/13.69 thf(f12052,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X8 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK575(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK576(X0),X1))) | ($true != vAPP(X0,$o,X1,X8))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8173])).
% 92.33/13.69 thf(f76535,plain,(
% 92.33/13.69 spl854_845),
% 92.33/13.69 inference(avatar_split_clause,[],[f11990,f76533])).
% 92.33/13.69 thf(f76533,plain,(
% 92.33/13.69 spl854_845 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK536(X0),X2))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK537(X0),X1))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_845])])).
% 92.33/13.69 thf(f11990,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK536(X0),X2))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK537(X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8075])).
% 92.33/13.69 thf(f8075,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK536(X0),X2))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK537(X0),X1)))) & ((! [X6 : X0] : ($true = vAPP(X0,$o,X2,X6)) & ! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK538(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK538(X0),X2),X1))))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK536,sK537,sK538])],[f8071,f8074,f8073,f8072])).
% 92.33/13.69 thf(f8072,plain,(
% 92.33/13.69 ! [X0 : $tType,X2 : X0 > $o] : (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) => ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK536(X0),X2))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8073,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o] : (? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK537(X0),X1))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8074,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X8 : X0] : (($true != vAPP(X0,$o,X2,X8)) | ($true != vAPP(X0,$o,X1,X8))) => (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK538(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK538(X0),X2),X1)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f8071,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) | ? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5))) & ((! [X6 : X0] : ($true = vAPP(X0,$o,X2,X6)) & ! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) | ? [X8 : X0] : (($true != vAPP(X0,$o,X2,X8)) | ($true != vAPP(X0,$o,X1,X8)))))),
% 92.33/13.69 inference(rectify,[],[f8070])).
% 92.33/13.69 thf(f8070,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) | ? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5))) & ((! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X1,X3)))))),
% 92.33/13.69 inference(flattening,[],[f8069])).
% 92.33/13.69 thf(f8069,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)))) & ((! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X1,X3)))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3974])).
% 92.33/13.69 thf(f3974,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) <=> (! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))))),
% 92.33/13.69 inference(fool_elimination,[],[f3973])).
% 92.33/13.69 thf(f3973,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X2,X3) & vAPP(X0,$o,X1,X3)) <=> (! [X4 : X0] : vAPP(X0,$o,X2,X4) & ! [X5 : X0] : vAPP(X0,$o,X1,X5)))),
% 92.33/13.69 inference(rectify,[],[f90])).
% 92.33/13.69 thf(f90,axiom,(
% 92.33/13.69 ! [X0 : $tType,X7 : X0 > $o,X41 : X0 > $o] : (! [X19 : X0] : (vAPP(X0,$o,X41,X19) & vAPP(X0,$o,X7,X19)) <=> (! [X23 : X0] : vAPP(X0,$o,X41,X23) & ! [X15 : X0] : vAPP(X0,$o,X7,X15)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__AND__THM)).
% 92.33/13.69 thf(f76531,plain,(
% 92.33/13.69 spl854_844),
% 92.33/13.69 inference(avatar_split_clause,[],[f11989,f76529])).
% 92.33/13.69 thf(f76529,plain,(
% 92.33/13.69 spl854_844 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK536(X0),X2))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK537(X0),X1))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_844])])).
% 92.33/13.69 thf(f11989,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK536(X0),X2))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK537(X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f8075])).
% 92.33/13.69 thf(f76415,plain,(
% 92.33/13.69 spl854_843),
% 92.33/13.69 inference(avatar_split_clause,[],[f11248,f76413])).
% 92.33/13.69 thf(f76413,plain,(
% 92.33/13.69 spl854_843 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : (vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(X0,sTfun(X1,$o)),c_2Erelation_2Einv(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X1),X2)) = X2)),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_843])])).
% 92.33/13.69 thf(f11248,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : ((vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(X0,sTfun(X1,$o)),c_2Erelation_2Einv(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X1),X2)) = X2)) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5144])).
% 92.33/13.69 thf(f5144,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o] : (vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(X0,sTfun(X1,$o)),c_2Erelation_2Einv(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X1),X2)) = X2)),
% 92.33/13.69 inference(rectify,[],[f582])).
% 92.33/13.69 thf(f582,axiom,(
% 92.33/13.69 ! [X0 : $tType,X5 : $tType,X143 : X0 > X5 > $o] : (vAPP(sTfun(X5,sTfun(X0,$o)),sTfun(X0,sTfun(X5,$o)),c_2Erelation_2Einv(X5,X0),vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(X5,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X5),X143)) = X143)),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Einv__inv)).
% 92.33/13.69 thf(f76411,plain,(
% 92.33/13.69 spl854_842),
% 92.33/13.69 inference(avatar_split_clause,[],[f10687,f76409])).
% 92.33/13.69 thf(f76409,plain,(
% 92.33/13.69 spl854_842 <=> ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) | (vAPP(sTfun(X0,X0),X0,sK318(X0),X1) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK318(X0),X1)))))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_842])])).
% 92.33/13.69 thf(f10687,plain,(
% 92.33/13.69 ( ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) | (vAPP(sTfun(X0,X0),X0,sK318(X0),X1) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK318(X0),X1))))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f7294])).
% 92.33/13.69 thf(f7294,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) | (vAPP(sTfun(X0,X0),X0,sK318(X0),X1) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK318(X0),X1))))) & (! [X3 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3)) = X3) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1))))),
% 92.33/13.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK318])],[f7292,f7293])).
% 92.33/13.69 thf(f7293,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : (? [X2 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)) != X2) => (vAPP(sTfun(X0,X0),X0,sK318(X0),X1) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK318(X0),X1)))))),
% 92.33/13.69 introduced(choice_axiom,[])).
% 92.33/13.69 thf(f7292,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) | ? [X2 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)) != X2)) & (! [X3 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3)) = X3) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1))))),
% 92.33/13.69 inference(rectify,[],[f7291])).
% 92.33/13.69 thf(f7291,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) | ? [X2 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)) != X2)) & (! [X2 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)) = X2) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1))))),
% 92.33/13.69 inference(nnf_transformation,[],[f3138])).
% 92.33/13.69 thf(f3138,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) <=> ! [X2 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)) = X2))),
% 92.33/13.69 inference(fool_elimination,[],[f3137])).
% 92.33/13.69 thf(f3137,plain,(
% 92.33/13.69 ! [X0 : $tType,X1 : X0 > X0] : (vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1) <=> ! [X2 : X0] : (vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)) = X2))),
% 92.33/13.69 inference(rectify,[],[f595])).
% 92.33/13.69 thf(f595,axiom,(
% 92.33/13.69 ! [X139 : $tType,X3 : X139 > X139] : (vAPP(sTfun(X139,X139),$o,c_2Erelation_2EINVOL(X139),X3) <=> ! [X4 : X139] : (vAPP(X139,X139,X3,vAPP(X139,X139,X3,X4)) = X4))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EINVOL)).
% 92.33/13.69 thf(f76407,plain,(
% 92.33/13.69 spl854_841),
% 92.33/13.69 inference(avatar_split_clause,[],[f10032,f76405])).
% 92.33/13.69 thf(f76405,plain,(
% 92.33/13.69 spl854_841 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_841])])).
% 92.33/13.69 thf(f10032,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5081])).
% 92.33/13.69 thf(f5081,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,c_2Earithmetic_2EZERO),X1)))),
% 92.33/13.69 inference(rectify,[],[f1401])).
% 92.33/13.69 thf(f1401,axiom,(
% 92.33/13.69 ! [X136 : tyop_2Enum_2Enum,X394 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)),X394) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X394))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)),X394) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X394))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,c_2Earithmetic_2EZERO),X394) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X394)))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__texp__help)).
% 92.33/13.69 thf(f76310,plain,(
% 92.33/13.69 spl854_840 | ~spl854_308 | ~spl854_833),
% 92.33/13.69 inference(avatar_split_clause,[],[f74704,f74701,f35574,f76308])).
% 92.33/13.69 thf(f76308,plain,(
% 92.33/13.69 spl854_840 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_840])])).
% 92.33/13.69 thf(f74701,plain,(
% 92.33/13.69 spl854_833 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_833])])).
% 92.33/13.69 thf(f74704,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1)) ) | (~spl854_308 | ~spl854_833)),
% 92.33/13.69 inference(forward_demodulation,[],[f74702,f35576])).
% 92.33/13.69 thf(f74702,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1)) ) | ~spl854_833),
% 92.33/13.69 inference(avatar_component_clause,[],[f74701])).
% 92.33/13.69 thf(f76275,plain,(
% 92.33/13.69 spl854_839 | ~spl854_4 | ~spl854_837),
% 92.33/13.69 inference(avatar_split_clause,[],[f75765,f74857,f21876,f76273])).
% 92.33/13.69 thf(f76273,plain,(
% 92.33/13.69 spl854_839 <=> ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone] : ($true = vAPP(sTfun(tyop_2Eone_2Eone,tyop_2Eone_2Eone),$o,sP94(tyop_2Eone_2Eone,tyop_2Eone_2Eone),X0))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_839])])).
% 92.33/13.69 thf(f74857,plain,(
% 92.33/13.69 spl854_837 <=> ! [X0 : $tType] : ($true = vAPP(sTfun(X0,X0),$o,sP94(X0,X0),iCOMB))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_837])])).
% 92.33/13.69 thf(f75765,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone] : (($true = vAPP(sTfun(tyop_2Eone_2Eone,tyop_2Eone_2Eone),$o,sP94(tyop_2Eone_2Eone,tyop_2Eone_2Eone),X0))) ) | (~spl854_4 | ~spl854_837)),
% 92.33/13.69 inference(superposition,[],[f74858,f21877])).
% 92.33/13.69 thf(f74858,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true = vAPP(sTfun(X0,X0),$o,sP94(X0,X0),iCOMB))) ) | ~spl854_837),
% 92.33/13.69 inference(avatar_component_clause,[],[f74857])).
% 92.33/13.69 thf(f75111,plain,(
% 92.33/13.69 spl854_838 | ~spl854_324 | ~spl854_745),
% 92.33/13.69 inference(avatar_split_clause,[],[f73114,f71140,f41605,f75109])).
% 92.33/13.69 thf(f41605,plain,(
% 92.33/13.69 spl854_324 <=> ! [X0 : $tType] : ($true = vAPP(sTfun(X0,X0),$o,vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),$o),c_2Eind__type_2EISO(X0,X0),iCOMB),iCOMB))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_324])])).
% 92.33/13.69 thf(f71140,plain,(
% 92.33/13.69 spl854_745 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_745])])).
% 92.33/13.69 thf(f73114,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true = vAPP(sTfun(X0,X0),$o,sP95(X0,X0),iCOMB))) ) | (~spl854_324 | ~spl854_745)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f73099])).
% 92.33/13.69 thf(f73099,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true != $true) | ($true = vAPP(sTfun(X0,X0),$o,sP95(X0,X0),iCOMB))) ) | (~spl854_324 | ~spl854_745)),
% 92.33/13.69 inference(superposition,[],[f71141,f41606])).
% 92.33/13.69 thf(f41606,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true = vAPP(sTfun(X0,X0),$o,vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),$o),c_2Eind__type_2EISO(X0,X0),iCOMB),iCOMB))) ) | ~spl854_324),
% 92.33/13.69 inference(avatar_component_clause,[],[f41605])).
% 92.33/13.69 thf(f71141,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1] : (($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)) | ($true = vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2))) ) | ~spl854_745),
% 92.33/13.69 inference(avatar_component_clause,[],[f71140])).
% 92.33/13.69 thf(f74859,plain,(
% 92.33/13.69 spl854_837 | ~spl854_324 | ~spl854_744),
% 92.33/13.69 inference(avatar_split_clause,[],[f73098,f71136,f41605,f74857])).
% 92.33/13.69 thf(f71136,plain,(
% 92.33/13.69 spl854_744 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_744])])).
% 92.33/13.69 thf(f73098,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true = vAPP(sTfun(X0,X0),$o,sP94(X0,X0),iCOMB))) ) | (~spl854_324 | ~spl854_744)),
% 92.33/13.69 inference(trivial_inequality_removal,[],[f73083])).
% 92.33/13.69 thf(f73083,plain,(
% 92.33/13.69 ( ! [X0 : $tType] : (($true != $true) | ($true = vAPP(sTfun(X0,X0),$o,sP94(X0,X0),iCOMB))) ) | (~spl854_324 | ~spl854_744)),
% 92.33/13.69 inference(superposition,[],[f71137,f41606])).
% 92.33/13.69 thf(f71137,plain,(
% 92.33/13.69 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1] : (($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)) | ($true = vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2))) ) | ~spl854_744),
% 92.33/13.69 inference(avatar_component_clause,[],[f71136])).
% 92.33/13.69 thf(f74716,plain,(
% 92.33/13.69 spl854_836 | ~spl854_308),
% 92.33/13.69 inference(avatar_split_clause,[],[f48844,f35574,f74714])).
% 92.33/13.69 thf(f74714,plain,(
% 92.33/13.69 spl854_836 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_836])])).
% 92.33/13.69 thf(f48844,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1)) ) | ~spl854_308),
% 92.33/13.69 inference(forward_demodulation,[],[f19134,f35576])).
% 92.33/13.69 thf(f19134,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f17555,f13567])).
% 92.33/13.69 thf(f17555,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) | (X0 = X1)) )),
% 92.33/13.69 inference(equality_proxy_clausification,[],[f17554])).
% 92.33/13.69 thf(f17554,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),X0),X1))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f17553])).
% 92.33/13.69 thf(f17553,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),X0),X1)))) )),
% 92.33/13.69 inference(not_proxy_clausification,[],[f14396])).
% 92.33/13.69 thf(f14396,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1)))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),X0),X1)))) )),
% 92.33/13.69 inference(definition_unfolding,[],[f10405,f13512])).
% 92.33/13.69 thf(f10405,plain,(
% 92.33/13.69 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),X0),X1)))) )),
% 92.33/13.69 inference(cnf_transformation,[],[f5760])).
% 92.33/13.69 thf(f5760,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),X0),X1))))),
% 92.33/13.69 inference(ennf_transformation,[],[f2950])).
% 92.33/13.69 thf(f2950,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),X0),X1))) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)))))),
% 92.33/13.69 inference(fool_elimination,[],[f2949])).
% 92.33/13.69 thf(f2949,plain,(
% 92.33/13.69 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(X0 = X1)) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1))))),
% 92.33/13.69 inference(rectify,[],[f1751])).
% 92.33/13.69 thf(f1751,axiom,(
% 92.33/13.69 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(X49 = X72)) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X72),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X49))))),
% 92.33/13.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__B__NEQ)).
% 92.33/13.69 thf(f74712,plain,(
% 92.33/13.69 spl854_835),
% 92.33/13.69 inference(avatar_split_clause,[],[f19735,f74710])).
% 92.33/13.69 thf(f74710,plain,(
% 92.33/13.69 spl854_835 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X1) != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)) = X1))),
% 92.33/13.69 introduced(avatar_definition,[new_symbols(naming,[spl854_835])])).
% 92.33/13.69 thf(f19735,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X1) != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)) = X1)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19734,f9293])).
% 92.33/13.69 thf(f19734,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)) = X1)) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19733,f9293])).
% 92.33/13.69 thf(f19733,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f19732,f9293])).
% 92.33/13.69 thf(f19732,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.69 inference(forward_demodulation,[],[f14985,f9293])).
% 92.33/13.69 thf(f14985,plain,(
% 92.33/13.69 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11358,f9121])).
% 92.33/13.70 thf(f11358,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7686])).
% 92.33/13.70 thf(f74708,plain,(
% 92.33/13.70 spl854_834),
% 92.33/13.70 inference(avatar_split_clause,[],[f19723,f74706])).
% 92.33/13.70 thf(f74706,plain,(
% 92.33/13.70 spl854_834 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),X1) != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)) = X1))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_834])])).
% 92.33/13.70 thf(f19723,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),X1) != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)) = X1)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19722,f9293])).
% 92.33/13.70 thf(f19722,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)) = X1)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19721,f9293])).
% 92.33/13.70 thf(f19721,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19720,f9293])).
% 92.33/13.70 thf(f19720,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14982,f9293])).
% 92.33/13.70 thf(f14982,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11361,f9121])).
% 92.33/13.70 thf(f11361,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2))),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7686])).
% 92.33/13.70 thf(f74703,plain,(
% 92.33/13.70 spl854_833),
% 92.33/13.70 inference(avatar_split_clause,[],[f19499,f74701])).
% 92.33/13.70 thf(f19499,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))) | (X0 = X1)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14836,f13567])).
% 92.33/13.70 thf(f14836,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1)))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11134,f13512])).
% 92.33/13.70 thf(f11134,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7639])).
% 92.33/13.70 thf(f7639,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1))) | (X0 != X1)) & ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)))))),
% 92.33/13.70 inference(nnf_transformation,[],[f3440])).
% 92.33/13.70 thf(f3440,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1))) <=> (X0 = X1))),
% 92.33/13.70 inference(fool_elimination,[],[f3439])).
% 92.33/13.70 thf(f3439,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) <=> (X0 = X1))),
% 92.33/13.70 inference(rectify,[],[f1750])).
% 92.33/13.70 thf(f1750,axiom,(
% 92.33/13.70 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X27)) <=> (X27 = X136))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__TWO__POW)).
% 92.33/13.70 thf(f74699,plain,(
% 92.33/13.70 spl854_832),
% 92.33/13.70 inference(avatar_split_clause,[],[f19186,f74697])).
% 92.33/13.70 thf(f74697,plain,(
% 92.33/13.70 spl854_832 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_832])])).
% 92.33/13.70 thf(f19186,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19185,f18124])).
% 92.33/13.70 thf(f19185,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19184,f13563])).
% 92.33/13.70 thf(f19184,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14453,f13548])).
% 92.33/13.70 thf(f14453,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f10487,f13512])).
% 92.33/13.70 thf(f10487,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7008])).
% 92.33/13.70 thf(f7008,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) & (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))))),
% 92.33/13.70 inference(nnf_transformation,[],[f6399])).
% 92.33/13.70 thf(f6399,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) <=> ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)))),
% 92.33/13.70 inference(definition_folding,[],[f5119,f6398])).
% 92.33/13.70 thf(f5119,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) <=> (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (c_2Enum_2E0 = X0)) | ((c_2Enum_2E0 = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0))))),
% 92.33/13.70 inference(rectify,[],[f1005])).
% 92.33/13.70 thf(f1005,axiom,(
% 92.33/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137)) <=> (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X137) & (c_2Enum_2E0 = X134)) | ((c_2Enum_2E0 = X137) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X134))))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__EQ__1)).
% 92.33/13.70 thf(f74695,plain,(
% 92.33/13.70 spl854_831),
% 92.33/13.70 inference(avatar_split_clause,[],[f19183,f74693])).
% 92.33/13.70 thf(f74693,plain,(
% 92.33/13.70 spl854_831 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_831])])).
% 92.33/13.70 thf(f19183,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19182,f18124])).
% 92.33/13.70 thf(f19182,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f19181,f13563])).
% 92.33/13.70 thf(f19181,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14452,f13548])).
% 92.33/13.70 thf(f14452,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f10488,f13512])).
% 92.33/13.70 thf(f10488,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X0),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7008])).
% 92.33/13.70 thf(f74691,plain,(
% 92.33/13.70 spl854_830),
% 92.33/13.70 inference(avatar_split_clause,[],[f18689,f74689])).
% 92.33/13.70 thf(f74689,plain,(
% 92.33/13.70 spl854_830 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)) = X1)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_830])])).
% 92.33/13.70 thf(f18689,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)) = X1)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14093,f17793])).
% 92.33/13.70 thf(f14093,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X1)) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9887,f13541])).
% 92.33/13.70 thf(f9887,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),c_2Epred__set_2EEMPTY(X0)) = X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4990])).
% 92.33/13.70 thf(f4990,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),c_2Epred__set_2EEMPTY(X0)) = X1)),
% 92.33/13.70 inference(rectify,[],[f1935])).
% 92.33/13.70 thf(f1935,axiom,(
% 92.33/13.70 ! [X0 : $tType,X111 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X111),c_2Epred__set_2EEMPTY(X0)) = X111)),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__EMPTY)).
% 92.33/13.70 thf(f74687,plain,(
% 92.33/13.70 spl854_829),
% 92.33/13.70 inference(avatar_split_clause,[],[f18688,f74685])).
% 92.33/13.70 thf(f74685,plain,(
% 92.33/13.70 spl854_829 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),X1) = vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_829])])).
% 92.33/13.70 thf(f18688,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),X1) = vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14090,f17793])).
% 92.33/13.70 thf(f14090,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),X1) = vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9884,f13541])).
% 92.33/13.70 thf(f9884,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2EEMPTY(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4987])).
% 92.33/13.70 thf(f4987,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : (c_2Epred__set_2EEMPTY(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X1),X1))),
% 92.33/13.70 inference(rectify,[],[f1939])).
% 92.33/13.70 thf(f1939,axiom,(
% 92.33/13.70 ! [X0 : $tType,X111 : X0 > $o] : (c_2Epred__set_2EEMPTY(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EDIFF(X0),X111),X111))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__EQ__EMPTY)).
% 92.33/13.70 thf(f74683,plain,(
% 92.33/13.70 spl854_828),
% 92.33/13.70 inference(avatar_split_clause,[],[f18384,f74681])).
% 92.33/13.70 thf(f74681,plain,(
% 92.33/13.70 spl854_828 <=> ! [X0 : $tType,X2 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X2) = X2)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_828])])).
% 92.33/13.70 thf(f18384,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X2) = X2)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f13802,f18095])).
% 92.33/13.70 thf(f13802,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X2) = X2)) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9494,f13541])).
% 92.33/13.70 thf(f9494,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),c_2Epred__set_2EEMPTY(X0)),X2) = X2)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4937])).
% 92.33/13.70 thf(f4937,plain,(
% 92.33/13.70 ! [X0 : $tType] : (! [X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),c_2Epred__set_2EEMPTY(X0)) = X1) & ! [X2 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),c_2Epred__set_2EEMPTY(X0)),X2) = X2))),
% 92.33/13.70 inference(rectify,[],[f1906])).
% 92.33/13.70 thf(f1906,axiom,(
% 92.33/13.70 ! [X0 : $tType] : (! [X157 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X157),c_2Epred__set_2EEMPTY(X0)) = X157) & ! [X111 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),c_2Epred__set_2EEMPTY(X0)),X111) = X111))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__EMPTY)).
% 92.33/13.70 thf(f74679,plain,(
% 92.33/13.70 spl854_827),
% 92.33/13.70 inference(avatar_split_clause,[],[f18383,f74677])).
% 92.33/13.70 thf(f74677,plain,(
% 92.33/13.70 spl854_827 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)) = X1)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_827])])).
% 92.33/13.70 thf(f18383,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)) = X1)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f13801,f18095])).
% 92.33/13.70 thf(f13801,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X1)) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9495,f13541])).
% 92.33/13.70 thf(f9495,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),c_2Epred__set_2EEMPTY(X0)) = X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4937])).
% 92.33/13.70 thf(f74675,plain,(
% 92.33/13.70 spl854_826),
% 92.33/13.70 inference(avatar_split_clause,[],[f18382,f74673])).
% 92.33/13.70 thf(f74673,plain,(
% 92.33/13.70 spl854_826 <=> ! [X0 : $tType,X2 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)),X2) = X2)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_826])])).
% 92.33/13.70 thf(f18382,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)),X2) = X2)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f13800,f13591])).
% 92.33/13.70 thf(f13800,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X2) = X2)) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9492,f13544])).
% 92.33/13.70 thf(f13544,plain,(
% 92.33/13.70 ( ! [X0 : $tType] : ((c_2Epred__set_2EUNIV(X0) = vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9354,f9976,f13514])).
% 92.33/13.70 thf(f9354,plain,(
% 92.33/13.70 ( ! [X0 : $tType] : ((c_2Epred__set_2EUNIV(X0) = vAPP($o,sTfun(X0,$o),kCOMB,c_2Ebool_2ET))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f2080])).
% 92.33/13.70 thf(f2080,plain,(
% 92.33/13.70 ! [X0 : $tType] : (c_2Epred__set_2EUNIV(X0) = vAPP($o,sTfun(X0,$o),kCOMB,c_2Ebool_2ET))),
% 92.33/13.70 inference(fool_elimination,[],[f2079])).
% 92.33/13.70 thf(f2079,plain,(
% 92.33/13.70 ! [X0 : $tType] : (c_2Epred__set_2EUNIV(X0) = (^[X1 : X0] : (c_2Ebool_2ET)))),
% 92.33/13.70 inference(rectify,[],[f1843])).
% 92.33/13.70 thf(f1843,axiom,(
% 92.33/13.70 ! [X0 : $tType] : (c_2Epred__set_2EUNIV(X0) = (^[X8 : X0] : (c_2Ebool_2ET)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__DEF)).
% 92.33/13.70 thf(f9492,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),c_2Epred__set_2EUNIV(X0)),X2) = X2)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4936])).
% 92.33/13.70 thf(f4936,plain,(
% 92.33/13.70 ! [X0 : $tType] : (! [X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),c_2Epred__set_2EUNIV(X0)) = X1) & ! [X2 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),c_2Epred__set_2EUNIV(X0)),X2) = X2))),
% 92.33/13.70 inference(rectify,[],[f1921])).
% 92.33/13.70 thf(f1921,axiom,(
% 92.33/13.70 ! [X0 : $tType] : (! [X157 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X157),c_2Epred__set_2EUNIV(X0)) = X157) & ! [X111 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),c_2Epred__set_2EUNIV(X0)),X111) = X111))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__UNIV)).
% 92.33/13.70 thf(f74671,plain,(
% 92.33/13.70 spl854_825),
% 92.33/13.70 inference(avatar_split_clause,[],[f18381,f74669])).
% 92.33/13.70 thf(f74669,plain,(
% 92.33/13.70 spl854_825 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)) = X1)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_825])])).
% 92.33/13.70 thf(f18381,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)) = X1)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f13799,f13591])).
% 92.33/13.70 thf(f13799,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X1)) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9493,f13544])).
% 92.33/13.70 thf(f9493,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),c_2Epred__set_2EUNIV(X0)) = X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4936])).
% 92.33/13.70 thf(f74667,plain,(
% 92.33/13.70 spl854_824),
% 92.33/13.70 inference(avatar_split_clause,[],[f17451,f74665])).
% 92.33/13.70 thf(f74665,plain,(
% 92.33/13.70 spl854_824 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_824])])).
% 92.33/13.70 thf(f17451,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0))) )),
% 92.33/13.70 inference(not_proxy_clausification,[],[f11056])).
% 92.33/13.70 thf(f11056,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7587])).
% 92.33/13.70 thf(f7587,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0)) | ! [X2 : tyop_2Enum_2Enum > $o] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X2,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X2,X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK371,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK371,X2))))))) & ((($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X1)) & ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X5)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X5))))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0))))),
% 92.33/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK371,sK372])],[f7584,f7586,f7585])).
% 92.33/13.70 thf(f7585,plain,(
% 92.33/13.70 ! [X2 : tyop_2Enum_2Enum > $o] : (? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X2,X3)) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))) => (($true != vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK371,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK371,X2))))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f7586,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (? [X4 : tyop_2Enum_2Enum > $o] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X4,X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X4,X1)) & ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X4,X5)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X4,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X5))))) => (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X1)) & ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X5)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X5))))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f7584,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0)) | ! [X2 : tyop_2Enum_2Enum > $o] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X2,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X2,X1)) | ? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X2,X3)) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))))) & (? [X4 : tyop_2Enum_2Enum > $o] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X4,X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X4,X1)) & ! [X5 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X4,X5)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X4,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X5))))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0))))),
% 92.33/13.70 inference(rectify,[],[f7583])).
% 92.33/13.70 thf(f7583,plain,(
% 92.33/13.70 ! [X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X0),X1)) | ! [X2 : tyop_2Enum_2Enum > $o] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X2,X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X2,X0)) | ? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X2,X3)) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))))) & (? [X2 : tyop_2Enum_2Enum > $o] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X2,X1))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,X0)) & ! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X2,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X0),X1))))),
% 92.33/13.70 inference(nnf_transformation,[],[f6419])).
% 92.33/13.70 thf(f6419,plain,(
% 92.33/13.70 ! [X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X0),X1)) <=> ? [X2 : tyop_2Enum_2Enum > $o] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X2,X1))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X2,X0)) & ! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X2,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))))))),
% 92.33/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.70 thf(f74663,plain,(
% 92.33/13.70 spl854_823),
% 92.33/13.70 inference(avatar_split_clause,[],[f17079,f74661])).
% 92.33/13.70 thf(f74661,plain,(
% 92.33/13.70 spl854_823 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X1),X2),X1),X3)) | ($false = X1))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_823])])).
% 92.33/13.70 thf(f17079,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X1),X2),X1),X3)) | ($false = X1)) )),
% 92.33/13.70 inference(not_proxy_clausification,[],[f16535])).
% 92.33/13.70 thf(f16535,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X1),X2),X1),X3)) | (vAPP($o,$o,vNOT,X1) = $true)) )),
% 92.33/13.70 inference(equality_resolution,[],[f12523])).
% 92.33/13.70 thf(f12523,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X2),X1),X3)) | (vAPP($o,$o,vNOT,X1) = $true) | (X0 != X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6501])).
% 92.33/13.70 thf(f6501,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X2),X1),X3)) | ((X2 != X3) & (vAPP($o,$o,vNOT,X1) = $true)) | (X0 != X1))),
% 92.33/13.70 inference(definition_folding,[],[f6085,f6500])).
% 92.33/13.70 thf(f6085,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))) | ((X2 != X3) & (vAPP($o,$o,vNOT,X1) = $true)) | (X0 != X1))),
% 92.33/13.70 inference(flattening,[],[f6084])).
% 92.33/13.70 thf(f6084,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))) | (((X2 != X3) & (vAPP($o,$o,vNOT,X1) = $true)) | (X0 != X1)))),
% 92.33/13.70 inference(ennf_transformation,[],[f4284])).
% 92.33/13.70 thf(f4284,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : ((((vAPP($o,$o,vNOT,X1) = $true) => (X2 = X3)) & (X0 = X1)) => ((($true = X2) | ($true = X0)) <=> (($true = X3) | ($true = X1))))),
% 92.33/13.70 inference(fool_elimination,[],[f4283])).
% 92.33/13.70 thf(f4283,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((vAPP($o,$o,vNOT,X1) => (X2 = X3)) & (X0 = X1)) => ((X2 | X0) <=> (X3 | X1)))),
% 92.33/13.70 inference(rectify,[],[f145])).
% 92.33/13.70 thf(f145,axiom,(
% 92.33/13.70 ! [X7 : $o,X61 : $o,X62 : $o,X63 : $o] : (((vAPP($o,$o,vNOT,X61) => (X62 = X63)) & (X7 = X61)) => ((X62 | X7) <=> (X63 | X61)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__CONG)).
% 92.33/13.70 thf(f74659,plain,(
% 92.33/13.70 ~spl854_822 | ~spl854_40 | spl854_712),
% 92.33/13.70 inference(avatar_split_clause,[],[f74614,f68675,f22095,f74656])).
% 92.33/13.70 thf(f74656,plain,(
% 92.33/13.70 spl854_822 <=> (sP9 = c_2Erelation_2EEMPTY__REL($o))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_822])])).
% 92.33/13.70 thf(f22095,plain,(
% 92.33/13.70 spl854_40 <=> ! [X0 : $tType] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),c_2Erelation_2EEMPTY__REL(X0)) = $true)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_40])])).
% 92.33/13.70 thf(f74614,plain,(
% 92.33/13.70 (sP9 != c_2Erelation_2EEMPTY__REL($o)) | (~spl854_40 | spl854_712)),
% 92.33/13.70 inference(trivial_inequality_removal,[],[f74601])).
% 92.33/13.70 thf(f74601,plain,(
% 92.33/13.70 ($true != $true) | (sP9 != c_2Erelation_2EEMPTY__REL($o)) | (~spl854_40 | spl854_712)),
% 92.33/13.70 inference(constrained_superposition,[],[f68677,f22096])).
% 92.33/13.70 thf(f22096,plain,(
% 92.33/13.70 ( ! [X0 : $tType] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),c_2Erelation_2EEMPTY__REL(X0)) = $true)) ) | ~spl854_40),
% 92.33/13.70 inference(avatar_component_clause,[],[f22095])).
% 92.33/13.70 thf(f74654,plain,(
% 92.33/13.70 spl854_821),
% 92.33/13.70 inference(avatar_split_clause,[],[f17076,f74652])).
% 92.33/13.70 thf(f74652,plain,(
% 92.33/13.70 spl854_821 <=> ! [X0 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X3),X1),X3)) | ($false = X3))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_821])])).
% 92.33/13.70 thf(f17076,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X3),X1),X3)) | ($false = X3)) )),
% 92.33/13.70 inference(not_proxy_clausification,[],[f16621])).
% 92.33/13.70 thf(f16621,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X3),X1),X3)) | ($true = vAPP($o,$o,vNOT,X3))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12603])).
% 92.33/13.70 thf(f12603,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | (X2 != X3) | ($true = vAPP($o,$o,vNOT,X2))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6527])).
% 92.33/13.70 thf(f74650,plain,(
% 92.33/13.70 spl854_820),
% 92.33/13.70 inference(avatar_split_clause,[],[f17075,f74648])).
% 92.33/13.70 thf(f74648,plain,(
% 92.33/13.70 spl854_820 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X1),X2),X1),X3)) | ($false = X1))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_820])])).
% 92.33/13.70 thf(f17075,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X1),X2),X1),X3)) | ($false = X1)) )),
% 92.33/13.70 inference(not_proxy_clausification,[],[f16622])).
% 92.33/13.70 thf(f16622,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X1),X2),X1),X3)) | (vAPP($o,$o,vNOT,X1) = $true)) )),
% 92.33/13.70 inference(equality_resolution,[],[f12602])).
% 92.33/13.70 thf(f12602,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | (vAPP($o,$o,vNOT,X1) = $true) | (X0 != X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6527])).
% 92.33/13.70 thf(f74646,plain,(
% 92.33/13.70 spl854_819),
% 92.33/13.70 inference(avatar_split_clause,[],[f16547,f74644])).
% 92.33/13.70 thf(f74644,plain,(
% 92.33/13.70 spl854_819 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X1),X2),X1),X3)) | ($true = X1))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_819])])).
% 92.33/13.70 thf(f16547,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X1),X2),X1),X3)) | ($true = X1)) )),
% 92.33/13.70 inference(equality_resolution,[],[f12530])).
% 92.33/13.70 thf(f12530,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)) | ($true = X1) | (X0 != X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6503])).
% 92.33/13.70 thf(f74642,plain,(
% 92.33/13.70 spl854_818),
% 92.33/13.70 inference(avatar_split_clause,[],[f16546,f74640])).
% 92.33/13.70 thf(f74640,plain,(
% 92.33/13.70 spl854_818 <=> ! [X0 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X3),X1),X3)) | ($true = X3))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_818])])).
% 92.33/13.70 thf(f16546,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X3),X1),X3)) | ($true = X3)) )),
% 92.33/13.70 inference(equality_resolution,[],[f12531])).
% 92.33/13.70 thf(f12531,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)) | (X2 != X3) | ($true = X2)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6503])).
% 92.33/13.70 thf(f74638,plain,(
% 92.33/13.70 spl854_817),
% 92.33/13.70 inference(avatar_split_clause,[],[f16543,f74636])).
% 92.33/13.70 thf(f74636,plain,(
% 92.33/13.70 spl854_817 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,$true),$true),X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_817])])).
% 92.33/13.70 thf(f16543,plain,(
% 92.33/13.70 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,$true),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16542])).
% 92.33/13.70 thf(f16542,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12525])).
% 92.33/13.70 thf(f12525,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != X2) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8459])).
% 92.33/13.70 thf(f8459,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : ((((($true = X2) & ($true = X3)) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | ($true != X2) | ($true != X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),X0)))),
% 92.33/13.70 inference(rectify,[],[f8458])).
% 92.33/13.70 thf(f8458,plain,(
% 92.33/13.70 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) & ($true = X0)) | ($true != X3) | ($true != X1)) & ((($true = X3) & ($true = X1)) | ($true != X2) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)))),
% 92.33/13.70 inference(flattening,[],[f8457])).
% 92.33/13.70 thf(f8457,plain,(
% 92.33/13.70 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) & ($true = X0)) | (($true != X3) | ($true != X1))) & ((($true = X3) & ($true = X1)) | (($true != X2) | ($true != X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)))),
% 92.33/13.70 inference(nnf_transformation,[],[f6502])).
% 92.33/13.70 thf(f74634,plain,(
% 92.33/13.70 spl854_816),
% 92.33/13.70 inference(avatar_split_clause,[],[f16541,f74632])).
% 92.33/13.70 thf(f74632,plain,(
% 92.33/13.70 spl854_816 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,$true),$true),X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_816])])).
% 92.33/13.70 thf(f16541,plain,(
% 92.33/13.70 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,$true),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16540])).
% 92.33/13.70 thf(f16540,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12526])).
% 92.33/13.70 thf(f12526,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X2) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8459])).
% 92.33/13.70 thf(f74630,plain,(
% 92.33/13.70 spl854_815),
% 92.33/13.70 inference(avatar_split_clause,[],[f16539,f74628])).
% 92.33/13.70 thf(f74628,plain,(
% 92.33/13.70 spl854_815 <=> ! [X2 : $o,X3 : $o] : (($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),$true),$true)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_815])])).
% 92.33/13.70 thf(f16539,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o] : (($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),$true),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16538])).
% 92.33/13.70 thf(f16538,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X3) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12527])).
% 92.33/13.70 thf(f12527,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X3) | ($true != X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8459])).
% 92.33/13.70 thf(f74626,plain,(
% 92.33/13.70 spl854_814),
% 92.33/13.70 inference(avatar_split_clause,[],[f16537,f74624])).
% 92.33/13.70 thf(f74624,plain,(
% 92.33/13.70 spl854_814 <=> ! [X2 : $o,X3 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),$true),$true)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_814])])).
% 92.33/13.70 thf(f16537,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),$true),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16536])).
% 92.33/13.70 thf(f16536,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X2) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12528])).
% 92.33/13.70 thf(f12528,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8459])).
% 92.33/13.70 thf(f74622,plain,(
% 92.33/13.70 spl854_813),
% 92.33/13.70 inference(avatar_split_clause,[],[f16528,f74620])).
% 92.33/13.70 thf(f74620,plain,(
% 92.33/13.70 spl854_813 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X1),X2),X1),X3)) | ($true = X1))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_813])])).
% 92.33/13.70 thf(f16528,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X1),X2),X1),X3)) | ($true = X1)) )),
% 92.33/13.70 inference(equality_resolution,[],[f12517])).
% 92.33/13.70 thf(f12517,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X2),X1),X3)) | ($true = X1) | (X0 != X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6499])).
% 92.33/13.70 thf(f6499,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X2),X1),X3)) | ((X2 != X3) & ($true = X1)) | (X0 != X1))),
% 92.33/13.70 inference(definition_folding,[],[f6083,f6498])).
% 92.33/13.70 thf(f6083,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true != X0)) <=> (($true = X3) | ($true != X1))) | ((X2 != X3) & ($true = X1)) | (X0 != X1))),
% 92.33/13.70 inference(flattening,[],[f6082])).
% 92.33/13.70 thf(f6082,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true != X0)) <=> (($true = X3) | ($true != X1))) | (((X2 != X3) & ($true = X1)) | (X0 != X1)))),
% 92.33/13.70 inference(ennf_transformation,[],[f4282])).
% 92.33/13.70 thf(f4282,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X1) => (X2 = X3)) & (X0 = X1)) => ((($true = X0) => ($true = X2)) <=> (($true = X1) => ($true = X3))))),
% 92.33/13.70 inference(fool_elimination,[],[f4281])).
% 92.33/13.70 thf(f4281,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X1 => (X2 = X3)) & (X0 = X1)) => ((X0 => X2) <=> (X1 => X3)))),
% 92.33/13.70 inference(rectify,[],[f141])).
% 92.33/13.70 thf(f141,axiom,(
% 92.33/13.70 ! [X8 : $o,X59 : $o,X12 : $o,X60 : $o] : (((X59 => (X12 = X60)) & (X8 = X59)) => ((X8 => X12) <=> (X59 => X60)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG)).
% 92.33/13.70 thf(f74618,plain,(
% 92.33/13.70 spl854_812),
% 92.33/13.70 inference(avatar_split_clause,[],[f16524,f74616])).
% 92.33/13.70 thf(f74616,plain,(
% 92.33/13.70 spl854_812 <=> ! [X0 : $o,X3 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),$true),$true),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_812])])).
% 92.33/13.70 thf(f16524,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),$true),$true),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16523])).
% 92.33/13.70 thf(f16523,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o] : (($true = X0) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),$true),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12514])).
% 92.33/13.70 thf(f12514,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8453])).
% 92.33/13.70 thf(f74600,plain,(
% 92.33/13.70 spl854_811),
% 92.33/13.70 inference(avatar_split_clause,[],[f16521,f74598])).
% 92.33/13.70 thf(f74598,plain,(
% 92.33/13.70 spl854_811 <=> ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,$true),X2),X1),$true)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_811])])).
% 92.33/13.70 thf(f16521,plain,(
% 92.33/13.70 ( ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,$true),X2),X1),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16520])).
% 92.33/13.70 thf(f16520,plain,(
% 92.33/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,$true),X2),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12516])).
% 92.33/13.70 thf(f12516,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X3) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8453])).
% 92.33/13.70 thf(f74596,plain,(
% 92.33/13.70 spl854_810),
% 92.33/13.70 inference(avatar_split_clause,[],[f16519,f74594])).
% 92.33/13.70 thf(f74594,plain,(
% 92.33/13.70 spl854_810 <=> ! [X2 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X1),X2),X1),X3)) | ($true = X1))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_810])])).
% 92.33/13.70 thf(f16519,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X1),X2),X1),X3)) | ($true = X1)) )),
% 92.33/13.70 inference(equality_resolution,[],[f12511])).
% 92.33/13.70 thf(f12511,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X2),X1),X3)) | ($true = X1) | (X0 != X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6497])).
% 92.33/13.70 thf(f6497,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X2),X1),X3)) | ((X2 != X3) & ($true = X1)) | (X0 != X1))),
% 92.33/13.70 inference(definition_folding,[],[f6081,f6496])).
% 92.33/13.70 thf(f6496,plain,(
% 92.33/13.70 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : (((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X2),X1),X3)))),
% 92.33/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.70 thf(f6081,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))) | ((X2 != X3) & ($true = X1)) | (X0 != X1))),
% 92.33/13.70 inference(flattening,[],[f6080])).
% 92.33/13.70 thf(f6080,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))) | (((X2 != X3) & ($true = X1)) | (X0 != X1)))),
% 92.33/13.70 inference(ennf_transformation,[],[f4280])).
% 92.33/13.70 thf(f4280,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X1) => (X2 = X3)) & (X0 = X1)) => ((($true = X2) & ($true = X0)) <=> (($true = X3) & ($true = X1))))),
% 92.33/13.70 inference(fool_elimination,[],[f4279])).
% 92.33/13.70 thf(f4279,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X1 => (X2 = X3)) & (X0 = X1)) => ((X2 & X0) <=> (X3 & X1)))),
% 92.33/13.70 inference(rectify,[],[f143])).
% 92.33/13.70 thf(f143,axiom,(
% 92.33/13.70 ! [X7 : $o,X61 : $o,X62 : $o,X63 : $o] : (((X61 => (X62 = X63)) & (X7 = X61)) => ((X62 & X7) <=> (X63 & X61)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__CONG)).
% 92.33/13.70 thf(f74592,plain,(
% 92.33/13.70 spl854_809),
% 92.33/13.70 inference(avatar_split_clause,[],[f16516,f74590])).
% 92.33/13.70 thf(f74590,plain,(
% 92.33/13.70 spl854_809 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,$true),$true),X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_809])])).
% 92.33/13.70 thf(f16516,plain,(
% 92.33/13.70 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,$true),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16515])).
% 92.33/13.70 thf(f16515,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12507])).
% 92.33/13.70 thf(f12507,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != X2) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8450])).
% 92.33/13.70 thf(f8450,plain,(
% 92.33/13.70 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : ((((($true = X2) & ($true = X3)) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | ($true != X2) | ($true != X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),X0)))),
% 92.33/13.70 inference(rectify,[],[f8449])).
% 92.33/13.70 thf(f8449,plain,(
% 92.33/13.70 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) & ($true = X0)) | ($true != X3) | ($true != X1)) & ((($true = X3) & ($true = X1)) | ($true != X2) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X2),X1),X3)))),
% 92.33/13.70 inference(flattening,[],[f8448])).
% 92.33/13.70 thf(f8448,plain,(
% 92.33/13.70 ! [X3 : $o,X1 : $o,X2 : $o,X0 : $o] : ((((($true = X2) & ($true = X0)) | (($true != X3) | ($true != X1))) & ((($true = X3) & ($true = X1)) | (($true != X2) | ($true != X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X2),X1),X3)))),
% 92.33/13.70 inference(nnf_transformation,[],[f6496])).
% 92.33/13.70 thf(f74588,plain,(
% 92.33/13.70 spl854_808),
% 92.33/13.70 inference(avatar_split_clause,[],[f16514,f74586])).
% 92.33/13.70 thf(f74586,plain,(
% 92.33/13.70 spl854_808 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,$true),$true),X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_808])])).
% 92.33/13.70 thf(f16514,plain,(
% 92.33/13.70 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,$true),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16513])).
% 92.33/13.70 thf(f16513,plain,(
% 92.33/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),$true),X1),X0))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12508])).
% 92.33/13.70 thf(f12508,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X2) | ($true != X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8450])).
% 92.33/13.70 thf(f74584,plain,(
% 92.33/13.70 spl854_807),
% 92.33/13.70 inference(avatar_split_clause,[],[f16512,f74582])).
% 92.33/13.70 thf(f74582,plain,(
% 92.33/13.70 spl854_807 <=> ! [X2 : $o,X3 : $o] : (($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),$true),$true)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_807])])).
% 92.33/13.70 thf(f16512,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o] : (($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),$true),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16511])).
% 92.33/13.70 thf(f16511,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X3) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12509])).
% 92.33/13.70 thf(f12509,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X3) | ($true != X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8450])).
% 92.33/13.70 thf(f74580,plain,(
% 92.33/13.70 spl854_806),
% 92.33/13.70 inference(avatar_split_clause,[],[f16510,f74578])).
% 92.33/13.70 thf(f74578,plain,(
% 92.33/13.70 spl854_806 <=> ! [X2 : $o,X3 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),$true),$true)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_806])])).
% 92.33/13.70 thf(f16510,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),$true),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f16509])).
% 92.33/13.70 thf(f16509,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X2) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),$true))) )),
% 92.33/13.70 inference(equality_resolution,[],[f12510])).
% 92.33/13.70 thf(f12510,plain,(
% 92.33/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X3),X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8450])).
% 92.33/13.70 thf(f74576,plain,(
% 92.33/13.70 spl854_805),
% 92.33/13.70 inference(avatar_split_clause,[],[f15154,f74574])).
% 92.33/13.70 thf(f74574,plain,(
% 92.33/13.70 spl854_805 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X1)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_805])])).
% 92.33/13.70 thf(f15154,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X1))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11795,f9121,f9121])).
% 92.33/13.70 thf(f11795,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7957])).
% 92.33/13.70 thf(f7957,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X1)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X1))))),
% 92.33/13.70 inference(nnf_transformation,[],[f5242])).
% 92.33/13.70 thf(f5242,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X1)) <=> (X0 = X1))),
% 92.33/13.70 inference(rectify,[],[f1049])).
% 92.33/13.70 thf(f1049,axiom,(
% 92.33/13.70 ! [X134 : tyop_2Enum_2Enum,X91 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135)),X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X135)),X91)) <=> (X91 = X134))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__MONO__EQ)).
% 92.33/13.70 thf(f74572,plain,(
% 92.33/13.70 spl854_804),
% 92.33/13.70 inference(avatar_split_clause,[],[f15152,f74570])).
% 92.33/13.70 thf(f74570,plain,(
% 92.33/13.70 spl854_804 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_804])])).
% 92.33/13.70 thf(f15152,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11793,f9121,f9121])).
% 92.33/13.70 thf(f11793,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7956])).
% 92.33/13.70 thf(f7956,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) | (X1 != X2)) & ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))))),
% 92.33/13.70 inference(nnf_transformation,[],[f5241])).
% 92.33/13.70 thf(f5241,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) <=> (X1 = X2))),
% 92.33/13.70 inference(rectify,[],[f1050])).
% 92.33/13.70 thf(f1050,axiom,(
% 92.33/13.70 ! [X26 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X135),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X26)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X27),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X26))) <=> (X27 = X135))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__SUC__EQ)).
% 92.33/13.70 thf(f74568,plain,(
% 92.33/13.70 spl854_803),
% 92.33/13.70 inference(avatar_split_clause,[],[f14979,f74566])).
% 92.33/13.70 thf(f74566,plain,(
% 92.33/13.70 spl854_803 <=> ! [X0 : $tType,X2 : X0 > tyop_2Enum_2Enum > X0,X1 : X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X1),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_803])])).
% 92.33/13.70 thf(f14979,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > tyop_2Enum_2Enum > X0,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X1),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11352,f9122])).
% 92.33/13.70 thf(f11352,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > tyop_2Enum_2Enum > X0,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X1),X2),c_2Enum_2E0) = X1)) )),
% 92.33/13.70 inference(cnf_transformation,[],[f5217])).
% 92.33/13.70 thf(f5217,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0,X2 : X0 > tyop_2Enum_2Enum > X0] : (! [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X1),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)) = vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),X2,vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X1),X2),X3)),X3)) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X1),X2),c_2Enum_2E0) = X1))),
% 92.33/13.70 inference(rectify,[],[f898])).
% 92.33/13.70 thf(f898,axiom,(
% 92.33/13.70 ! [X0 : $tType,X8 : X0,X25 : X0 > tyop_2Enum_2Enum > X0] : (! [X104 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X8),X25),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X104)) = vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),X25,vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X8),X25),X104)),X104)) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2EPRIM__REC(X0),X8),X25),c_2Enum_2E0) = X8))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2EPRIM__REC__THM)).
% 92.33/13.70 thf(f74564,plain,(
% 92.33/13.70 spl854_802),
% 92.33/13.70 inference(avatar_split_clause,[],[f12292,f74562])).
% 92.33/13.70 thf(f74562,plain,(
% 92.33/13.70 spl854_802 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_802])])).
% 92.33/13.70 thf(f12292,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8373])).
% 92.33/13.70 thf(f8373,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) | ((($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X2))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X2) & (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) | (c_2Enum_2E0 != X2)) & ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X2) | (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) & (c_2Enum_2E0 = X2)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0))))),
% 92.33/13.70 inference(flattening,[],[f8372])).
% 92.33/13.70 thf(f8372,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) | ((($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X2))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X2) & (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) | (c_2Enum_2E0 != X2)) & ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)))) & (((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X2) | (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) & (c_2Enum_2E0 = X2)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0))))),
% 92.33/13.70 inference(nnf_transformation,[],[f6488])).
% 92.33/13.70 thf(f6488,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) <=> ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X2))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X2) | (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) & (c_2Enum_2E0 = X2)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0))))),
% 92.33/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.70 thf(f74560,plain,(
% 92.33/13.70 spl854_801),
% 92.33/13.70 inference(avatar_split_clause,[],[f12215,f74558])).
% 92.33/13.70 thf(f74558,plain,(
% 92.33/13.70 spl854_801 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_801])])).
% 92.33/13.70 thf(f12215,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8329])).
% 92.33/13.70 thf(f8329,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0)) | (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK620,X2),X1),X0)),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK620,X2),X1),X0)),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK620,X2),X1),X0)),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2))) & ((! [X4 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X4),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X4),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X4),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0))))),
% 92.33/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK620])],[f8327,f8328])).
% 92.33/13.70 thf(f8328,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2))) => (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK620,X2),X1),X0)),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK620,X2),X1),X0)),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK620,X2),X1),X0)),X2))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f8327,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0)) | ? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2))) & ((! [X4 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X4),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X4),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X4),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0))))),
% 92.33/13.70 inference(rectify,[],[f8326])).
% 92.33/13.70 thf(f8326,plain,(
% 92.33/13.70 ! [X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X0),X1),X2)) | ? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) & ((! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X0),X1),X2))))),
% 92.33/13.70 inference(flattening,[],[f8325])).
% 92.33/13.70 thf(f8325,plain,(
% 92.33/13.70 ! [X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X0),X1),X2)) | (? [X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)))) & ((! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X0),X1),X2))))),
% 92.33/13.70 inference(nnf_transformation,[],[f6477])).
% 92.33/13.70 thf(f6477,plain,(
% 92.33/13.70 ! [X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X0),X1),X2)) <=> (! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X3),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))))),
% 92.33/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.70 thf(f74556,plain,(
% 92.33/13.70 spl854_800),
% 92.33/13.70 inference(avatar_split_clause,[],[f12214,f74554])).
% 92.33/13.70 thf(f74554,plain,(
% 92.33/13.70 spl854_800 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_800])])).
% 92.33/13.70 thf(f12214,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP56,X2),X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8329])).
% 92.33/13.70 thf(f74552,plain,(
% 92.33/13.70 spl854_799),
% 92.33/13.70 inference(avatar_split_clause,[],[f12206,f74550])).
% 92.33/13.70 thf(f74550,plain,(
% 92.33/13.70 spl854_799 <=> ! [X0 : $tType,X4 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,X4)) | ($true != vAPP(X0,$o,X1,X4)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_799])])).
% 92.33/13.70 thf(f12206,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true != vAPP(X0,$o,X1,X4)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f8319])).
% 92.33/13.70 thf(f8319,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK618(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK618(X0),X2),X1))))) & (! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true != vAPP(X0,$o,X1,X4))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))))),
% 92.33/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK618])],[f8317,f8318])).
% 92.33/13.70 thf(f8318,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) => (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK618(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK618(X0),X2),X1)))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f8317,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3)))) & (! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true != vAPP(X0,$o,X1,X4))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))))),
% 92.33/13.70 inference(rectify,[],[f8316])).
% 92.33/13.70 thf(f8316,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3)))) & (! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X1,X3))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))))),
% 92.33/13.70 inference(nnf_transformation,[],[f6067])).
% 92.33/13.70 thf(f6067,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)) <=> ! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X1,X3))))),
% 92.33/13.70 inference(ennf_transformation,[],[f4134])).
% 92.33/13.70 thf(f4134,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)) <=> ! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X2,X3))))),
% 92.33/13.70 inference(fool_elimination,[],[f4133])).
% 92.33/13.70 thf(f4133,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2) <=> ! [X3 : X0] : (vAPP(X0,$o,X1,X3) => vAPP(X0,$o,X2,X3)))),
% 92.33/13.70 inference(rectify,[],[f1880])).
% 92.33/13.70 thf(f1880,axiom,(
% 92.33/13.70 ! [X0 : $tType,X111 : X0 > $o,X40 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X111),X40) <=> ! [X19 : X0] : (vAPP(X0,$o,X111,X19) => vAPP(X0,$o,X40,X19)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__applied)).
% 92.33/13.70 thf(f74548,plain,(
% 92.33/13.70 spl854_798),
% 92.33/13.70 inference(avatar_split_clause,[],[f11174,f74546])).
% 92.33/13.70 thf(f74546,plain,(
% 92.33/13.70 spl854_798 <=> ! [X0 : $tType,X4 : X0,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | (vAPP(sTfun(X0,$o),X0,sK383(X0),X1) != vAPP(sTfun(X0,$o),X0,sK384(X0),X1)) | ($true != vAPP(X0,$o,X1,X4)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_798])])).
% 92.33/13.70 thf(f11174,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X4 : X0] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | (vAPP(sTfun(X0,$o),X0,sK383(X0),X1) != vAPP(sTfun(X0,$o),X0,sK384(X0),X1)) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7675])).
% 92.33/13.70 thf(f7675,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ((vAPP(sTfun(X0,$o),X0,sK383(X0),X1) != vAPP(sTfun(X0,$o),X0,sK384(X0),X1)) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK384(X0),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK383(X0),X1)))) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) & ((! [X5 : X0,X6 : X0] : ((X5 = X6) | ($true != vAPP(X0,$o,X1,X6)) | ($true != vAPP(X0,$o,X1,X5))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK385(X0),X1)))) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1))))),
% 92.33/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK383,sK384,sK385])],[f7672,f7674,f7673])).
% 92.33/13.70 thf(f7673,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,X1,X3)) & ($true = vAPP(X0,$o,X1,X2))) => ((vAPP(sTfun(X0,$o),X0,sK383(X0),X1) != vAPP(sTfun(X0,$o),X0,sK384(X0),X1)) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK384(X0),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK383(X0),X1)))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f7674,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK385(X0),X1))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f7672,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,X1,X3)) & ($true = vAPP(X0,$o,X1,X2))) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) & ((! [X5 : X0,X6 : X0] : ((X5 = X6) | ($true != vAPP(X0,$o,X1,X6)) | ($true != vAPP(X0,$o,X1,X5))) & ? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1))))),
% 92.33/13.70 inference(rectify,[],[f7671])).
% 92.33/13.70 thf(f7671,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,X1,X3)) & ($true = vAPP(X0,$o,X1,X2))) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) & ((! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true != vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,X2))) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4))) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1))))),
% 92.33/13.70 inference(flattening,[],[f7670])).
% 92.33/13.70 thf(f7670,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | (? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,X1,X3)) & ($true = vAPP(X0,$o,X1,X2))) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4)))) & ((! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true != vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,X2))) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4))) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1))))),
% 92.33/13.70 inference(nnf_transformation,[],[f6423])).
% 92.33/13.70 thf(f6423,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) <=> (! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true != vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,X2))) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4))))),
% 92.33/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.33/13.70 thf(f74544,plain,(
% 92.33/13.70 spl854_797),
% 92.33/13.70 inference(avatar_split_clause,[],[f11055,f74542])).
% 92.33/13.70 thf(f74542,plain,(
% 92.33/13.70 spl854_797 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_797])])).
% 92.33/13.70 thf(f11055,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sK372,X1),X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP22,X1),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7587])).
% 92.33/13.70 thf(f74540,plain,(
% 92.33/13.70 spl854_796),
% 92.33/13.70 inference(avatar_split_clause,[],[f9716,f74538])).
% 92.33/13.70 thf(f74538,plain,(
% 92.33/13.70 spl854_796 <=> ! [X0 : tyop_2Emin_2Eind,X3 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X3,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,c_2Enum_2EZERO__REP)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_796])])).
% 92.33/13.70 thf(f9716,plain,(
% 92.33/13.70 ( ! [X3 : tyop_2Emin_2Eind > $o,X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,X3,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,X3,vAPP(sTfun(tyop_2Emin_2Eind,$o),tyop_2Emin_2Eind,sK184,X3))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X3,c_2Enum_2EZERO__REP)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6788])).
% 92.33/13.70 thf(f74536,plain,(
% 92.33/13.70 spl854_795),
% 92.33/13.70 inference(avatar_split_clause,[],[f9505,f74534])).
% 92.33/13.70 thf(f74534,plain,(
% 92.33/13.70 spl854_795 <=> ! [X0 : $tType,X3 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum > X0,X1 : X0] : (vAPP(tyop_2Enum_2Enum,X0,X2,X3) = vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X1),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_795])])).
% 92.33/13.70 thf(f9505,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X2 : tyop_2Enum_2Enum > X0,X3 : tyop_2Enum_2Enum,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,X2,X3) = vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X1),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4942])).
% 92.33/13.70 thf(f4942,plain,(
% 92.33/13.70 ! [X0 : $tType] : (! [X1 : X0,X2 : tyop_2Enum_2Enum > X0,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,X2,X3) = vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X1),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) & ! [X4 : X0,X5 : tyop_2Enum_2Enum > X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X4),X5),c_2Enum_2E0) = X4))),
% 92.33/13.70 inference(rectify,[],[f1524])).
% 92.33/13.70 thf(f1524,axiom,(
% 92.33/13.70 ! [X0 : $tType] : (! [X83 : X0,X75 : tyop_2Enum_2Enum > X0,X303 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,X75,X303) = vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X83),X75),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X303))) & ! [X72 : X0,X25 : tyop_2Enum_2Enum > X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X72),X25),c_2Enum_2E0) = X72))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EFCONS)).
% 92.33/13.70 thf(f74532,plain,(
% 92.33/13.70 spl854_794),
% 92.33/13.70 inference(avatar_split_clause,[],[f9360,f74530])).
% 92.33/13.70 thf(f74530,plain,(
% 92.33/13.70 spl854_794 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT,X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Ebit_2EBIT),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_794])])).
% 92.33/13.70 thf(f9360,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT,X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Ebit_2EBIT),X0)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f2092])).
% 92.33/13.70 thf(f2092,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT,X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Ebit_2EBIT),X0)))),
% 92.33/13.70 inference(fool_elimination,[],[f2091])).
% 92.33/13.70 thf(f2091,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT,X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X1),X0)))))),
% 92.33/13.70 inference(rectify,[],[f1710])).
% 92.33/13.70 thf(f1710,axiom,(
% 92.33/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT,X136) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X91 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X91),X136)))))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ELOWEST__SET__BIT__def)).
% 92.33/13.70 thf(f74469,plain,(
% 92.33/13.70 ~spl854_793 | ~spl854_40 | spl854_701),
% 92.33/13.70 inference(avatar_split_clause,[],[f74343,f68630,f22095,f74466])).
% 92.33/13.70 thf(f74466,plain,(
% 92.33/13.70 spl854_793 <=> (sP10 = c_2Erelation_2EEMPTY__REL($o))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_793])])).
% 92.33/13.70 thf(f74343,plain,(
% 92.33/13.70 (sP10 != c_2Erelation_2EEMPTY__REL($o)) | (~spl854_40 | spl854_701)),
% 92.33/13.70 inference(trivial_inequality_removal,[],[f74330])).
% 92.33/13.70 thf(f74330,plain,(
% 92.33/13.70 ($true != $true) | (sP10 != c_2Erelation_2EEMPTY__REL($o)) | (~spl854_40 | spl854_701)),
% 92.33/13.70 inference(constrained_superposition,[],[f68632,f22096])).
% 92.33/13.70 thf(f74149,plain,(
% 92.33/13.70 spl854_792 | ~spl854_9),
% 92.33/13.70 inference(avatar_split_clause,[],[f30270,f21928,f74147])).
% 92.33/13.70 thf(f74147,plain,(
% 92.33/13.70 spl854_792 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_792])])).
% 92.33/13.70 thf(f30270,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) ) | ~spl854_9),
% 92.33/13.70 inference(forward_demodulation,[],[f30269,f21929])).
% 92.33/13.70 thf(f30269,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) ) | ~spl854_9),
% 92.33/13.70 inference(forward_demodulation,[],[f13570,f21929])).
% 92.33/13.70 thf(f13570,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9174,f9121])).
% 92.33/13.70 thf(f9174,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4843])).
% 92.33/13.70 thf(f74145,plain,(
% 92.33/13.70 spl854_791 | ~spl854_9),
% 92.33/13.70 inference(avatar_split_clause,[],[f30264,f21928,f74143])).
% 92.33/13.70 thf(f74143,plain,(
% 92.33/13.70 spl854_791 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_791])])).
% 92.33/13.70 thf(f30264,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) ) | ~spl854_9),
% 92.33/13.70 inference(forward_demodulation,[],[f30263,f21929])).
% 92.33/13.70 thf(f30263,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) ) | ~spl854_9),
% 92.33/13.70 inference(forward_demodulation,[],[f9160,f21929])).
% 92.33/13.70 thf(f9160,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4839])).
% 92.33/13.70 thf(f74141,plain,(
% 92.33/13.70 spl854_790),
% 92.33/13.70 inference(avatar_split_clause,[],[f20094,f74139])).
% 92.33/13.70 thf(f74139,plain,(
% 92.33/13.70 spl854_790 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,$false),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_790])])).
% 92.33/13.70 thf(f20094,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,$false),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f15350,f17793])).
% 92.33/13.70 thf(f15350,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f12455,f13520,f13512])).
% 92.33/13.70 thf(f12455,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X2))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f5308])).
% 92.33/13.70 thf(f5308,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : $o,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X2),X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X2),X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X2),X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X2),X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),c_2Earithmetic_2EZERO)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X2),X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X2),X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X2),X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X2),X3)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X3))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X2)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X2),c_2Earithmetic_2EZERO) = X2) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X1),c_2Earithmetic_2EZERO),X0)))),
% 92.33/13.70 inference(rectify,[],[f1386])).
% 92.33/13.70 thf(f1386,axiom,(
% 92.33/13.70 ! [X8 : tyop_2Enum_2Enum,X49 : $o,X135 : tyop_2Enum_2Enum,X307 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X135),X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X135),X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X135),X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X135),X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X135)),c_2Earithmetic_2EZERO)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X135),X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X135),X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X135),X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X307)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X135),X307))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135)),c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X135)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X135),c_2Earithmetic_2EZERO) = X135) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X49),c_2Earithmetic_2EZERO),X8)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiSUB__THM)).
% 92.33/13.70 thf(f74137,plain,(
% 92.33/13.70 spl854_789),
% 92.33/13.70 inference(avatar_split_clause,[],[f20088,f74135])).
% 92.33/13.70 thf(f74135,plain,(
% 92.33/13.70 spl854_789 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,$false),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_789])])).
% 92.33/13.70 thf(f20088,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,$false),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f15345,f17793])).
% 92.33/13.70 thf(f15345,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f12460,f13520,f13512])).
% 92.33/13.70 thf(f12460,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2)),c_2Earithmetic_2EZERO))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f5308])).
% 92.33/13.70 thf(f74133,plain,(
% 92.33/13.70 spl854_788),
% 92.33/13.70 inference(avatar_split_clause,[],[f19139,f74131])).
% 92.33/13.70 thf(f74131,plain,(
% 92.33/13.70 spl854_788 <=> ! [X0 : $tType,X1 : X0 > $o] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false) = X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_788])])).
% 92.33/13.70 thf(f19139,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false) = X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f14406,f17793])).
% 92.33/13.70 thf(f14406,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f10436,f13541])).
% 92.33/13.70 thf(f10436,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2EEMPTY(X0) = X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6974])).
% 92.33/13.70 thf(f6974,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : (((c_2Epred__set_2EEMPTY(X0) = X1) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1))) & (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1)) | (c_2Epred__set_2EEMPTY(X0) != X1)))),
% 92.33/13.70 inference(nnf_transformation,[],[f2976])).
% 92.33/13.70 thf(f2976,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2EEMPTY(X0) = X1) <=> ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1)))),
% 92.33/13.70 inference(fool_elimination,[],[f2975])).
% 92.33/13.70 thf(f2975,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((c_2Epred__set_2EEMPTY(X0) = X1) <=> vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),X1))),
% 92.33/13.70 inference(rectify,[],[f1928])).
% 92.33/13.70 thf(f1928,axiom,(
% 92.33/13.70 ! [X0 : $tType,X111 : X0 > $o] : ((c_2Epred__set_2EEMPTY(X0) = X111) <=> vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X111),X111))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__EMPTY__REFL)).
% 92.33/13.70 thf(f74129,plain,(
% 92.33/13.70 spl854_787),
% 92.33/13.70 inference(avatar_split_clause,[],[f18350,f74127])).
% 92.33/13.70 thf(f74127,plain,(
% 92.33/13.70 spl854_787 <=> ! [X0 : $o] : ((vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0) != vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true)))) | ($true = X0))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_787])])).
% 92.33/13.70 thf(f18350,plain,(
% 92.33/13.70 ( ! [X0 : $o] : ((vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0) != vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true)))) | ($true = X0)) )),
% 92.33/13.70 inference(forward_demodulation,[],[f13754,f18174])).
% 92.33/13.70 thf(f13754,plain,(
% 92.33/13.70 ( ! [X0 : $o] : (($true = X0) | (vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0) != vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9427,f13522])).
% 92.33/13.70 thf(f9427,plain,(
% 92.33/13.70 ( ! [X0 : $o] : (($true = X0) | (vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) != vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f6613])).
% 92.33/13.70 thf(f6613,plain,(
% 92.33/13.70 ! [X0 : $o] : (((c_2Eoption_2ENONE(tyop_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) | ($true != vAPP($o,$o,vNOT,X0))) & (($true = vAPP($o,$o,vNOT,X0)) | (c_2Eoption_2ENONE(tyop_2Eone_2Eone) != vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0))) & ((vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) | ($true != X0)) & (($true = X0) | (vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) != vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0))))),
% 92.33/13.70 inference(flattening,[],[f6612])).
% 92.33/13.70 thf(f6612,plain,(
% 92.33/13.70 ! [X0 : $o] : ((((c_2Eoption_2ENONE(tyop_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) | ($true != vAPP($o,$o,vNOT,X0))) & (($true = vAPP($o,$o,vNOT,X0)) | (c_2Eoption_2ENONE(tyop_2Eone_2Eone) != vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)))) & (((vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) | ($true != X0)) & (($true = X0) | (vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) != vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)))))),
% 92.33/13.70 inference(nnf_transformation,[],[f2118])).
% 92.33/13.70 thf(f2118,plain,(
% 92.33/13.70 ! [X0 : $o] : (((c_2Eoption_2ENONE(tyop_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) <=> ($true = vAPP($o,$o,vNOT,X0))) & ((vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) <=> ($true = X0)))),
% 92.33/13.70 inference(fool_elimination,[],[f2117])).
% 92.33/13.70 thf(f2117,plain,(
% 92.33/13.70 ! [X0 : $o] : (((c_2Eoption_2ENONE(tyop_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) <=> vAPP($o,$o,vNOT,X0)) & ((vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) <=> X0))),
% 92.33/13.70 inference(rectify,[],[f758])).
% 92.33/13.70 thf(f758,axiom,(
% 92.33/13.70 ! [X35 : $o] : (((c_2Eoption_2ENONE(tyop_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X35)) <=> vAPP($o,$o,vNOT,X35)) & ((vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X35)) <=> X35))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__GUARD__EQ__THM)).
% 92.33/13.70 thf(f74125,plain,(
% 92.33/13.70 spl854_786),
% 92.33/13.70 inference(avatar_split_clause,[],[f18308,f74123])).
% 92.33/13.70 thf(f74123,plain,(
% 92.33/13.70 spl854_786 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_786])])).
% 92.33/13.70 thf(f18308,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f18307,f9370])).
% 92.33/13.70 thf(f9370,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4916])).
% 92.33/13.70 thf(f4916,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,c_2Earithmetic_2EZERO)))),
% 92.33/13.70 inference(rectify,[],[f1378])).
% 92.33/13.70 thf(f1378,axiom,(
% 92.33/13.70 ! [X136 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,c_2Earithmetic_2EZERO)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__iisuc)).
% 92.33/13.70 thf(f18307,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))))) )),
% 92.33/13.70 inference(forward_demodulation,[],[f9399,f9165])).
% 92.33/13.70 thf(f9165,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4841])).
% 92.33/13.70 thf(f9399,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4925])).
% 92.33/13.70 thf(f4925,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0)) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,c_2Earithmetic_2EZERO)))),
% 92.33/13.70 inference(rectify,[],[f1637])).
% 92.33/13.70 thf(f1637,axiom,(
% 92.33/13.70 ! [X136 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)))) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136))) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136))) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0)) & (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,c_2Earithmetic_2EZERO)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Elogroot_2Enumeral__sqrt)).
% 92.33/13.70 thf(f74121,plain,(
% 92.33/13.70 spl854_785),
% 92.33/13.70 inference(avatar_split_clause,[],[f15147,f74119])).
% 92.33/13.70 thf(f74119,plain,(
% 92.33/13.70 spl854_785 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),X0)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_785])])).
% 92.33/13.70 thf(f15147,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),X0))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11775,f9122,f9121,f9121])).
% 92.33/13.70 thf(f11775,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (c_2Enum_2E0 = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7947])).
% 92.33/13.70 thf(f7947,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0)) | ((X1 != X2) & (c_2Enum_2E0 != X0))) & ((X1 = X2) | (c_2Enum_2E0 = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0))))),
% 92.33/13.70 inference(flattening,[],[f7946])).
% 92.33/13.70 thf(f7946,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0)) | ((X1 != X2) & (c_2Enum_2E0 != X0))) & (((X1 = X2) | (c_2Enum_2E0 = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0))))),
% 92.33/13.70 inference(nnf_transformation,[],[f5233])).
% 92.33/13.70 thf(f5233,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0)) <=> ((X1 = X2) | (c_2Enum_2E0 = X0)))),
% 92.33/13.70 inference(rectify,[],[f1055])).
% 92.33/13.70 thf(f1055,axiom,(
% 92.33/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum,X108 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X137),X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X108),X134)) <=> ((X108 = X137) | (c_2Enum_2E0 = X134)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MULT__RCANCEL)).
% 92.33/13.70 thf(f74117,plain,(
% 92.33/13.70 spl854_784),
% 92.33/13.70 inference(avatar_split_clause,[],[f15144,f74115])).
% 92.33/13.70 thf(f74115,plain,(
% 92.33/13.70 spl854_784 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X2)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_784])])).
% 92.33/13.70 thf(f15144,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X2))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11772,f9122,f9121,f9121])).
% 92.33/13.70 thf(f11772,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (c_2Enum_2E0 = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X2))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7945])).
% 92.33/13.70 thf(f7945,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X2)) | ((X1 != X2) & (c_2Enum_2E0 != X0))) & ((X1 = X2) | (c_2Enum_2E0 = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X2))))),
% 92.33/13.70 inference(flattening,[],[f7944])).
% 92.33/13.70 thf(f7944,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X2)) | ((X1 != X2) & (c_2Enum_2E0 != X0))) & (((X1 = X2) | (c_2Enum_2E0 = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X2))))),
% 92.33/13.70 inference(nnf_transformation,[],[f5232])).
% 92.33/13.70 thf(f5232,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X2)) <=> ((X1 = X2) | (c_2Enum_2E0 = X0)))),
% 92.33/13.70 inference(rectify,[],[f1054])).
% 92.33/13.70 thf(f1054,axiom,(
% 92.33/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum,X108 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X108)) <=> ((X108 = X137) | (c_2Enum_2E0 = X134)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MULT__LCANCEL)).
% 92.33/13.70 thf(f74113,plain,(
% 92.33/13.70 spl854_783),
% 92.33/13.70 inference(avatar_split_clause,[],[f15141,f74111])).
% 92.33/13.70 thf(f74111,plain,(
% 92.33/13.70 spl854_783 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_783])])).
% 92.33/13.70 thf(f15141,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f11769,f9122])).
% 92.33/13.70 thf(f11769,plain,(
% 92.33/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (c_2Enum_2E0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7943])).
% 92.33/13.70 thf(f7943,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2)) | ((X0 != X1) & (c_2Enum_2E0 != X2))) & ((X0 = X1) | (c_2Enum_2E0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2))))),
% 92.33/13.70 inference(flattening,[],[f7942])).
% 92.33/13.70 thf(f7942,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2)) | ((X0 != X1) & (c_2Enum_2E0 != X2))) & (((X0 = X1) | (c_2Enum_2E0 = X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2))))),
% 92.33/13.70 inference(nnf_transformation,[],[f5231])).
% 92.33/13.70 thf(f5231,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X2)) <=> ((X0 = X1) | (c_2Enum_2E0 = X2)))),
% 92.33/13.70 inference(rectify,[],[f1215])).
% 92.33/13.70 thf(f1215,axiom,(
% 92.33/13.70 ! [X99 : tyop_2Enum_2Enum,X100 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X99),X19) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X100),X19)) <=> ((X99 = X100) | (c_2Enum_2E0 = X19)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEXP__EXP__INJECTIVE)).
% 92.33/13.70 thf(f74109,plain,(
% 92.33/13.70 spl854_782),
% 92.33/13.70 inference(avatar_split_clause,[],[f13688,f74107])).
% 92.33/13.70 thf(f74107,plain,(
% 92.33/13.70 spl854_782 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Einvtri0,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_782])])).
% 92.33/13.70 thf(f13688,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Einvtri0,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.33/13.70 inference(definition_unfolding,[],[f9329,f9122])).
% 92.33/13.70 thf(f9329,plain,(
% 92.33/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Einvtri0,X0),c_2Enum_2E0)))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f4901])).
% 92.33/13.70 thf(f4901,plain,(
% 92.33/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Einvtri0,X0),c_2Enum_2E0)))),
% 92.33/13.70 inference(rectify,[],[f1647])).
% 92.33/13.70 thf(f1647,axiom,(
% 92.33/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X136) = vAPP(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Einvtri0,X136),c_2Enum_2E0)))),
% 92.33/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Einvtri__def)).
% 92.33/13.70 thf(f74105,plain,(
% 92.33/13.70 spl854_781),
% 92.33/13.70 inference(avatar_split_clause,[],[f10772,f74103])).
% 92.33/13.70 thf(f74103,plain,(
% 92.33/13.70 spl854_781 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1)))),
% 92.33/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_781])])).
% 92.33/13.70 thf(f10772,plain,(
% 92.33/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1))) )),
% 92.33/13.70 inference(cnf_transformation,[],[f7369])).
% 92.33/13.70 thf(f7369,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1))))) & (! [X4 : X0,X5 : X0] : ((X4 = X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))))),
% 92.33/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK346,sK347])],[f7367,f7368])).
% 92.33/13.70 thf(f7368,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK346(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK347(X0),X1)))))),
% 92.33/13.70 introduced(choice_axiom,[])).
% 92.33/13.70 thf(f7367,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & (! [X4 : X0,X5 : X0] : ((X4 = X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))))),
% 92.33/13.70 inference(rectify,[],[f7366])).
% 92.33/13.70 thf(f7366,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & (! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))))),
% 92.33/13.70 inference(nnf_transformation,[],[f5789])).
% 92.33/13.70 thf(f5789,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) <=> ! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.33/13.70 inference(flattening,[],[f5788])).
% 92.33/13.70 thf(f5788,plain,(
% 92.33/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) <=> ! [X2 : X0,X3 : X0] : ((X2 = X3) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 92.92/13.70 inference(ennf_transformation,[],[f3182])).
% 92.92/13.70 thf(f3182,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) <=> ! [X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => (X2 = X3)))),
% 92.92/13.70 inference(fool_elimination,[],[f3181])).
% 92.92/13.70 thf(f3181,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1) <=> ! [X2 : X0,X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) => (X2 = X3)))),
% 92.92/13.70 inference(rectify,[],[f412])).
% 92.92/13.70 thf(f412,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X143) <=> ! [X4 : X0,X12 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X12),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12)) => (X4 = X12)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Eantisymmetric__def)).
% 92.92/13.70 thf(f74101,plain,(
% 92.92/13.70 ~spl854_780 | ~spl854_40 | spl854_694),
% 92.92/13.70 inference(avatar_split_clause,[],[f74018,f68537,f22095,f74098])).
% 92.92/13.70 thf(f74098,plain,(
% 92.92/13.70 spl854_780 <=> (c_2Emarker_2EAC = c_2Erelation_2EEMPTY__REL($o))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_780])])).
% 92.92/13.70 thf(f74018,plain,(
% 92.92/13.70 (c_2Emarker_2EAC != c_2Erelation_2EEMPTY__REL($o)) | (~spl854_40 | spl854_694)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f74005])).
% 92.92/13.70 thf(f74005,plain,(
% 92.92/13.70 ($true != $true) | (c_2Emarker_2EAC != c_2Erelation_2EEMPTY__REL($o)) | (~spl854_40 | spl854_694)),
% 92.92/13.70 inference(constrained_superposition,[],[f68539,f22096])).
% 92.92/13.70 thf(f74096,plain,(
% 92.92/13.70 spl854_779),
% 92.92/13.70 inference(avatar_split_clause,[],[f10761,f74094])).
% 92.92/13.70 thf(f74094,plain,(
% 92.92/13.70 spl854_779 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_779])])).
% 92.92/13.70 thf(f10761,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7359])).
% 92.92/13.70 thf(f7359,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1))) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1))))) & (! [X4 : X0,X5 : X0] : ((X4 = X5) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK340,sK341])],[f7357,f7358])).
% 92.92/13.70 thf(f7358,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1))) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK340(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK341(X0),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7357,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & (! [X4 : X0,X5 : X0] : ((X4 = X5) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1))))),
% 92.92/13.70 inference(rectify,[],[f7356])).
% 92.92/13.70 thf(f7356,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ? [X2 : X0,X3 : X0] : ((X2 != X3) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & (! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3178])).
% 92.92/13.70 thf(f3178,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) <=> ! [X2 : X0,X3 : X0] : ((X2 = X3) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.70 inference(fool_elimination,[],[f3177])).
% 92.92/13.70 thf(f3177,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1) <=> ! [X2 : X0,X3 : X0] : ((X2 = X3) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))),
% 92.92/13.70 inference(rectify,[],[f415])).
% 92.92/13.70 thf(f415,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X143) <=> ! [X73 : X0,X79 : X0] : ((X73 = X79) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X79),X73) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X73),X79)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Etrichotomous)).
% 92.92/13.70 thf(f74092,plain,(
% 92.92/13.70 spl854_778),
% 92.92/13.70 inference(avatar_split_clause,[],[f10305,f74090])).
% 92.92/13.70 thf(f74090,plain,(
% 92.92/13.70 spl854_778 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_778])])).
% 92.92/13.70 thf(f10305,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5680])).
% 92.92/13.70 thf(f5680,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)))),
% 92.92/13.70 inference(ennf_transformation,[],[f2798])).
% 92.92/13.70 thf(f2798,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2797])).
% 92.92/13.70 thf(f2797,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1))),
% 92.92/13.70 inference(rectify,[],[f593])).
% 92.92/13.70 thf(f593,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X143) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X143) = X143))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Esymmetric__inv__identity)).
% 92.92/13.70 thf(f74088,plain,(
% 92.92/13.70 spl854_777),
% 92.92/13.70 inference(avatar_split_clause,[],[f10294,f74086])).
% 92.92/13.70 thf(f74086,plain,(
% 92.92/13.70 spl854_777 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_777])])).
% 92.92/13.70 thf(f10294,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5671])).
% 92.92/13.70 thf(f5671,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)))),
% 92.92/13.70 inference(ennf_transformation,[],[f2780])).
% 92.92/13.70 thf(f2780,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2779])).
% 92.92/13.70 thf(f2779,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X1) = X1))),
% 92.92/13.70 inference(rectify,[],[f594])).
% 92.92/13.70 thf(f594,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X143) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),X143) = X143))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Eequivalence__inv__identity)).
% 92.92/13.70 thf(f74084,plain,(
% 92.92/13.70 spl854_776),
% 92.92/13.70 inference(avatar_split_clause,[],[f10136,f74082])).
% 92.92/13.70 thf(f74082,plain,(
% 92.92/13.70 spl854_776 <=> ! [X1 : $tType,X0 : $tType,X3 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),X3)) = X3)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_776])])).
% 92.92/13.70 thf(f10136,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X3 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),X3)) = X3)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6848])).
% 92.92/13.70 thf(f6848,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : $o > X0 > X1 > $o] : ((($true = vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),$o,c_2Esum_2EIS__SUM__REP(X0,X1),X2)) | (vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),X2)) != X2)) & ((vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),X2)) = X2) | ($true != vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),$o,c_2Esum_2EIS__SUM__REP(X0,X1),X2)))) & ! [X3 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),X3)) = X3))),
% 92.92/13.70 inference(nnf_transformation,[],[f2600])).
% 92.92/13.70 thf(f2600,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : $o > X0 > X1 > $o] : (($true = vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),$o,c_2Esum_2EIS__SUM__REP(X0,X1),X2)) <=> (vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),X2)) = X2)) & ! [X3 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),X3)) = X3))),
% 92.92/13.70 inference(fool_elimination,[],[f2599])).
% 92.92/13.70 thf(f2599,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : $o > X0 > X1 > $o] : (vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),$o,c_2Esum_2EIS__SUM__REP(X0,X1),X2) <=> (vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),X2)) = X2)) & ! [X3 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(sTfun($o,sTfun(X0,sTfun(X1,$o))),tyop_2Esum_2Esum(X0,X1),c_2Esum_2EABS__sum(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),sTfun($o,sTfun(X0,sTfun(X1,$o))),c_2Esum_2EREP__sum(X0,X1),X3)) = X3))),
% 92.92/13.70 inference(rectify,[],[f661])).
% 92.92/13.70 thf(f661,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType] : (! [X112 : $o > X0 > X5 > $o] : (vAPP(sTfun($o,sTfun(X0,sTfun(X5,$o))),$o,c_2Esum_2EIS__SUM__REP(X0,X5),X112) <=> (vAPP(tyop_2Esum_2Esum(X0,X5),sTfun($o,sTfun(X0,sTfun(X5,$o))),c_2Esum_2EREP__sum(X0,X5),vAPP(sTfun($o,sTfun(X0,sTfun(X5,$o))),tyop_2Esum_2Esum(X0,X5),c_2Esum_2EABS__sum(X0,X5),X112)) = X112)) & ! [X72 : tyop_2Esum_2Esum(X0,X5)] : (vAPP(sTfun($o,sTfun(X0,sTfun(X5,$o))),tyop_2Esum_2Esum(X0,X5),c_2Esum_2EABS__sum(X0,X5),vAPP(tyop_2Esum_2Esum(X0,X5),sTfun($o,sTfun(X0,sTfun(X5,$o))),c_2Esum_2EREP__sum(X0,X5),X72)) = X72))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2Esum__ISO__DEF)).
% 92.92/13.70 thf(f74080,plain,(
% 92.92/13.70 spl854_775),
% 92.92/13.70 inference(avatar_split_clause,[],[f9262,f74078])).
% 92.92/13.70 thf(f74078,plain,(
% 92.92/13.70 spl854_775 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0)),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_775])])).
% 92.92/13.70 thf(f9262,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0)),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4857])).
% 92.92/13.70 thf(f4857,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0)),X0)) & ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X2),X3)),X2))),
% 92.92/13.70 inference(rectify,[],[f1579])).
% 92.92/13.70 thf(f1579,axiom,(
% 92.92/13.70 ! [X83 : tyop_2Enum_2Enum,X80 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X83),X80) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X80),X83)),X83)) & ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X72),X49)),X72))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__ADD__L__THM)).
% 92.92/13.70 thf(f74076,plain,(
% 92.92/13.70 spl854_774),
% 92.92/13.70 inference(avatar_split_clause,[],[f9261,f74074])).
% 92.92/13.70 thf(f74074,plain,(
% 92.92/13.70 spl854_774 <=> ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X2),X3)),X2))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_774])])).
% 92.92/13.70 thf(f9261,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X2),X3)),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4857])).
% 92.92/13.70 thf(f74072,plain,(
% 92.92/13.70 spl854_773),
% 92.92/13.70 inference(avatar_split_clause,[],[f9260,f74070])).
% 92.92/13.70 thf(f74070,plain,(
% 92.92/13.70 spl854_773 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_773])])).
% 92.92/13.70 thf(f9260,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4856])).
% 92.92/13.70 thf(f4856,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0))) & ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X2),X3)))),
% 92.92/13.70 inference(rectify,[],[f1577])).
% 92.92/13.70 thf(f1577,axiom,(
% 92.92/13.70 ! [X83 : tyop_2Enum_2Enum,X80 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X83),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X80),X83)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X83),X80)) & ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X72),X49)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__ADD__R__THM)).
% 92.92/13.70 thf(f74068,plain,(
% 92.92/13.70 spl854_772),
% 92.92/13.70 inference(avatar_split_clause,[],[f9259,f74066])).
% 92.92/13.70 thf(f74066,plain,(
% 92.92/13.70 spl854_772 <=> ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X2),X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_772])])).
% 92.92/13.70 thf(f9259,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X2),X3)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4856])).
% 92.92/13.70 thf(f73946,plain,(
% 92.92/13.70 spl854_771 | ~spl854_308 | ~spl854_760),
% 92.92/13.70 inference(avatar_split_clause,[],[f71233,f71230,f35574,f73944])).
% 92.92/13.70 thf(f73944,plain,(
% 92.92/13.70 spl854_771 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_771])])).
% 92.92/13.70 thf(f71230,plain,(
% 92.92/13.70 spl854_760 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_760])])).
% 92.92/13.70 thf(f71233,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) ) | (~spl854_308 | ~spl854_760)),
% 92.92/13.70 inference(forward_demodulation,[],[f71231,f35576])).
% 92.92/13.70 thf(f71231,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) ) | ~spl854_760),
% 92.92/13.70 inference(avatar_component_clause,[],[f71230])).
% 92.92/13.70 thf(f73942,plain,(
% 92.92/13.70 spl854_770 | ~spl854_308 | ~spl854_759),
% 92.92/13.70 inference(avatar_split_clause,[],[f71228,f71225,f35574,f73940])).
% 92.92/13.70 thf(f73940,plain,(
% 92.92/13.70 spl854_770 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_770])])).
% 92.92/13.70 thf(f71225,plain,(
% 92.92/13.70 spl854_759 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_759])])).
% 92.92/13.70 thf(f71228,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) ) | (~spl854_308 | ~spl854_759)),
% 92.92/13.70 inference(forward_demodulation,[],[f71226,f35576])).
% 92.92/13.70 thf(f71226,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) ) | ~spl854_759),
% 92.92/13.70 inference(avatar_component_clause,[],[f71225])).
% 92.92/13.70 thf(f73082,plain,(
% 92.92/13.70 ~spl854_769 | ~spl854_40 | spl854_693),
% 92.92/13.70 inference(avatar_split_clause,[],[f71309,f68269,f22095,f73079])).
% 92.92/13.70 thf(f73079,plain,(
% 92.92/13.70 spl854_769 <=> (sP61 = c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_769])])).
% 92.92/13.70 thf(f71309,plain,(
% 92.92/13.70 (sP61 != c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum)) | (~spl854_40 | spl854_693)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f71296])).
% 92.92/13.70 thf(f71296,plain,(
% 92.92/13.70 ($true != $true) | (sP61 != c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum)) | (~spl854_40 | spl854_693)),
% 92.92/13.70 inference(constrained_superposition,[],[f68271,f22096])).
% 92.92/13.70 thf(f71293,plain,(
% 92.92/13.70 spl854_768 | ~spl854_9 | ~spl854_160),
% 92.92/13.70 inference(avatar_split_clause,[],[f32112,f22950,f21928,f71291])).
% 92.92/13.70 thf(f71291,plain,(
% 92.92/13.70 spl854_768 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_768])])).
% 92.92/13.70 thf(f32112,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) ) | (~spl854_9 | ~spl854_160)),
% 92.92/13.70 inference(forward_demodulation,[],[f18579,f29755])).
% 92.92/13.70 thf(f18579,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14004,f13567])).
% 92.92/13.70 thf(f14004,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9759,f9122,f13512])).
% 92.92/13.70 thf(f9759,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6800])).
% 92.92/13.70 thf(f6800,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) & ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f2390])).
% 92.92/13.70 thf(f2390,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),
% 92.92/13.70 inference(fool_elimination,[],[f2389])).
% 92.92/13.70 thf(f2389,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),
% 92.92/13.70 inference(rectify,[],[f1283])).
% 92.92/13.70 thf(f1283,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X8) <=> (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X8),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__MOD2)).
% 92.92/13.70 thf(f71289,plain,(
% 92.92/13.70 spl854_767 | ~spl854_9 | ~spl854_160),
% 92.92/13.70 inference(avatar_split_clause,[],[f30454,f22950,f21928,f71287])).
% 92.92/13.70 thf(f71287,plain,(
% 92.92/13.70 spl854_767 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_767])])).
% 92.92/13.70 thf(f30454,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) ) | (~spl854_9 | ~spl854_160)),
% 92.92/13.70 inference(forward_demodulation,[],[f18580,f29755])).
% 92.92/13.70 thf(f18580,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14005,f13567])).
% 92.92/13.70 thf(f14005,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9758,f9122,f13512])).
% 92.92/13.70 thf(f9758,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6800])).
% 92.92/13.70 thf(f71285,plain,(
% 92.92/13.70 spl854_766),
% 92.92/13.70 inference(avatar_split_clause,[],[f20019,f71283])).
% 92.92/13.70 thf(f71283,plain,(
% 92.92/13.70 spl854_766 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_766])])).
% 92.92/13.70 thf(f20019,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f17107,f17793])).
% 92.92/13.70 thf(f17107,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(equality_proxy_clausification,[],[f17106])).
% 92.92/13.70 thf(f17106,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2)))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f15309])).
% 92.92/13.70 thf(f15309,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f12383,f13541])).
% 92.92/13.70 thf(f12383,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),c_2Epred__set_2EEMPTY(X0)),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4232])).
% 92.92/13.70 thf(f4232,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),c_2Epred__set_2EEMPTY(X0)),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2))))),
% 92.92/13.70 inference(fool_elimination,[],[f4231])).
% 92.92/13.70 thf(f4231,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : vAPP($o,$o,vNOT,(c_2Epred__set_2EEMPTY(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X1),X2)))),
% 92.92/13.70 inference(rectify,[],[f1961])).
% 92.92/13.70 thf(f1961,axiom,(
% 92.92/13.70 ! [X0 : $tType,X8 : X0,X157 : X0 > $o] : vAPP($o,$o,vNOT,(c_2Epred__set_2EEMPTY(X0) = vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X8),X157)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__EMPTY__INSERT)).
% 92.92/13.70 thf(f71281,plain,(
% 92.92/13.70 spl854_765),
% 92.92/13.70 inference(avatar_split_clause,[],[f19169,f71279])).
% 92.92/13.70 thf(f71279,plain,(
% 92.92/13.70 spl854_765 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_765])])).
% 92.92/13.70 thf(f19169,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19168,f18124])).
% 92.92/13.70 thf(f19168,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19167,f13563])).
% 92.92/13.70 thf(f19167,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19166,f13548])).
% 92.92/13.70 thf(f19166,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19165,f18124])).
% 92.92/13.70 thf(f19165,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19164,f13563])).
% 92.92/13.70 thf(f19164,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14445,f13548])).
% 92.92/13.70 thf(f14445,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10478,f13512,f13512,f9121])).
% 92.92/13.70 thf(f10478,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7004])).
% 92.92/13.70 thf(f7004,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0)) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))))),
% 92.92/13.70 inference(flattening,[],[f7003])).
% 92.92/13.70 thf(f7003,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) | ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5118])).
% 92.92/13.70 thf(f5118,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) <=> ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)))),
% 92.92/13.70 inference(rectify,[],[f1077])).
% 92.92/13.70 thf(f1077,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum,X18 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X8),X18)) <=> ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X18) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X8)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__1)).
% 92.92/13.70 thf(f71277,plain,(
% 92.92/13.70 spl854_764),
% 92.92/13.70 inference(avatar_split_clause,[],[f19163,f71275])).
% 92.92/13.70 thf(f71275,plain,(
% 92.92/13.70 spl854_764 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_764])])).
% 92.92/13.70 thf(f19163,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19162,f18124])).
% 92.92/13.70 thf(f19162,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19161,f13563])).
% 92.92/13.70 thf(f19161,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19160,f13548])).
% 92.92/13.70 thf(f19160,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19159,f18124])).
% 92.92/13.70 thf(f19159,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19158,f13563])).
% 92.92/13.70 thf(f19158,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14444,f13548])).
% 92.92/13.70 thf(f14444,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10479,f13512,f13512,f9121])).
% 92.92/13.70 thf(f10479,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7004])).
% 92.92/13.70 thf(f71273,plain,(
% 92.92/13.70 spl854_763),
% 92.92/13.70 inference(avatar_split_clause,[],[f18604,f71271])).
% 92.92/13.70 thf(f71271,plain,(
% 92.92/13.70 spl854_763 <=> ! [X0 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_763])])).
% 92.92/13.70 thf(f18604,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18603,f18124])).
% 92.92/13.70 thf(f18603,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18602,f13563])).
% 92.92/13.70 thf(f18602,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18601,f13548])).
% 92.92/13.70 thf(f18601,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18600,f18124])).
% 92.92/13.70 thf(f18600,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18599,f13563])).
% 92.92/13.70 thf(f18599,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14023,f13548])).
% 92.92/13.70 thf(f14023,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9778,f13512,f13512])).
% 92.92/13.70 thf(f9778,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6814])).
% 92.92/13.70 thf(f6814,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))),
% 92.92/13.70 inference(nnf_transformation,[],[f2414])).
% 92.92/13.70 thf(f2414,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0))),
% 92.92/13.70 inference(fool_elimination,[],[f2413])).
% 92.92/13.70 thf(f2413,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0))),
% 92.92/13.70 inference(rectify,[],[f1468])).
% 92.92/13.70 thf(f1468,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X8),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X8))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EDIVIDES__ONE)).
% 92.92/13.70 thf(f71242,plain,(
% 92.92/13.70 spl854_762 | ~spl854_101 | ~spl854_288 | ~spl854_705 | ~spl854_761),
% 92.92/13.70 inference(avatar_split_clause,[],[f71238,f71235,f68647,f23881,f22587,f71240])).
% 92.92/13.70 thf(f71240,plain,(
% 92.92/13.70 spl854_762 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_762])])).
% 92.92/13.70 thf(f22587,plain,(
% 92.92/13.70 spl854_101 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_101])])).
% 92.92/13.70 thf(f23881,plain,(
% 92.92/13.70 spl854_288 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_288])])).
% 92.92/13.70 thf(f71235,plain,(
% 92.92/13.70 spl854_761 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_761])])).
% 92.92/13.70 thf(f71238,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) ) | (~spl854_101 | ~spl854_288 | ~spl854_705 | ~spl854_761)),
% 92.92/13.70 inference(forward_demodulation,[],[f71236,f68954])).
% 92.92/13.70 thf(f68954,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0)))) ) | (~spl854_101 | ~spl854_288 | ~spl854_705)),
% 92.92/13.70 inference(forward_demodulation,[],[f68925,f22588])).
% 92.92/13.70 thf(f22588,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0))) ) | ~spl854_101),
% 92.92/13.70 inference(avatar_component_clause,[],[f22587])).
% 92.92/13.70 thf(f68925,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0)))) ) | (~spl854_288 | ~spl854_705)),
% 92.92/13.70 inference(superposition,[],[f68648,f23882])).
% 92.92/13.70 thf(f23882,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) ) | ~spl854_288),
% 92.92/13.70 inference(avatar_component_clause,[],[f23881])).
% 92.92/13.70 thf(f71236,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) ) | ~spl854_761),
% 92.92/13.70 inference(avatar_component_clause,[],[f71235])).
% 92.92/13.70 thf(f71237,plain,(
% 92.92/13.70 spl854_761),
% 92.92/13.70 inference(avatar_split_clause,[],[f18595,f71235])).
% 92.92/13.70 thf(f18595,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18594,f18222])).
% 92.92/13.70 thf(f18222,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18221,f9309])).
% 92.92/13.70 thf(f9309,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4883])).
% 92.92/13.70 thf(f4883,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0))),
% 92.92/13.70 inference(rectify,[],[f1369])).
% 92.92/13.70 thf(f1369,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X8) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X8),X8))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiDUB)).
% 92.92/13.70 thf(f18221,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f13690,f13567])).
% 92.92/13.70 thf(f13690,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9332,f9121,f13512])).
% 92.92/13.70 thf(f9332,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4903])).
% 92.92/13.70 thf(f4903,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0))),
% 92.92/13.70 inference(rectify,[],[f1047])).
% 92.92/13.70 thf(f1047,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X136))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ETIMES2)).
% 92.92/13.70 thf(f18594,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14012,f13567])).
% 92.92/13.70 thf(f14012,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9765,f9121,f13512,f13519])).
% 92.92/13.70 thf(f9765,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6809])).
% 92.92/13.70 thf(f6809,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) != X0)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK188])],[f6807,f6808])).
% 92.92/13.70 thf(f6808,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2)) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK188,X0))) = X0))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f6807,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) != X0)) & (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))))),
% 92.92/13.70 inference(rectify,[],[f6806])).
% 92.92/13.70 thf(f6806,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) != X0)) & (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f2398])).
% 92.92/13.70 thf(f2398,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) <=> ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0))),
% 92.92/13.70 inference(fool_elimination,[],[f2397])).
% 92.92/13.70 thf(f2397,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0) <=> ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0))),
% 92.92/13.70 inference(rectify,[],[f1095])).
% 92.92/13.70 thf(f1095,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X136) <=> ? [X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X27)) = X136))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS)).
% 92.92/13.70 thf(f71232,plain,(
% 92.92/13.70 spl854_760),
% 92.92/13.70 inference(avatar_split_clause,[],[f18583,f71230])).
% 92.92/13.70 thf(f18583,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14007,f13567])).
% 92.92/13.70 thf(f14007,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9760,f9121,f13512])).
% 92.92/13.70 thf(f9760,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6804])).
% 92.92/13.70 thf(f6804,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) != X0)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK187])],[f6802,f6803])).
% 92.92/13.70 thf(f6803,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK187,X0)) = X0))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f6802,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) != X0)) & (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(rectify,[],[f6801])).
% 92.92/13.70 thf(f6801,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) != X0)) & (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f2392])).
% 92.92/13.70 thf(f2392,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) <=> ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) = X0))),
% 92.92/13.70 inference(fool_elimination,[],[f2391])).
% 92.92/13.70 thf(f2391,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0) <=> ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) = X0))),
% 92.92/13.70 inference(rectify,[],[f1094])).
% 92.92/13.70 thf(f1094,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X136) <=> ? [X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X27) = X136))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS)).
% 92.92/13.70 thf(f71227,plain,(
% 92.92/13.70 spl854_759),
% 92.92/13.70 inference(avatar_split_clause,[],[f18346,f71225])).
% 92.92/13.70 thf(f18346,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f13738,f13567])).
% 92.92/13.70 thf(f13738,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9413,f9121,f13512])).
% 92.92/13.70 thf(f9413,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6607])).
% 92.92/13.70 thf(f6607,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK126,sK127])],[f5423,f6606,f6605])).
% 92.92/13.70 thf(f6605,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f6606,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK127,X0)) = X0))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f5423,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))) & (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(ennf_transformation,[],[f2114])).
% 92.92/13.70 thf(f2114,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0)) & (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) => ? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2) = X0)))),
% 92.92/13.70 inference(fool_elimination,[],[f2113])).
% 92.92/13.70 thf(f2113,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) = X0)) & (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0) => ? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X2) = X0)))),
% 92.92/13.70 inference(rectify,[],[f1093])).
% 92.92/13.70 thf(f1093,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X136) => ? [X104 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X104)) = X136)) & (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X136) => ? [X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X27) = X136)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__ODD__EXISTS)).
% 92.92/13.70 thf(f71196,plain,(
% 92.92/13.70 spl854_758 | ~spl854_101 | ~spl854_288 | ~spl854_705 | ~spl854_757),
% 92.92/13.70 inference(avatar_split_clause,[],[f71192,f71189,f68647,f23881,f22587,f71194])).
% 92.92/13.70 thf(f71194,plain,(
% 92.92/13.70 spl854_758 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_758])])).
% 92.92/13.70 thf(f71189,plain,(
% 92.92/13.70 spl854_757 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_757])])).
% 92.92/13.70 thf(f71192,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) ) | (~spl854_101 | ~spl854_288 | ~spl854_705 | ~spl854_757)),
% 92.92/13.70 inference(forward_demodulation,[],[f71190,f68954])).
% 92.92/13.70 thf(f71190,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) ) | ~spl854_757),
% 92.92/13.70 inference(avatar_component_clause,[],[f71189])).
% 92.92/13.70 thf(f71191,plain,(
% 92.92/13.70 spl854_757),
% 92.92/13.70 inference(avatar_split_clause,[],[f18345,f71189])).
% 92.92/13.70 thf(f18345,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18344,f18222])).
% 92.92/13.70 thf(f18344,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f13737,f13567])).
% 92.92/13.70 thf(f13737,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9414,f9121,f13512,f13519])).
% 92.92/13.70 thf(f9414,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK126,X0))) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6607])).
% 92.92/13.70 thf(f71187,plain,(
% 92.92/13.70 spl854_756),
% 92.92/13.70 inference(avatar_split_clause,[],[f17007,f71185])).
% 92.92/13.70 thf(f71185,plain,(
% 92.92/13.70 spl854_756 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X5 : X1,X2 : X0 > X1 > $o] : (($false = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_756])])).
% 92.92/13.70 thf(f17007,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X5 : X1] : (($false = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12824])).
% 92.92/13.70 thf(f12824,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X5 : X1] : (($true = vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8667])).
% 92.92/13.70 thf(f8667,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3)) | ($true != vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),vAPP(sTfun(X0,sTfun(X1,$o)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,$o)),X1),sK697(X0,X1),X3),X2))))) & (! [X5 : X1] : ($true = vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK697])],[f8665,f8666])).
% 92.92/13.70 thf(f8666,plain,(
% 92.92/13.70 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0] : (? [X4 : X1] : ($true != vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) => ($true != vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),vAPP(sTfun(X0,sTfun(X1,$o)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,$o)),X1),sK697(X0,X1),X3),X2)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8665,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3)) | ? [X4 : X1] : ($true != vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))) & (! [X5 : X1] : ($true = vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3))))),
% 92.92/13.70 inference(rectify,[],[f8664])).
% 92.92/13.70 thf(f8664,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3)) | ? [X4 : X1] : ($true != vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))) & (! [X4 : X1] : ($true = vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4458])).
% 92.92/13.70 thf(f4458,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3)) <=> ! [X4 : X1] : ($true = vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))))),
% 92.92/13.70 inference(fool_elimination,[],[f4457])).
% 92.92/13.70 thf(f4457,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X1),X2),X3) <=> ! [X4 : X1] : vAPP($o,$o,vNOT,vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 92.92/13.70 inference(rectify,[],[f458])).
% 92.92/13.70 thf(f458,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X143 : X0 > X5 > $o,X4 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(X0,$o),c_2Erelation_2Enf(X0,X5),X143),X4) <=> ! [X12 : X5] : vAPP($o,$o,vNOT,vAPP(X5,$o,vAPP(X0,sTfun(X5,$o),X143,X4),X12)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Enf__def)).
% 92.92/13.70 thf(f71183,plain,(
% 92.92/13.70 spl854_755),
% 92.92/13.70 inference(avatar_split_clause,[],[f16663,f71181])).
% 92.92/13.70 thf(f71181,plain,(
% 92.92/13.70 spl854_755 <=> ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X0 : X2 > X1,X10 : X2] : (($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X10))) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_755])])).
% 92.92/13.70 thf(f16663,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X10 : X2,X0 : X2 > X1] : (($true = vAPP(X1,$o,X3,vAPP(X2,X1,X0,X10))) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0))) )),
% 92.92/13.70 inference(equality_resolution,[],[f12836])).
% 92.92/13.70 thf(f12836,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X2 : $tType,X3 : X1 > $o,X10 : X2,X0 : X2 > X1,X9 : X1] : (($true = vAPP(X1,$o,X3,X9)) | (vAPP(X2,X1,X0,X10) != X9) | ($true != vAPP(sTfun(X2,X1),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X2,X1),$o),sP104(X1,X2),X3),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8691])).
% 92.92/13.70 thf(f71179,plain,(
% 92.92/13.70 spl854_754),
% 92.92/13.70 inference(avatar_split_clause,[],[f16632,f71177])).
% 92.92/13.70 thf(f71177,plain,(
% 92.92/13.70 spl854_754 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X5 : X1,X2 : X1 > X0] : ((vAPP(X0,X1,X3,vAPP(X1,X0,X2,X5)) = X5) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_754])])).
% 92.92/13.70 thf(f16632,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1,X5 : X1] : ((vAPP(X0,X1,X3,vAPP(X1,X0,X2,X5)) = X5) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2))) )),
% 92.92/13.70 inference(equality_resolution,[],[f12713])).
% 92.92/13.70 thf(f12713,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1,X4 : X0,X5 : X1] : ((vAPP(X0,X1,X3,X4) = X5) | (vAPP(X1,X0,X2,X5) != X4) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8571])).
% 92.92/13.70 thf(f8571,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X0 > X1] : ((! [X4 : X0,X5 : X1] : (((vAPP(X1,X0,X2,X5) = X4) | (vAPP(X0,X1,X3,X4) != X5)) & ((vAPP(X0,X1,X3,X4) = X5) | (vAPP(X1,X0,X2,X5) != X4))) & ($true = vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2)) & ($true = vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.92/13.70 inference(nnf_transformation,[],[f6546])).
% 92.92/13.70 thf(f6546,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X0 > X1] : ((! [X4 : X0,X5 : X1] : ((vAPP(X1,X0,X2,X5) = X4) <=> (vAPP(X0,X1,X3,X4) = X5)) & ($true = vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2)) & ($true = vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.92/13.70 inference(definition_folding,[],[f6193,f6545,f6544])).
% 92.92/13.70 thf(f6193,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X0 > X1] : ((! [X4 : X0,X5 : X1] : ((vAPP(X1,X0,X2,X5) = X4) <=> (vAPP(X0,X1,X3,X4) = X5)) & ! [X6 : X0 > $o] : (? [X7 : X0] : ($true = vAPP(X0,$o,X6,X7)) <=> ? [X8 : X1] : ($true = vAPP(X0,$o,X6,vAPP(X1,X0,X2,X8)))) & ! [X9 : X0 > $o] : (! [X10 : X0] : ($true = vAPP(X0,$o,X9,X10)) <=> ! [X11 : X1] : ($true = vAPP(X0,$o,X9,vAPP(X1,X0,X2,X11))))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.92/13.70 inference(ennf_transformation,[],[f4412])).
% 92.92/13.70 thf(f4412,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X0 > X1] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)) => (! [X4 : X0,X5 : X1] : ((vAPP(X1,X0,X2,X5) = X4) <=> (vAPP(X0,X1,X3,X4) = X5)) & ! [X6 : X0 > $o] : (? [X7 : X0] : ($true = vAPP(X0,$o,X6,X7)) <=> ? [X8 : X1] : ($true = vAPP(X0,$o,X6,vAPP(X1,X0,X2,X8)))) & ! [X9 : X0 > $o] : (! [X10 : X0] : ($true = vAPP(X0,$o,X9,X10)) <=> ! [X11 : X1] : ($true = vAPP(X0,$o,X9,vAPP(X1,X0,X2,X11))))))),
% 92.92/13.70 inference(fool_elimination,[],[f4411])).
% 92.92/13.70 thf(f4411,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X0 > X1] : (vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2) => (! [X4 : X0,X5 : X1] : ((vAPP(X1,X0,X2,X5) = X4) <=> (vAPP(X0,X1,X3,X4) = X5)) & ! [X6 : X0 > $o] : (? [X7 : X0] : vAPP(X0,$o,X6,X7) <=> ? [X8 : X1] : vAPP(X0,$o,X6,vAPP(X1,X0,X2,X8))) & ! [X9 : X0 > $o] : (! [X10 : X0] : vAPP(X0,$o,X9,X10) <=> ! [X11 : X1] : vAPP(X0,$o,X9,vAPP(X1,X0,X2,X11)))))),
% 92.92/13.70 inference(rectify,[],[f1549])).
% 92.92/13.70 thf(f1549,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X66 : X5 > X0,X25 : X0 > X5] : (vAPP(sTfun(X5,X0),$o,vAPP(sTfun(X0,X5),sTfun(sTfun(X5,X0),$o),c_2Eind__type_2EISO(X0,X5),X25),X66) => (! [X290 : X0,X291 : X5] : ((vAPP(X5,X0,X66,X291) = X290) <=> (vAPP(X0,X5,X25,X290) = X291)) & ! [X445 : X0 > $o] : (? [X33 : X0] : vAPP(X0,$o,X445,X33) <=> ? [X93 : X5] : vAPP(X0,$o,X445,vAPP(X5,X0,X66,X93))) & ! [X133 : X0 > $o] : (! [X15 : X0] : vAPP(X0,$o,X133,X15) <=> ! [X23 : X5] : vAPP(X0,$o,X133,vAPP(X5,X0,X66,X23)))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EISO__USAGE)).
% 92.92/13.70 thf(f71175,plain,(
% 92.92/13.70 spl854_753),
% 92.92/13.70 inference(avatar_split_clause,[],[f16631,f71173])).
% 92.92/13.70 thf(f71173,plain,(
% 92.92/13.70 spl854_753 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X4 : X0,X3 : X0 > X1] : ((vAPP(X1,X0,X2,vAPP(X0,X1,X3,X4)) = X4) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_753])])).
% 92.92/13.70 thf(f16631,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1,X4 : X0] : ((vAPP(X1,X0,X2,vAPP(X0,X1,X3,X4)) = X4) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2))) )),
% 92.92/13.70 inference(equality_resolution,[],[f12714])).
% 92.92/13.70 thf(f12714,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1,X4 : X0,X5 : X1] : ((vAPP(X1,X0,X2,X5) = X4) | (vAPP(X0,X1,X3,X4) != X5) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8571])).
% 92.92/13.70 thf(f71171,plain,(
% 92.92/13.70 ~spl854_752 | ~spl854_40 | spl854_691),
% 92.92/13.70 inference(avatar_split_clause,[],[f70441,f66975,f22095,f71168])).
% 92.92/13.70 thf(f71168,plain,(
% 92.92/13.70 spl854_752 <=> (c_2Edivides_2Edivides = c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_752])])).
% 92.92/13.70 thf(f70441,plain,(
% 92.92/13.70 (c_2Edivides_2Edivides != c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum)) | (~spl854_40 | spl854_691)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f70428])).
% 92.92/13.70 thf(f70428,plain,(
% 92.92/13.70 ($true != $true) | (c_2Edivides_2Edivides != c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum)) | (~spl854_40 | spl854_691)),
% 92.92/13.70 inference(constrained_superposition,[],[f66977,f22096])).
% 92.92/13.70 thf(f71166,plain,(
% 92.92/13.70 spl854_751),
% 92.92/13.70 inference(avatar_split_clause,[],[f15880,f71164])).
% 92.92/13.70 thf(f71164,plain,(
% 92.92/13.70 spl854_751 <=> ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_751])])).
% 92.92/13.70 thf(f15880,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.70 inference(equality_resolution,[],[f14594])).
% 92.92/13.70 thf(f14594,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X1) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10692,f9122,f9122])).
% 92.92/13.70 thf(f10692,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | (c_2Enum_2E0 != X1) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7303])).
% 92.92/13.70 thf(f7303,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0)) | ((($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK320,X1),X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK320,X1),X0)) = X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) & (c_2Enum_2E0 = X1)))) & (! [X3 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3) != X1)) & (($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | (c_2Enum_2E0 != X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK320])],[f7301,f7302])).
% 92.92/13.70 thf(f7302,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : ((($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) = X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) & (c_2Enum_2E0 = X1))) => ((($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK320,X1),X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum),sK320,X1),X0)) = X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) & (c_2Enum_2E0 = X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7301,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0)) | ? [X2 : tyop_2Enum_2Enum] : ((($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) = X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) & (c_2Enum_2E0 = X1)))) & (! [X3 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3) != X1)) & (($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | (c_2Enum_2E0 != X1))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f7300])).
% 92.92/13.70 thf(f7300,plain,(
% 92.92/13.70 ! [X1 : tyop_2Enum_2Enum > $o,X0 : tyop_2Enum_2Enum] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)) | ? [X2 : tyop_2Enum_2Enum] : ((($true != vAPP(tyop_2Enum_2Enum,$o,X1,X2)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) = X0)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X1,c_2Enum_2E0)) & (c_2Enum_2E0 = X0)))) & (! [X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X1,X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) != X0)) & (($true = vAPP(tyop_2Enum_2Enum,$o,X1,c_2Enum_2E0)) | (c_2Enum_2E0 != X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6407])).
% 92.92/13.70 thf(f6407,plain,(
% 92.92/13.70 ! [X1 : tyop_2Enum_2Enum > $o,X0 : tyop_2Enum_2Enum] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)) <=> ! [X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X1,X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) != X0)) & (($true = vAPP(tyop_2Enum_2Enum,$o,X1,c_2Enum_2E0)) | (c_2Enum_2E0 != X0))))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f71162,plain,(
% 92.92/13.70 spl854_750),
% 92.92/13.70 inference(avatar_split_clause,[],[f13811,f71160])).
% 92.92/13.70 thf(f71160,plain,(
% 92.92/13.70 spl854_750 <=> ! [X0 : $tType,X4 : X0,X5 : tyop_2Enum_2Enum > X0] : (vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X4),X5) = X4)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_750])])).
% 92.92/13.70 thf(f13811,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X4 : X0,X5 : tyop_2Enum_2Enum > X0] : ((vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X4),X5) = X4)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9506,f9122])).
% 92.92/13.70 thf(f9506,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X4 : X0,X5 : tyop_2Enum_2Enum > X0] : ((vAPP(sTfun(tyop_2Enum_2Enum,X0),X0,vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0),vAPP(tyop_2Enum_2Enum,sTfun(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),X0)),c_2Earithmetic_2Enum__CASE(X0),c_2Enum_2E0),X4),X5) = X4)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4943])).
% 92.92/13.70 thf(f71158,plain,(
% 92.92/13.70 spl854_749),
% 92.92/13.70 inference(avatar_split_clause,[],[f12832,f71156])).
% 92.92/13.70 thf(f71156,plain,(
% 92.92/13.70 spl854_749 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X5 : X0,X2 : X0 > X1 > X0] : ((vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X5),X3) = X5) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_749])])).
% 92.92/13.70 thf(f12832,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > X0,X3 : X1,X5 : X0] : ((vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X5),X3) = X5) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8683])).
% 92.92/13.70 thf(f8683,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X0,X3 : X1] : ((($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3)) | (vAPP(sTfun(X0,sTfun(X1,X0)),X0,vAPP(X1,sTfun(sTfun(X0,sTfun(X1,X0)),X0),sK701(X0,X1),X3),X2) != vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,vAPP(sTfun(X0,sTfun(X1,X0)),X0,vAPP(X1,sTfun(sTfun(X0,sTfun(X1,X0)),X0),sK701(X0,X1),X3),X2)),X3))) & (! [X5 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X5),X3) = X5) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK701])],[f8681,f8682])).
% 92.92/13.70 thf(f8682,plain,(
% 92.92/13.70 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > X0,X3 : X1] : (? [X4 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X4),X3) != X4) => (vAPP(sTfun(X0,sTfun(X1,X0)),X0,vAPP(X1,sTfun(sTfun(X0,sTfun(X1,X0)),X0),sK701(X0,X1),X3),X2) != vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,vAPP(sTfun(X0,sTfun(X1,X0)),X0,vAPP(X1,sTfun(sTfun(X0,sTfun(X1,X0)),X0),sK701(X0,X1),X3),X2)),X3)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8681,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X0,X3 : X1] : ((($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3)) | ? [X4 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X4),X3) != X4)) & (! [X5 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X5),X3) = X5) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3))))),
% 92.92/13.70 inference(rectify,[],[f8680])).
% 92.92/13.70 thf(f8680,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X0,X3 : X1] : ((($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3)) | ? [X4 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X4),X3) != X4)) & (! [X4 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X4),X3) = X4) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4466])).
% 92.92/13.70 thf(f4466,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X0,X3 : X1] : (($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3)) <=> ! [X4 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X4),X3) = X4))),
% 92.92/13.70 inference(fool_elimination,[],[f4465])).
% 92.92/13.70 thf(f4465,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X0,X3 : X1] : (vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,X0)),sTfun(X1,$o),c_2Ecombin_2ERIGHT__ID(X0,X1),X2),X3) <=> ! [X4 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),X2,X4),X3) = X4))),
% 92.92/13.70 inference(rectify,[],[f325])).
% 92.92/13.70 thf(f325,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X3 : X0 > X5 > X0,X117 : X5] : (vAPP(X5,$o,vAPP(sTfun(X0,sTfun(X5,X0)),sTfun(X5,$o),c_2Ecombin_2ERIGHT__ID(X0,X5),X3),X117) <=> ! [X19 : X0] : (vAPP(X5,X0,vAPP(X0,sTfun(X5,X0),X3,X19),X117) = X19))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2ERIGHT__ID__DEF)).
% 92.92/13.70 thf(f71154,plain,(
% 92.92/13.70 spl854_748),
% 92.92/13.70 inference(avatar_split_clause,[],[f12830,f71152])).
% 92.92/13.70 thf(f71152,plain,(
% 92.92/13.70 spl854_748 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X5 : X1,X2 : X0 > X1 > X1] : ((vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X5) = X5) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_748])])).
% 92.92/13.70 thf(f12830,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > X1,X3 : X0,X5 : X1] : ((vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X5) = X5) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8679])).
% 92.92/13.70 thf(f8679,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3)) | (vAPP(sTfun(X0,sTfun(X1,X1)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,X1)),X1),sK700(X0,X1),X3),X2) != vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),vAPP(sTfun(X0,sTfun(X1,X1)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,X1)),X1),sK700(X0,X1),X3),X2)))) & (! [X5 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X5) = X5) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK700])],[f8677,f8678])).
% 92.92/13.70 thf(f8678,plain,(
% 92.92/13.70 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > X1,X3 : X0] : (? [X4 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4) != X4) => (vAPP(sTfun(X0,sTfun(X1,X1)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,X1)),X1),sK700(X0,X1),X3),X2) != vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),vAPP(sTfun(X0,sTfun(X1,X1)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,X1)),X1),sK700(X0,X1),X3),X2))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8677,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3)) | ? [X4 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4) != X4)) & (! [X5 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X5) = X5) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3))))),
% 92.92/13.70 inference(rectify,[],[f8676])).
% 92.92/13.70 thf(f8676,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3)) | ? [X4 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4) != X4)) & (! [X4 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4) = X4) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4464])).
% 92.92/13.70 thf(f4464,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3)) <=> ! [X4 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4) = X4))),
% 92.92/13.70 inference(fool_elimination,[],[f4463])).
% 92.92/13.70 thf(f4463,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > X1,X3 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,X1)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X1),X2),X3) <=> ! [X4 : X1] : (vAPP(X1,X1,vAPP(X0,sTfun(X1,X1),X2,X3),X4) = X4))),
% 92.92/13.70 inference(rectify,[],[f326])).
% 92.92/13.70 thf(f326,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X3 : X0 > X5 > X5,X117 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X5,X5)),sTfun(X0,$o),c_2Ecombin_2ELEFT__ID(X0,X5),X3),X117) <=> ! [X19 : X5] : (vAPP(X5,X5,vAPP(X0,sTfun(X5,X5),X3,X117),X19) = X19))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2ELEFT__ID__DEF)).
% 92.92/13.70 thf(f71150,plain,(
% 92.92/13.70 spl854_747),
% 92.92/13.70 inference(avatar_split_clause,[],[f12829,f71148])).
% 92.92/13.70 thf(f71148,plain,(
% 92.92/13.70 spl854_747 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X0,X2 : X0 > X1 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_747])])).
% 92.92/13.70 thf(f12829,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8675])).
% 92.92/13.70 thf(f8675,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3)) | ! [X4 : X1] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) & (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),vAPP(sTfun(X0,sTfun(X1,$o)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,$o)),X1),sK699(X0,X1),X3),X2))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK699])],[f8673,f8674])).
% 92.92/13.70 thf(f8674,plain,(
% 92.92/13.70 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0] : (? [X5 : X1] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5)) => ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),vAPP(sTfun(X0,sTfun(X1,$o)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,$o)),X1),sK699(X0,X1),X3),X2))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8673,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3)) | ! [X4 : X1] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) & (? [X5 : X1] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X5)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3))))),
% 92.92/13.70 inference(rectify,[],[f8672])).
% 92.92/13.70 thf(f8672,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3)) | ! [X4 : X1] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) & (? [X4 : X1] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4462])).
% 92.92/13.70 thf(f4462,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3)) <=> ? [X4 : X1] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 92.92/13.70 inference(fool_elimination,[],[f4461])).
% 92.92/13.70 thf(f4461,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X1),X2),X3) <=> ? [X4 : X1] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))),
% 92.92/13.70 inference(rectify,[],[f448])).
% 92.92/13.70 thf(f448,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X143 : X0 > X5 > $o,X4 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(X0,$o),c_2Erelation_2ERDOM(X0,X5),X143),X4) <=> ? [X12 : X5] : vAPP(X5,$o,vAPP(X0,sTfun(X5,$o),X143,X4),X12))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERDOM__DEF)).
% 92.92/13.70 thf(f71146,plain,(
% 92.92/13.70 spl854_746),
% 92.92/13.70 inference(avatar_split_clause,[],[f12827,f71144])).
% 92.92/13.70 thf(f71144,plain,(
% 92.92/13.70 spl854_746 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_746])])).
% 92.92/13.70 thf(f12827,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X1,X4 : X0] : (($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8671])).
% 92.92/13.70 thf(f8671,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X1] : ((($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3)) | ! [X4 : X0] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3))) & (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,vAPP(X1,sTfun(sTfun(X0,sTfun(X1,$o)),X0),sK698(X0,X1),X3),X2)),X3)) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK698])],[f8669,f8670])).
% 92.92/13.70 thf(f8670,plain,(
% 92.92/13.70 ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X1] : (? [X5 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X3)) => ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,vAPP(X1,sTfun(sTfun(X0,sTfun(X1,$o)),X0),sK698(X0,X1),X3),X2)),X3)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8669,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X1] : ((($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3)) | ! [X4 : X0] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3))) & (? [X5 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X5),X3)) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3))))),
% 92.92/13.70 inference(rectify,[],[f8668])).
% 92.92/13.70 thf(f8668,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X1] : ((($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3)) | ! [X4 : X0] : ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3))) & (? [X4 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3)) | ($true != vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4460])).
% 92.92/13.70 thf(f4460,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X1] : (($true = vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3)) <=> ? [X4 : X0] : ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3)))),
% 92.92/13.70 inference(fool_elimination,[],[f4459])).
% 92.92/13.70 thf(f4459,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X1] : (vAPP(X1,$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X1,$o),c_2Erelation_2ERRANGE(X0,X1),X2),X3) <=> ? [X4 : X0] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X4),X3))),
% 92.92/13.70 inference(rectify,[],[f449])).
% 92.92/13.70 thf(f449,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X143 : X0 > X5 > $o,X18 : X5] : (vAPP(X5,$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(X5,$o),c_2Erelation_2ERRANGE(X0,X5),X143),X18) <=> ? [X19 : X0] : vAPP(X5,$o,vAPP(X0,sTfun(X5,$o),X143,X19),X18))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERRANGE)).
% 92.92/13.70 thf(f71142,plain,(
% 92.92/13.70 spl854_745),
% 92.92/13.70 inference(avatar_split_clause,[],[f12712,f71140])).
% 92.92/13.70 thf(f12712,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1] : (($true = vAPP(sTfun(X1,X0),$o,sP95(X0,X1),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8571])).
% 92.92/13.70 thf(f71138,plain,(
% 92.92/13.70 spl854_744),
% 92.92/13.70 inference(avatar_split_clause,[],[f12711,f71136])).
% 92.92/13.70 thf(f12711,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X0 > X1] : (($true = vAPP(sTfun(X1,X0),$o,sP94(X0,X1),X2)) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X1,X0),$o),c_2Eind__type_2EISO(X0,X1),X3),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8571])).
% 92.92/13.70 thf(f71134,plain,(
% 92.92/13.70 spl854_743),
% 92.92/13.70 inference(avatar_split_clause,[],[f12066,f71132])).
% 92.92/13.70 thf(f71132,plain,(
% 92.92/13.70 spl854_743 <=> ! [X0 : $tType,X4 : X0,X2 : $o,X1 : X0 > $o] : (($true = X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK579(X0),X2),X1))) | ($true = vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_743])])).
% 92.92/13.70 thf(f12066,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X4 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK579(X0),X2),X1))) | ($true = vAPP(X0,$o,X1,X4))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8187])).
% 92.92/13.70 thf(f8187,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK579(X0),X2),X1)))) | (($true != X2) & ! [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & (($true = X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK580(X0),X1))) | ! [X6 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK579,sK580])],[f8184,f8186,f8185])).
% 92.92/13.70 thf(f8185,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) => (($true = X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK579(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8186,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK580(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8184,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((? [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ! [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & (($true = X2) | ? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)) | ! [X6 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(rectify,[],[f8183])).
% 92.92/13.70 thf(f8183,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((? [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ! [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & (($true = X2) | ? [X4 : X0] : ($true != vAPP(X0,$o,X1,X4)) | ! [X3 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(flattening,[],[f8182])).
% 92.92/13.70 thf(f8182,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((? [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ! [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & ((($true = X2) | ? [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) | ! [X3 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6059])).
% 92.92/13.70 thf(f6059,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) <=> (($true = X2) | ? [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))))),
% 92.92/13.70 inference(ennf_transformation,[],[f4020])).
% 92.92/13.70 thf(f4020,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = X2)) <=> (! [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)) => ($true = X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f4019])).
% 92.92/13.70 thf(f4019,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (vAPP(X0,$o,X1,X3) => X2) <=> (! [X4 : X0] : vAPP(X0,$o,X1,X4) => X2))),
% 92.92/13.70 inference(rectify,[],[f106])).
% 92.92/13.70 thf(f106,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : (? [X19 : X0] : (vAPP(X0,$o,X7,X19) => X41) <=> (! [X15 : X0] : vAPP(X0,$o,X7,X15) => X41))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__IMP__THM)).
% 92.92/13.70 thf(f71130,plain,(
% 92.92/13.70 spl854_742),
% 92.92/13.70 inference(avatar_split_clause,[],[f12017,f71128])).
% 92.92/13.70 thf(f71128,plain,(
% 92.92/13.70 spl854_742 <=> ! [X0 : $tType,X5 : X0,X2 : $o,X1 : X0 > $o] : (($true = X2) | ($true != vAPP(X0,$o,X1,X5)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK548(X0),X2),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_742])])).
% 92.92/13.70 thf(f12017,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X5 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X5)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK548(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8111])).
% 92.92/13.70 thf(f8111,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((! [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK547(X0),X1))))) & (($true = X2) | ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)) | (($true != X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK548(X0),X2),X1))))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK547,sK548])],[f8108,f8110,f8109])).
% 92.92/13.70 thf(f8109,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK547(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8110,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X6 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X6))) => (($true != X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK548(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8108,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((! [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & (($true = X2) | ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5)) | ? [X6 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(rectify,[],[f8107])).
% 92.92/13.70 thf(f8107,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((! [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & (($true = X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4)) | ? [X3 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(flattening,[],[f8106])).
% 92.92/13.70 thf(f8106,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((! [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) | (($true != X2) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)))) & ((($true = X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) | ? [X3 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6056])).
% 92.92/13.70 thf(f6056,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (! [X3 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3))) <=> (($true = X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))))),
% 92.92/13.70 inference(ennf_transformation,[],[f3990])).
% 92.92/13.70 thf(f3990,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = X2)) <=> (? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4)) => ($true = X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f3989])).
% 92.92/13.70 thf(f3989,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) => X2) <=> (? [X4 : X0] : vAPP(X0,$o,X1,X4) => X2))),
% 92.92/13.70 inference(rectify,[],[f103])).
% 92.92/13.70 thf(f103,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : (! [X19 : X0] : (vAPP(X0,$o,X7,X19) => X41) <=> (? [X15 : X0] : vAPP(X0,$o,X7,X15) => X41))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__IMP__THM)).
% 92.92/13.70 thf(f71126,plain,(
% 92.92/13.70 spl854_741),
% 92.92/13.70 inference(avatar_split_clause,[],[f11848,f71124])).
% 92.92/13.70 thf(f71124,plain,(
% 92.92/13.70 spl854_741 <=> ! [X0 : $tType,X6 : X0,X2 : $o,X1 : X0 > $o] : (($true = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK530(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X6)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_741])])).
% 92.92/13.70 thf(f11848,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X6 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK530(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X6))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7996])).
% 92.92/13.70 thf(f7996,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((($true = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK529(X0),X1))) | ! [X4 : X0] : (($true != X2) & ($true != vAPP(X0,$o,X1,X4)))) & ((($true = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK530(X0),X2),X1)))) | (($true != X2) & ! [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK529,sK530])],[f7993,f7995,f7994])).
% 92.92/13.70 thf(f7994,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK529(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7995,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X5 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,X5))) => (($true = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK530(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7993,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((($true = X2) | ? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) | ! [X4 : X0] : (($true != X2) & ($true != vAPP(X0,$o,X1,X4)))) & (? [X5 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,X5))) | (($true != X2) & ! [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(rectify,[],[f7992])).
% 92.92/13.70 thf(f7992,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((($true = X2) | ? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) | ! [X4 : X0] : (($true != X2) & ($true != vAPP(X0,$o,X1,X4)))) & (? [X4 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,X4))) | (($true != X2) & ! [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(flattening,[],[f7991])).
% 92.92/13.70 thf(f7991,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) | ? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) | ! [X4 : X0] : (($true != X2) & ($true != vAPP(X0,$o,X1,X4)))) & (? [X4 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,X4))) | (($true != X2) & ! [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3950])).
% 92.92/13.70 thf(f3950,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((($true = X2) | ? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) <=> ? [X4 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,X4))))),
% 92.92/13.70 inference(fool_elimination,[],[f3949])).
% 92.92/13.70 thf(f3949,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((X2 | ? [X3 : X0] : vAPP(X0,$o,X1,X3)) <=> ? [X4 : X0] : (X2 | vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 inference(rectify,[],[f94])).
% 92.92/13.70 thf(f94,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : ((X41 | ? [X19 : X0] : vAPP(X0,$o,X7,X19)) <=> ? [X15 : X0] : (X41 | vAPP(X0,$o,X7,X15)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__EXISTS__THM)).
% 92.92/13.70 thf(f71122,plain,(
% 92.92/13.70 spl854_740),
% 92.92/13.70 inference(avatar_split_clause,[],[f11666,f71120])).
% 92.92/13.70 thf(f71120,plain,(
% 92.92/13.70 spl854_740 <=> ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),X2)) = X2) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_740])])).
% 92.92/13.70 thf(f11666,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),X2)) = X2) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5981])).
% 92.92/13.70 thf(f5981,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),X2)) = X2) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2)))),
% 92.92/13.70 inference(ennf_transformation,[],[f3816])).
% 92.92/13.70 thf(f3816,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2)) => (vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),X2)) = X2))),
% 92.92/13.70 inference(fool_elimination,[],[f3815])).
% 92.92/13.70 thf(f3815,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2) => (vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),X2)) = X2))),
% 92.92/13.70 inference(rectify,[],[f684])).
% 92.92/13.70 thf(f684,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X8 : tyop_2Esum_2Esum(X0,X5)] : (vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISL(X0,X5),X8) => (vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),vAPP(tyop_2Esum_2Esum(X0,X5),X0,c_2Esum_2EOUTL(X0,X5),X8)) = X8))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EINL)).
% 92.92/13.70 thf(f71118,plain,(
% 92.92/13.70 spl854_739),
% 92.92/13.70 inference(avatar_split_clause,[],[f11665,f71116])).
% 92.92/13.70 thf(f71116,plain,(
% 92.92/13.70 spl854_739 <=> ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),X2)) = X2) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_739])])).
% 92.92/13.70 thf(f11665,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),X2)) = X2) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5980])).
% 92.92/13.70 thf(f5980,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : ((vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),X2)) = X2) | ($true != vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2)))),
% 92.92/13.70 inference(ennf_transformation,[],[f3814])).
% 92.92/13.70 thf(f3814,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2)) => (vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),X2)) = X2))),
% 92.92/13.70 inference(fool_elimination,[],[f3813])).
% 92.92/13.70 thf(f3813,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2) => (vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),X2)) = X2))),
% 92.92/13.70 inference(rectify,[],[f685])).
% 92.92/13.70 thf(f685,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType,X8 : tyop_2Esum_2Esum(X0,X5)] : (vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISR(X0,X5),X8) => (vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),vAPP(tyop_2Esum_2Esum(X0,X5),X5,c_2Esum_2EOUTR(X0,X5),X8)) = X8))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EINR)).
% 92.92/13.70 thf(f71114,plain,(
% 92.92/13.70 spl854_738),
% 92.92/13.70 inference(avatar_split_clause,[],[f11430,f71112])).
% 92.92/13.70 thf(f71112,plain,(
% 92.92/13.70 spl854_738 <=> ! [X0 : $tType,X11 : X0,X2 : $o,X1 : X0 > $o] : (($true = X2) | ($true != vAPP(X0,$o,X1,X11)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK394(X0),X2),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_738])])).
% 92.92/13.70 thf(f11430,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X11 : X0,X1 : X0 > $o] : (($true = X2) | ($true != vAPP(X0,$o,X1,X11)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK394(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7704])).
% 92.92/13.70 thf(f7704,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK390(X0),X1))) & ($true = X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK391(X0),X2),X1))) & ($true = X2)) | ! [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)) | ($true != X2)) & ((($true = X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK392(X0),X1)))) | ! [X8 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X8)))) & ((($true = X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK393(X0),X2),X1)))) | ($true != X2) | ! [X10 : X0] : ($true != vAPP(X0,$o,X1,X10))) & (($true = X2) | ! [X11 : X0] : ($true != vAPP(X0,$o,X1,X11)) | (($true != X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK394(X0),X2),X1))))) & (! [X13 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X13))) | (($true != X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK395(X0),X1))))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK390,sK391,sK392,sK393,sK394,sK395])],[f7697,f7703,f7702,f7701,f7700,f7699,f7698])).
% 92.92/13.70 thf(f7698,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK390(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7699,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) & ($true = X2)) => (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK391(X0),X2),X1))) & ($true = X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7700,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK392(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7701,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X9 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X9))) => (($true = X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK393(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7702,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X12 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X12))) => (($true != X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK394(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7703,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X14 : X0] : ($true = vAPP(X0,$o,X1,X14)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK395(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7697,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & (? [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) & ($true = X2)) | ! [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)) | ($true != X2)) & ((($true = X2) & ? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) | ! [X8 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X8)))) & (? [X9 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X9))) | ($true != X2) | ! [X10 : X0] : ($true != vAPP(X0,$o,X1,X10))) & (($true = X2) | ! [X11 : X0] : ($true != vAPP(X0,$o,X1,X11)) | ? [X12 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X12)))) & (! [X13 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X13))) | (($true != X2) & ? [X14 : X0] : ($true = vAPP(X0,$o,X1,X14)))))),
% 92.92/13.70 inference(rectify,[],[f7696])).
% 92.92/13.70 thf(f7696,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & (? [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2)) | ! [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)) | ($true != X2)) & ((($true = X2) & ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ! [X6 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X6)))) & (? [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6))) | ($true != X2) | ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5))) & (($true = X2) | ! [X7 : X0] : ($true != vAPP(X0,$o,X1,X7)) | ? [X8 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X8)))) & (! [X8 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X8))) | (($true != X2) & ? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)))))),
% 92.92/13.70 inference(flattening,[],[f7695])).
% 92.92/13.70 thf(f7695,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((((? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & (? [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2)) | (! [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)) | ($true != X2)))) & (((($true = X2) & ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ! [X6 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X6)))) & (? [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6))) | (($true != X2) | ! [X5 : X0] : ($true != vAPP(X0,$o,X1,X5))))) & (((($true = X2) | ! [X7 : X0] : ($true != vAPP(X0,$o,X1,X7))) | ? [X8 : X0] : (($true != X2) & ($true = vAPP(X0,$o,X1,X8)))) & (! [X8 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X8))) | (($true != X2) & ? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5826])).
% 92.92/13.70 thf(f5826,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) <=> ? [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2))) & ((($true = X2) & ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) <=> ? [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6)))) & ((($true = X2) | ! [X7 : X0] : ($true != vAPP(X0,$o,X1,X7))) <=> ! [X8 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X8)))))),
% 92.92/13.70 inference(ennf_transformation,[],[f3630])).
% 92.92/13.70 thf(f3630,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) <=> ? [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2))) & ((($true = X2) & ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) <=> ? [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6)))) & ((? [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) => ($true = X2)) <=> ! [X8 : X0] : (($true = vAPP(X0,$o,X1,X8)) => ($true = X2))))),
% 92.92/13.70 inference(fool_elimination,[],[f3629])).
% 92.92/13.70 thf(f3629,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((? [X3 : X0] : vAPP(X0,$o,X1,X3) & X2) <=> ? [X4 : X0] : (vAPP(X0,$o,X1,X4) & X2)) & ((X2 & ? [X5 : X0] : vAPP(X0,$o,X1,X5)) <=> ? [X6 : X0] : (X2 & vAPP(X0,$o,X1,X6))) & ((? [X7 : X0] : vAPP(X0,$o,X1,X7) => X2) <=> ! [X8 : X0] : (vAPP(X0,$o,X1,X8) => X2)))),
% 92.92/13.70 inference(rectify,[],[f194])).
% 92.92/13.70 thf(f194,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : (((? [X33 : X0] : vAPP(X0,$o,X7,X33) & X41) <=> ? [X93 : X0] : (vAPP(X0,$o,X7,X93) & X41)) & ((X41 & ? [X23 : X0] : vAPP(X0,$o,X7,X23)) <=> ? [X92 : X0] : (X41 & vAPP(X0,$o,X7,X92))) & ((? [X19 : X0] : vAPP(X0,$o,X7,X19) => X41) <=> ! [X15 : X0] : (vAPP(X0,$o,X7,X15) => X41)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EPULL__EXISTS)).
% 92.92/13.70 thf(f71110,plain,(
% 92.92/13.70 spl854_737),
% 92.92/13.70 inference(avatar_split_clause,[],[f10309,f71108])).
% 92.92/13.70 thf(f71108,plain,(
% 92.92/13.70 spl854_737 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_737])])).
% 92.92/13.70 thf(f10309,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5684])).
% 92.92/13.70 thf(f5684,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)))),
% 92.92/13.70 inference(ennf_transformation,[],[f2806])).
% 92.92/13.70 thf(f2806,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1) = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2805])).
% 92.92/13.70 thf(f2805,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1) = X1))),
% 92.92/13.70 inference(rectify,[],[f515])).
% 92.92/13.70 thf(f515,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X143) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X143) = X143))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Etransitive__TC__identity)).
% 92.92/13.70 thf(f71106,plain,(
% 92.92/13.70 spl854_736),
% 92.92/13.70 inference(avatar_split_clause,[],[f10307,f71104])).
% 92.92/13.70 thf(f71104,plain,(
% 92.92/13.70 spl854_736 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_736])])).
% 92.92/13.70 thf(f10307,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5682])).
% 92.92/13.70 thf(f5682,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.92/13.70 inference(ennf_transformation,[],[f2802])).
% 92.92/13.70 thf(f2802,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1) = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2801])).
% 92.92/13.70 thf(f2801,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1) = X1))),
% 92.92/13.70 inference(rectify,[],[f513])).
% 92.92/13.70 thf(f513,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X143) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143) = X143))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ereflexive__RC__identity)).
% 92.92/13.70 thf(f71102,plain,(
% 92.92/13.70 spl854_735),
% 92.92/13.70 inference(avatar_split_clause,[],[f10304,f71100])).
% 92.92/13.70 thf(f71100,plain,(
% 92.92/13.70 spl854_735 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_735])])).
% 92.92/13.70 thf(f10304,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5679])).
% 92.92/13.70 thf(f5679,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1) = X1) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)))),
% 92.92/13.70 inference(ennf_transformation,[],[f2796])).
% 92.92/13.70 thf(f2796,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1) = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2795])).
% 92.92/13.70 thf(f2795,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1) = X1))),
% 92.92/13.70 inference(rectify,[],[f514])).
% 92.92/13.70 thf(f514,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X143) => (vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X143) = X143))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Esymmetric__SC__identity)).
% 92.92/13.70 thf(f71098,plain,(
% 92.92/13.70 spl854_734),
% 92.92/13.70 inference(avatar_split_clause,[],[f9985,f71096])).
% 92.92/13.70 thf(f71096,plain,(
% 92.92/13.70 spl854_734 <=> ! [X0 : $tType,X1 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0)),X1)) = X1)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_734])])).
% 92.92/13.70 thf(f9985,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0)),X1)) = X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f2564])).
% 92.92/13.70 thf(f2564,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0)),X1)) = X1)),
% 92.92/13.70 inference(fool_elimination,[],[f2563])).
% 92.92/13.70 thf(f2563,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),(^[X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X1)))) = X1)),
% 92.92/13.70 inference(rectify,[],[f84])).
% 92.92/13.70 thf(f84,axiom,(
% 92.92/13.70 ! [X0 : $tType,X8 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),(^[X18 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X18),X8)))) = X8)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESELECT__REFL)).
% 92.92/13.70 thf(f71094,plain,(
% 92.92/13.70 spl854_733),
% 92.92/13.70 inference(avatar_split_clause,[],[f9488,f71092])).
% 92.92/13.70 thf(f71092,plain,(
% 92.92/13.70 spl854_733 <=> ! [X0 : $tType,X2 : tyop_2Eoption_2Eoption(X0),X1 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)),X2))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_733])])).
% 92.92/13.70 thf(f9488,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : tyop_2Eoption_2Eoption(X0),X1 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__CHOICE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4935])).
% 92.92/13.70 thf(f71090,plain,(
% 92.92/13.70 spl854_732),
% 92.92/13.70 inference(avatar_split_clause,[],[f9483,f71088])).
% 92.92/13.70 thf(f71088,plain,(
% 92.92/13.70 spl854_732 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > tyop_2Enum_2Enum] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(X0,tyop_2Enum_2Enum,X1,X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_732])])).
% 92.92/13.70 thf(f9483,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0 > tyop_2Enum_2Enum] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum,vAPP(sTfun(X0,tyop_2Enum_2Enum),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Enum_2Enum),c_2EbasicSize_2Eoption__size(X0),X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(X0,tyop_2Enum_2Enum,X1,X2)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4933])).
% 92.92/13.70 thf(f71086,plain,(
% 92.92/13.70 spl854_731 | ~spl854_44 | ~spl854_727),
% 92.92/13.70 inference(avatar_split_clause,[],[f70903,f68750,f22112,f71084])).
% 92.92/13.70 thf(f71084,plain,(
% 92.92/13.70 spl854_731 <=> ! [X0 : $o] : (($true = X0) | (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_731])])).
% 92.92/13.70 thf(f68750,plain,(
% 92.92/13.70 spl854_727 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) | ($true = X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_727])])).
% 92.92/13.70 thf(f70903,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true = X0) | (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),X0))) ) | (~spl854_44 | ~spl854_727)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f70792])).
% 92.92/13.70 thf(f70792,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true = $false) | ($true = X0) | (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),X0))) ) | (~spl854_44 | ~spl854_727)),
% 92.92/13.70 inference(constrained_superposition,[],[f68751,f22114])).
% 92.92/13.70 thf(f68751,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) | ($true = X1)) ) | ~spl854_727),
% 92.92/13.70 inference(avatar_component_clause,[],[f68750])).
% 92.92/13.70 thf(f68825,plain,(
% 92.92/13.70 ~spl854_730 | ~spl854_40 | spl854_680),
% 92.92/13.70 inference(avatar_split_clause,[],[f68732,f66930,f22095,f68822])).
% 92.92/13.70 thf(f68822,plain,(
% 92.92/13.70 spl854_730 <=> (c_2Earithmetic_2E_3E_3D = c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_730])])).
% 92.92/13.70 thf(f68732,plain,(
% 92.92/13.70 (c_2Earithmetic_2E_3E_3D != c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum)) | (~spl854_40 | spl854_680)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f68719])).
% 92.92/13.70 thf(f68719,plain,(
% 92.92/13.70 ($true != $true) | (c_2Earithmetic_2E_3E_3D != c_2Erelation_2EEMPTY__REL(tyop_2Enum_2Enum)) | (~spl854_40 | spl854_680)),
% 92.92/13.70 inference(constrained_superposition,[],[f66932,f22096])).
% 92.92/13.70 thf(f68761,plain,(
% 92.92/13.70 spl854_729 | ~spl854_9 | ~spl854_160),
% 92.92/13.70 inference(avatar_split_clause,[],[f34159,f22950,f21928,f68759])).
% 92.92/13.70 thf(f68759,plain,(
% 92.92/13.70 spl854_729 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_729])])).
% 92.92/13.70 thf(f34159,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0)))) ) | (~spl854_9 | ~spl854_160)),
% 92.92/13.70 inference(forward_demodulation,[],[f18663,f29755])).
% 92.92/13.70 thf(f18663,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0)))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14066,f13567])).
% 92.92/13.70 thf(f14066,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9834,f13512])).
% 92.92/13.70 thf(f9834,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f2508])).
% 92.92/13.70 thf(f2508,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0)))),
% 92.92/13.70 inference(fool_elimination,[],[f2507])).
% 92.92/13.70 thf(f2507,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0))),
% 92.92/13.70 inference(rectify,[],[f1749])).
% 92.92/13.70 thf(f1749,axiom,(
% 92.92/13.70 ! [X35 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X35),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X35))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__B)).
% 92.92/13.70 thf(f68757,plain,(
% 92.92/13.70 spl854_728),
% 92.92/13.70 inference(avatar_split_clause,[],[f21827,f68754])).
% 92.92/13.70 thf(f68754,plain,(
% 92.92/13.70 spl854_728 <=> ($true = vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),vAPP($o,sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)),cCOMB,c_2Emin_2E_3D_3D_3E),$false)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_728])])).
% 92.92/13.70 thf(f21827,plain,(
% 92.92/13.70 ($true = vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),vAPP($o,sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)),cCOMB,c_2Emin_2E_3D_3D_3E),$false)))),
% 92.92/13.70 inference(forward_demodulation,[],[f15643,f17793])).
% 92.92/13.70 thf(f15643,plain,(
% 92.92/13.70 ($true = vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),vAPP($o,sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)),cCOMB,c_2Emin_2E_3D_3D_3E),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.70 inference(definition_unfolding,[],[f13499,f13521])).
% 92.92/13.70 thf(f13521,plain,(
% 92.92/13.70 (c_2Ebool_2E_7E = vAPP($o,sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)),cCOMB,c_2Emin_2E_3D_3D_3E),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.70 inference(definition_unfolding,[],[f9136,f13520])).
% 92.92/13.70 thf(f9136,plain,(
% 92.92/13.70 (c_2Ebool_2E_7E = vAPP($o,sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)),cCOMB,c_2Emin_2E_3D_3D_3E),c_2Ebool_2EF))),
% 92.92/13.70 inference(cnf_transformation,[],[f2018])).
% 92.92/13.70 thf(f2018,plain,(
% 92.92/13.70 (c_2Ebool_2E_7E = vAPP($o,sTfun($o,$o),vAPP(sTfun($o,sTfun($o,$o)),sTfun($o,sTfun($o,$o)),cCOMB,c_2Emin_2E_3D_3D_3E),c_2Ebool_2EF))),
% 92.92/13.70 inference(fool_elimination,[],[f2017])).
% 92.92/13.70 thf(f2017,plain,(
% 92.92/13.70 (c_2Ebool_2E_7E = (^[X0 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),c_2Ebool_2EF))))),
% 92.92/13.70 inference(rectify,[],[f25])).
% 92.92/13.70 thf(f25,axiom,(
% 92.92/13.70 (c_2Ebool_2E_7E = (^[X6 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X6),c_2Ebool_2EF))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__DEF)).
% 92.92/13.70 thf(f13499,plain,(
% 92.92/13.70 (vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),c_2Ebool_2E_7E) = $true)),
% 92.92/13.70 inference(cnf_transformation,[],[f4810])).
% 92.92/13.70 thf(f4810,plain,(
% 92.92/13.70 (vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),c_2Ebool_2E_7E) = $true)),
% 92.92/13.70 inference(fool_elimination,[],[f4809])).
% 92.92/13.70 thf(f4809,plain,(
% 92.92/13.70 vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),c_2Ebool_2E_7E)),
% 92.92/13.70 inference(rectify,[],[f598])).
% 92.92/13.70 thf(f598,axiom,(
% 92.92/13.70 vAPP(sTfun($o,$o),$o,c_2Erelation_2EINVOL($o),c_2Ebool_2E_7E)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ENOT__INVOL)).
% 92.92/13.70 thf(f68752,plain,(
% 92.92/13.70 spl854_727),
% 92.92/13.70 inference(avatar_split_clause,[],[f17130,f68750])).
% 92.92/13.70 thf(f17130,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) | ($true = X1)) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12280])).
% 92.92/13.70 thf(f12280,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8367])).
% 92.92/13.70 thf(f8367,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) | (($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X2)) & (vAPP($o,$o,vNOT,X1) != $true))) & (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2))))),
% 92.92/13.70 inference(flattening,[],[f8366])).
% 92.92/13.70 thf(f8366,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) | (($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X2)) & (vAPP($o,$o,vNOT,X1) != $true))) & ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X2)) | (vAPP($o,$o,vNOT,X1) = $true)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4168])).
% 92.92/13.70 thf(f4168,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2)) <=> (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X2)) | (vAPP($o,$o,vNOT,X1) = $true)))),
% 92.92/13.70 inference(fool_elimination,[],[f4167])).
% 92.92/13.70 thf(f4167,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X1)),X2) <=> (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X2) | vAPP($o,$o,vNOT,X1)))),
% 92.92/13.70 inference(rectify,[],[f1891])).
% 92.92/13.70 thf(f1891,axiom,(
% 92.92/13.70 ! [X0 : $tType,X8 : $o,X18 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),X8)),X18) <=> (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EUNIV(X0)),X18) | vAPP($o,$o,vNOT,X8)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EK__SUBSET)).
% 92.92/13.70 thf(f68748,plain,(
% 92.92/13.70 spl854_726),
% 92.92/13.70 inference(avatar_split_clause,[],[f16620,f68746])).
% 92.92/13.70 thf(f68746,plain,(
% 92.92/13.70 spl854_726 <=> ! [X1 : $o,X3 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X1),X3),X1),X3))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_726])])).
% 92.92/13.70 thf(f16620,plain,(
% 92.92/13.70 ( ! [X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X1),X3),X1),X3))) )),
% 92.92/13.70 inference(equality_resolution,[],[f16619])).
% 92.92/13.70 thf(f16619,plain,(
% 92.92/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X3),X1),X3)) | (X0 != X1)) )),
% 92.92/13.70 inference(equality_resolution,[],[f12604])).
% 92.92/13.70 thf(f12604,plain,(
% 92.92/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP84,X0),X2),X1),X3)) | (X2 != X3) | (X0 != X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6527])).
% 92.92/13.70 thf(f68744,plain,(
% 92.92/13.70 spl854_725),
% 92.92/13.70 inference(avatar_split_clause,[],[f16545,f68742])).
% 92.92/13.70 thf(f68742,plain,(
% 92.92/13.70 spl854_725 <=> ! [X1 : $o,X3 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X1),X3),X1),X3))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_725])])).
% 92.92/13.70 thf(f16545,plain,(
% 92.92/13.70 ( ! [X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X1),X3),X1),X3))) )),
% 92.92/13.70 inference(equality_resolution,[],[f16544])).
% 92.92/13.70 thf(f16544,plain,(
% 92.92/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X3),X1),X3)) | (X0 != X1)) )),
% 92.92/13.70 inference(equality_resolution,[],[f12532])).
% 92.92/13.70 thf(f12532,plain,(
% 92.92/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP70,X0),X2),X1),X3)) | (X2 != X3) | (X0 != X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6503])).
% 92.92/13.70 thf(f68740,plain,(
% 92.92/13.70 spl854_724),
% 92.92/13.70 inference(avatar_split_clause,[],[f16534,f68738])).
% 92.92/13.70 thf(f68738,plain,(
% 92.92/13.70 spl854_724 <=> ! [X1 : $o,X3 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X1),X3),X1),X3))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_724])])).
% 92.92/13.70 thf(f16534,plain,(
% 92.92/13.70 ( ! [X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X1),X3),X1),X3))) )),
% 92.92/13.70 inference(equality_resolution,[],[f16533])).
% 92.92/13.70 thf(f16533,plain,(
% 92.92/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X3),X1),X3)) | (X0 != X1)) )),
% 92.92/13.70 inference(equality_resolution,[],[f12524])).
% 92.92/13.70 thf(f12524,plain,(
% 92.92/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP69,X0),X2),X1),X3)) | (X2 != X3) | (X0 != X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6501])).
% 92.92/13.70 thf(f68736,plain,(
% 92.92/13.70 spl854_723),
% 92.92/13.70 inference(avatar_split_clause,[],[f16527,f68734])).
% 92.92/13.70 thf(f68734,plain,(
% 92.92/13.70 spl854_723 <=> ! [X1 : $o,X3 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X1),X3),X1),X3))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_723])])).
% 92.92/13.70 thf(f16527,plain,(
% 92.92/13.70 ( ! [X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X1),X3),X1),X3))) )),
% 92.92/13.70 inference(equality_resolution,[],[f16526])).
% 92.92/13.70 thf(f16526,plain,(
% 92.92/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X3),X1),X3)) | (X0 != X1)) )),
% 92.92/13.70 inference(equality_resolution,[],[f12518])).
% 92.92/13.70 thf(f12518,plain,(
% 92.92/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP68,X0),X2),X1),X3)) | (X2 != X3) | (X0 != X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6499])).
% 92.92/13.70 thf(f68718,plain,(
% 92.92/13.70 spl854_722),
% 92.92/13.70 inference(avatar_split_clause,[],[f16518,f68716])).
% 92.92/13.70 thf(f68716,plain,(
% 92.92/13.70 spl854_722 <=> ! [X1 : $o,X3 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X1),X3),X1),X3))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_722])])).
% 92.92/13.70 thf(f16518,plain,(
% 92.92/13.70 ( ! [X3 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X1),X3),X1),X3))) )),
% 92.92/13.70 inference(equality_resolution,[],[f16517])).
% 92.92/13.70 thf(f16517,plain,(
% 92.92/13.70 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X3),X1),X3)) | (X0 != X1)) )),
% 92.92/13.70 inference(equality_resolution,[],[f12512])).
% 92.92/13.70 thf(f12512,plain,(
% 92.92/13.70 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP67,X0),X2),X1),X3)) | (X2 != X3) | (X0 != X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6497])).
% 92.92/13.70 thf(f68714,plain,(
% 92.92/13.70 spl854_721),
% 92.92/13.70 inference(avatar_split_clause,[],[f14785,f68712])).
% 92.92/13.70 thf(f68712,plain,(
% 92.92/13.70 spl854_721 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_721])])).
% 92.92/13.70 thf(f14785,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11080,f9121])).
% 92.92/13.70 thf(f11080,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7605])).
% 92.92/13.70 thf(f7605,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) | (($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) & ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))) & (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)))))),
% 92.92/13.70 inference(flattening,[],[f7604])).
% 92.92/13.70 thf(f7604,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) | (($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) & ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3396])).
% 92.92/13.70 thf(f3396,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) <=> (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))))),
% 92.92/13.70 inference(fool_elimination,[],[f3395])).
% 92.92/13.70 thf(f3395,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) <=> (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1) | vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.70 inference(rectify,[],[f1088])).
% 92.92/13.70 thf(f1088,axiom,(
% 92.92/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X137)) <=> (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X137) | vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X134)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__MULT)).
% 92.92/13.70 thf(f68710,plain,(
% 92.92/13.70 spl854_720),
% 92.92/13.70 inference(avatar_split_clause,[],[f14426,f68708])).
% 92.92/13.70 thf(f68708,plain,(
% 92.92/13.70 spl854_720 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_720])])).
% 92.92/13.70 thf(f14426,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10457,f9122,f9122,f9122,f9121])).
% 92.92/13.70 thf(f10457,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6988])).
% 92.92/13.70 thf(f6988,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) | ((c_2Enum_2E0 != X1) & (c_2Enum_2E0 != X0))) & ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))))),
% 92.92/13.70 inference(flattening,[],[f6987])).
% 92.92/13.70 thf(f6987,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) | ((c_2Enum_2E0 != X1) & (c_2Enum_2E0 != X0))) & (((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5112])).
% 92.92/13.70 thf(f5112,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1)) <=> ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0)))),
% 92.92/13.70 inference(rectify,[],[f1076])).
% 92.92/13.70 thf(f1076,axiom,(
% 92.92/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X137)) <=> ((c_2Enum_2E0 = X137) | (c_2Enum_2E0 = X134)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__0)).
% 92.92/13.70 thf(f68706,plain,(
% 92.92/13.70 spl854_719),
% 92.92/13.70 inference(avatar_split_clause,[],[f14413,f68704])).
% 92.92/13.70 thf(f68704,plain,(
% 92.92/13.70 spl854_719 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_719])])).
% 92.92/13.70 thf(f14413,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10444,f9122,f9122,f9122])).
% 92.92/13.70 thf(f10444,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6980])).
% 92.92/13.70 thf(f6980,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0)) | ((c_2Enum_2E0 != X0) & (c_2Enum_2E0 != X1))) & ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))))),
% 92.92/13.70 inference(flattening,[],[f6979])).
% 92.92/13.70 thf(f6979,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0)) | ((c_2Enum_2E0 != X0) & (c_2Enum_2E0 != X1))) & (((c_2Enum_2E0 = X0) | (c_2Enum_2E0 = X1)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5109])).
% 92.92/13.70 thf(f5109,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0)) <=> ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 = X1)))),
% 92.92/13.70 inference(rectify,[],[f1235])).
% 92.92/13.70 thf(f1235,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X27),X136)) <=> ((c_2Enum_2E0 = X136) | (c_2Enum_2E0 = X27)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMIN__EQ__0)).
% 92.92/13.70 thf(f68702,plain,(
% 92.92/13.70 spl854_718),
% 92.92/13.70 inference(avatar_split_clause,[],[f13958,f68700])).
% 92.92/13.70 thf(f68700,plain,(
% 92.92/13.70 spl854_718 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_718])])).
% 92.92/13.70 thf(f13958,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9697,f9122])).
% 92.92/13.70 thf(f9697,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK170,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6754])).
% 92.92/13.70 thf(f68698,plain,(
% 92.92/13.70 spl854_717),
% 92.92/13.70 inference(avatar_split_clause,[],[f13844,f68696])).
% 92.92/13.70 thf(f68696,plain,(
% 92.92/13.70 spl854_717 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_717])])).
% 92.92/13.70 thf(f13844,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9553,f9122])).
% 92.92/13.70 thf(f9553,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6654])).
% 92.92/13.70 thf(f6654,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK146,X0)),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK146,sK147])],[f6652,f6653])).
% 92.92/13.70 thf(f6653,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X2),X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) => (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK146,X0)),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK147,X0)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f6652,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X2),X3))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.92/13.70 inference(rectify,[],[f5437])).
% 92.92/13.70 thf(f5437,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ? [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)))),
% 92.92/13.70 inference(flattening,[],[f5436])).
% 92.92/13.70 thf(f5436,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | (? [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))))),
% 92.92/13.70 inference(ennf_transformation,[],[f2160])).
% 92.92/13.70 thf(f2160,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X2)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) => ! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)))),
% 92.92/13.70 inference(fool_elimination,[],[f2159])).
% 92.92/13.70 thf(f2159,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,X0,X2) => vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X2))) & vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) => ! [X3 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X3))),
% 92.92/13.70 inference(rectify,[],[f1687])).
% 92.92/13.70 thf(f1687,axiom,(
% 92.92/13.70 ! [X7 : tyop_2Enum_2Enum > $o] : ((! [X462 : tyop_2Enum_2Enum,X11 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,X7,X11) => vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X462),X11))) & vAPP(tyop_2Enum_2Enum,$o,X7,c_2Enum_2E0)) => ! [X298 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X298))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__ind)).
% 92.92/13.70 thf(f68694,plain,(
% 92.92/13.70 spl854_716),
% 92.92/13.70 inference(avatar_split_clause,[],[f13842,f68692])).
% 92.92/13.70 thf(f68692,plain,(
% 92.92/13.70 spl854_716 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_716])])).
% 92.92/13.70 thf(f13842,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9551,f9122])).
% 92.92/13.70 thf(f9551,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK145,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6651])).
% 92.92/13.70 thf(f68690,plain,(
% 92.92/13.70 spl854_715),
% 92.92/13.70 inference(avatar_split_clause,[],[f11791,f68688])).
% 92.92/13.70 thf(f68688,plain,(
% 92.92/13.70 spl854_715 <=> ! [X0 : $tType,X2 : tyop_2Eind__type_2Erecspace(X0),X1 : tyop_2Eind__type_2Erecspace(X0)] : ((X1 = X2) | (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2) != vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_715])])).
% 92.92/13.70 thf(f11791,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : tyop_2Eind__type_2Erecspace(X0),X1 : tyop_2Eind__type_2Erecspace(X0)] : ((X1 = X2) | (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2) != vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7955])).
% 92.92/13.70 thf(f7955,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eind__type_2Erecspace(X0),X2 : tyop_2Eind__type_2Erecspace(X0)] : (((vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2) = vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X1)) | (X1 != X2)) & ((X1 = X2) | (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2) != vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5240])).
% 92.92/13.70 thf(f5240,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eind__type_2Erecspace(X0),X2 : tyop_2Eind__type_2Erecspace(X0)] : ((vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2) = vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X1)) <=> (X1 = X2))),
% 92.92/13.70 inference(rectify,[],[f1541])).
% 92.92/13.70 thf(f1541,axiom,(
% 92.92/13.70 ! [X0 : $tType,X8 : tyop_2Eind__type_2Erecspace(X0),X18 : tyop_2Eind__type_2Erecspace(X0)] : ((vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X8) = vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X18)) <=> (X8 = X18))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EDEST__REC__INJ)).
% 92.92/13.70 thf(f68686,plain,(
% 92.92/13.70 spl854_714),
% 92.92/13.70 inference(avatar_split_clause,[],[f11567,f68684])).
% 92.92/13.70 thf(f68684,plain,(
% 92.92/13.70 spl854_714 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_714])])).
% 92.92/13.70 thf(f11567,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5868])).
% 92.92/13.70 thf(f5868,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X2)))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))),
% 92.92/13.70 inference(flattening,[],[f5867])).
% 92.92/13.70 thf(f5867,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X2)))) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))))),
% 92.92/13.70 inference(ennf_transformation,[],[f3686])).
% 92.92/13.70 thf(f3686,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) => (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X2)))))),
% 92.92/13.70 inference(fool_elimination,[],[f3685])).
% 92.92/13.70 thf(f3685,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,X0,X2) & vAPP(tyop_2Enum_2Enum,$o,X0,X1)) => (vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X2)) & vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X2))))),
% 92.92/13.70 inference(rectify,[],[f1227])).
% 92.92/13.70 thf(f1227,axiom,(
% 92.92/13.70 ! [X7 : tyop_2Enum_2Enum > $o,X27 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,X7,X135) & vAPP(tyop_2Enum_2Enum,$o,X7,X27)) => (vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X27),X135)) & vAPP(tyop_2Enum_2Enum,$o,X7,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X27),X135))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMIN__MAX__PRED)).
% 92.92/13.70 thf(f68682,plain,(
% 92.92/13.70 spl854_713),
% 92.92/13.70 inference(avatar_split_clause,[],[f11566,f68680])).
% 92.92/13.70 thf(f68680,plain,(
% 92.92/13.70 spl854_713 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_713])])).
% 92.92/13.70 thf(f11566,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5868])).
% 92.92/13.70 thf(f68678,plain,(
% 92.92/13.70 ~spl854_712 | ~spl854_41 | ~spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f61701,f60411,f22099,f68675])).
% 92.92/13.70 thf(f22099,plain,(
% 92.92/13.70 spl854_41 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_41])])).
% 92.92/13.70 thf(f60411,plain,(
% 92.92/13.70 spl854_622 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : ((X2 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_622])])).
% 92.92/13.70 thf(f61701,plain,(
% 92.92/13.70 ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9)) | (~spl854_41 | ~spl854_622)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61386])).
% 92.92/13.70 thf(f61386,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true != $true) | (X0 != X0) | ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP9))) ) | (~spl854_41 | ~spl854_622)),
% 92.92/13.70 inference(superposition,[],[f60412,f22100])).
% 92.92/13.70 thf(f22100,plain,(
% 92.92/13.70 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X1))) ) | ~spl854_41),
% 92.92/13.70 inference(avatar_component_clause,[],[f22099])).
% 92.92/13.70 thf(f60412,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (X2 != X3) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) ) | ~spl854_622),
% 92.92/13.70 inference(avatar_component_clause,[],[f60411])).
% 92.92/13.70 thf(f68673,plain,(
% 92.92/13.70 spl854_711),
% 92.92/13.70 inference(avatar_split_clause,[],[f11214,f68671])).
% 92.92/13.70 thf(f68671,plain,(
% 92.92/13.70 spl854_711 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_711])])).
% 92.92/13.70 thf(f11214,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f3538])).
% 92.92/13.70 thf(f3538,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)))),
% 92.92/13.70 inference(fool_elimination,[],[f3537])).
% 92.92/13.70 thf(f3537,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))),
% 92.92/13.70 inference(rectify,[],[f1570])).
% 92.92/13.70 thf(f1570,axiom,(
% 92.92/13.70 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X72),X49),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__IS__GCD)).
% 92.92/13.70 thf(f68669,plain,(
% 92.92/13.70 spl854_710),
% 92.92/13.70 inference(avatar_split_clause,[],[f11173,f68667])).
% 92.92/13.70 thf(f68667,plain,(
% 92.92/13.70 spl854_710 <=> ! [X0 : $tType,X4 : X0,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK384(X0),X1))) | ($true != vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_710])])).
% 92.92/13.70 thf(f11173,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X4 : X0] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK384(X0),X1))) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7675])).
% 92.92/13.70 thf(f68665,plain,(
% 92.92/13.70 spl854_709),
% 92.92/13.70 inference(avatar_split_clause,[],[f11172,f68663])).
% 92.92/13.70 thf(f68663,plain,(
% 92.92/13.70 spl854_709 <=> ! [X0 : $tType,X4 : X0,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK383(X0),X1))) | ($true != vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_709])])).
% 92.92/13.70 thf(f11172,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X4 : X0] : (($true = vAPP(sTfun(X0,$o),$o,sP24(X0),X1)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK383(X0),X1))) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7675])).
% 92.92/13.70 thf(f68661,plain,(
% 92.92/13.70 spl854_708),
% 92.92/13.70 inference(avatar_split_clause,[],[f10569,f68659])).
% 92.92/13.70 thf(f68659,plain,(
% 92.92/13.70 spl854_708 <=> ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o,X3 : X0] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK260(X0),X1))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_708])])).
% 92.92/13.70 thf(f10569,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X3 : X0,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK260(X0),X1))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7064])).
% 92.92/13.70 thf(f7064,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK260(X0),X1))) | (! [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))) & (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),X0,sK261(X0),X1)))) | ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))) | ! [X5 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X5))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK260,sK261])],[f7061,f7063,f7062])).
% 92.92/13.70 thf(f7062,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) => ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK260(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7063,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X4 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4))) => ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),X0,sK261(X0),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7061,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | (! [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))) & (? [X4 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4))) | ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))) | ! [X5 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X5))))),
% 92.92/13.70 inference(rectify,[],[f7060])).
% 92.92/13.70 thf(f7060,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | (! [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))) & (? [X3 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) | ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))) | ! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2))))),
% 92.92/13.70 inference(flattening,[],[f7059])).
% 92.92/13.70 thf(f7059,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | (! [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))) & ((? [X3 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) | ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) | ! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3020])).
% 92.92/13.70 thf(f3020,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) <=> (? [X3 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) | ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))))),
% 92.92/13.70 inference(fool_elimination,[],[f3019])).
% 92.92/13.70 thf(f3019,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X2 : tyop_2Eoption_2Eoption(X0)] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2) <=> (? [X3 : X0] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3)) | vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))),
% 92.92/13.70 inference(rectify,[],[f727])).
% 92.92/13.70 thf(f727,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X216 : tyop_2Eoption_2Eoption(X0)] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X7,X216) <=> (? [X19 : X0] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X7,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X19)) | vAPP(tyop_2Eoption_2Eoption(X0),$o,X7,c_2Eoption_2ENONE(X0))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EEXISTS__OPTION)).
% 92.92/13.70 thf(f68657,plain,(
% 92.92/13.70 spl854_707),
% 92.92/13.70 inference(avatar_split_clause,[],[f10560,f68655])).
% 92.92/13.70 thf(f68655,plain,(
% 92.92/13.70 spl854_707 <=> ! [X0 : $tType,X4 : X0,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK257(X0),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_707])])).
% 92.92/13.70 thf(f10560,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o,X4 : X0] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK257(X0),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7050])).
% 92.92/13.70 thf(f7050,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),X0,sK256(X0),X1)))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) & ((! [X4 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4))) & ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK257(X0),X1)))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK256,sK257])],[f7047,f7049,f7048])).
% 92.92/13.70 thf(f7048,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) => ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),X0,sK256(X0),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7049,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (? [X5 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X5)) => ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(sTfun(tyop_2Eoption_2Eoption(X0),$o),tyop_2Eoption_2Eoption(X0),sK257(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7047,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | ? [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) & ((! [X4 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4))) & ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) | ? [X5 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X5))))),
% 92.92/13.70 inference(rectify,[],[f7046])).
% 92.92/13.70 thf(f7046,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | ? [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) & ((! [X3 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) | ? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2))))),
% 92.92/13.70 inference(flattening,[],[f7045])).
% 92.92/13.70 thf(f7045,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : ((! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) | (? [X3 : X0] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))) & ((! [X3 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))) | ? [X2 : tyop_2Eoption_2Eoption(X0)] : ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3012])).
% 92.92/13.70 thf(f3012,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (! [X2 : tyop_2Eoption_2Eoption(X0)] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2)) <=> (! [X3 : X0] : ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3))) & ($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0)))))),
% 92.92/13.70 inference(fool_elimination,[],[f3011])).
% 92.92/13.70 thf(f3011,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0) > $o] : (! [X2 : tyop_2Eoption_2Eoption(X0)] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,X2) <=> (! [X3 : X0] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3)) & vAPP(tyop_2Eoption_2Eoption(X0),$o,X1,c_2Eoption_2ENONE(X0))))),
% 92.92/13.70 inference(rectify,[],[f726])).
% 92.92/13.70 thf(f726,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : tyop_2Eoption_2Eoption(X0) > $o] : (! [X216 : tyop_2Eoption_2Eoption(X0)] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X7,X216) <=> (! [X19 : X0] : vAPP(tyop_2Eoption_2Eoption(X0),$o,X7,vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X19)) & vAPP(tyop_2Eoption_2Eoption(X0),$o,X7,c_2Eoption_2ENONE(X0))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EFORALL__OPTION)).
% 92.92/13.70 thf(f68653,plain,(
% 92.92/13.70 spl854_706),
% 92.92/13.70 inference(avatar_split_clause,[],[f9899,f68651])).
% 92.92/13.70 thf(f68651,plain,(
% 92.92/13.70 spl854_706 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_706])])).
% 92.92/13.70 thf(f9899,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5002])).
% 92.92/13.70 thf(f5002,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))),
% 92.92/13.70 inference(rectify,[],[f1109])).
% 92.92/13.70 thf(f1109,axiom,(
% 92.92/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)),X134))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUC__ADD__SYM)).
% 92.92/13.70 thf(f68649,plain,(
% 92.92/13.70 spl854_705),
% 92.92/13.70 inference(avatar_split_clause,[],[f9898,f68647])).
% 92.92/13.70 thf(f68645,plain,(
% 92.92/13.70 spl854_704),
% 92.92/13.70 inference(avatar_split_clause,[],[f9897,f68643])).
% 92.92/13.70 thf(f68643,plain,(
% 92.92/13.70 spl854_704 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0)),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_704])])).
% 92.92/13.70 thf(f9897,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0)),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5000])).
% 92.92/13.70 thf(f5000,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0)),X1))),
% 92.92/13.70 inference(rectify,[],[f1003])).
% 92.92/13.70 thf(f1003,axiom,(
% 92.92/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X134),X137)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X134)),X137))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EPRE__SUB)).
% 92.92/13.70 thf(f68641,plain,(
% 92.92/13.70 spl854_703),
% 92.92/13.70 inference(avatar_split_clause,[],[f9896,f68639])).
% 92.92/13.70 thf(f68639,plain,(
% 92.92/13.70 spl854_703 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_703])])).
% 92.92/13.70 thf(f9896,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4999])).
% 92.92/13.70 thf(f4999,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))),
% 92.92/13.70 inference(rectify,[],[f987])).
% 92.92/13.70 thf(f987,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X136),X27) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X27)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__MONO__EQ)).
% 92.92/13.70 thf(f68637,plain,(
% 92.92/13.70 spl854_702),
% 92.92/13.70 inference(avatar_split_clause,[],[f9895,f68635])).
% 92.92/13.70 thf(f68635,plain,(
% 92.92/13.70 spl854_702 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_702])])).
% 92.92/13.70 thf(f9895,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4998])).
% 92.92/13.70 thf(f4998,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))),
% 92.92/13.70 inference(rectify,[],[f1255])).
% 92.92/13.70 thf(f1255,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X136),X27) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X27)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__SUC)).
% 92.92/13.70 thf(f68633,plain,(
% 92.92/13.70 ~spl854_701 | ~spl854_42 | ~spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f61700,f60411,f22103,f68630])).
% 92.92/13.70 thf(f22103,plain,(
% 92.92/13.70 spl854_42 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_42])])).
% 92.92/13.70 thf(f61700,plain,(
% 92.92/13.70 ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10)) | (~spl854_42 | ~spl854_622)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61387])).
% 92.92/13.70 thf(f61387,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true != $true) | (X0 != X0) | ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),sP10))) ) | (~spl854_42 | ~spl854_622)),
% 92.92/13.70 inference(superposition,[],[f60412,f22104])).
% 92.92/13.70 thf(f22104,plain,(
% 92.92/13.70 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X1))) ) | ~spl854_42),
% 92.92/13.70 inference(avatar_component_clause,[],[f22103])).
% 92.92/13.70 thf(f68628,plain,(
% 92.92/13.70 spl854_700),
% 92.92/13.70 inference(avatar_split_clause,[],[f9894,f68626])).
% 92.92/13.70 thf(f68626,plain,(
% 92.92/13.70 spl854_700 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X1),X1),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_700])])).
% 92.92/13.70 thf(f9894,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X1),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4997])).
% 92.92/13.70 thf(f4997,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X1),X1),X0))),
% 92.92/13.70 inference(rectify,[],[f1706])).
% 92.92/13.70 thf(f1706,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBITV,X136),X49) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X49),X49),X136))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBITV__def)).
% 92.92/13.70 thf(f68624,plain,(
% 92.92/13.70 spl854_699),
% 92.92/13.70 inference(avatar_split_clause,[],[f9696,f68622])).
% 92.92/13.70 thf(f68622,plain,(
% 92.92/13.70 spl854_699 <=> ! [X0 : tyop_2Enum_2Enum > $o,X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_699])])).
% 92.92/13.70 thf(f9696,plain,(
% 92.92/13.70 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6754])).
% 92.92/13.70 thf(f68620,plain,(
% 92.92/13.70 spl854_698),
% 92.92/13.70 inference(avatar_split_clause,[],[f9407,f68618])).
% 92.92/13.70 thf(f68618,plain,(
% 92.92/13.70 spl854_698 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Emin_2E_3D(tyop_2Enum_2Enum)),X0)) = X0)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_698])])).
% 92.92/13.70 thf(f9407,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Emin_2E_3D(tyop_2Enum_2Enum)),X0)) = X0)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f2110])).
% 92.92/13.70 thf(f2110,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0)) = X0) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Emin_2E_3D(tyop_2Enum_2Enum)),X0)) = X0))),
% 92.92/13.70 inference(fool_elimination,[],[f2109])).
% 92.92/13.70 thf(f2109,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0),X1)))) = X0) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X2),X0)))) = X0))),
% 92.92/13.70 inference(rectify,[],[f1429])).
% 92.92/13.70 thf(f1429,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X8),X135)))) = X8) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X137),X8)))) = X8))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2ELEAST__EQ)).
% 92.92/13.70 thf(f68616,plain,(
% 92.92/13.70 spl854_697),
% 92.92/13.70 inference(avatar_split_clause,[],[f9243,f68614])).
% 92.92/13.70 thf(f68614,plain,(
% 92.92/13.70 spl854_697 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_697])])).
% 92.92/13.70 thf(f9243,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4852])).
% 92.92/13.70 thf(f4852,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,c_2Enum_2E0),X2))),
% 92.92/13.70 inference(rectify,[],[f1372])).
% 92.92/13.70 thf(f1372,axiom,(
% 92.92/13.70 ! [X137 : tyop_2Enum_2Enum,X358 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)),X358) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,X137),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X358))) & ! [X357 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,c_2Enum_2E0),X357) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X357))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Etexp__help__def)).
% 92.92/13.70 thf(f68612,plain,(
% 92.92/13.70 spl854_696),
% 92.92/13.70 inference(avatar_split_clause,[],[f9238,f68610])).
% 92.92/13.70 thf(f68610,plain,(
% 92.92/13.70 spl854_696 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_696])])).
% 92.92/13.70 thf(f9238,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4850])).
% 92.92/13.70 thf(f4850,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1)) & ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X2) = X2)),
% 92.92/13.70 inference(rectify,[],[f914])).
% 92.92/13.70 thf(f914,axiom,(
% 92.92/13.70 ! [X27 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X27)),X135) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X27),X135))) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X136) = X136)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD)).
% 92.92/13.70 thf(f68608,plain,(
% 92.92/13.70 spl854_695),
% 92.92/13.70 inference(avatar_split_clause,[],[f9185,f68606])).
% 92.92/13.70 thf(f68606,plain,(
% 92.92/13.70 spl854_695 <=> ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_695])])).
% 92.92/13.70 thf(f9185,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4847])).
% 92.92/13.70 thf(f4847,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1)) & ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)),X3) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) & ! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,c_2Earithmetic_2EZERO),X4) = X4)),
% 92.92/13.70 inference(rectify,[],[f1373])).
% 92.92/13.70 thf(f1373,axiom,(
% 92.92/13.70 ! [X298 : tyop_2Enum_2Enum,X23 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X298)),X23)) & ! [X137 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X137)),X19) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X137),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X19))) & ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,c_2Earithmetic_2EZERO),X8) = X8)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Eonecount__def)).
% 92.92/13.70 thf(f68540,plain,(
% 92.92/13.70 ~spl854_694 | ~spl854_43 | ~spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f61535,f60411,f22107,f68537])).
% 92.92/13.70 thf(f22107,plain,(
% 92.92/13.70 spl854_43 <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,$true),$true))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_43])])).
% 92.92/13.70 thf(f61535,plain,(
% 92.92/13.70 ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC)) | (~spl854_43 | ~spl854_622)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61534])).
% 92.92/13.70 thf(f61534,plain,(
% 92.92/13.70 ($true != $true) | ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC)) | (~spl854_43 | ~spl854_622)),
% 92.92/13.70 inference(duplicate_literal_removal,[],[f61461])).
% 92.92/13.70 thf(f61461,plain,(
% 92.92/13.70 ($true != $true) | ($true != $true) | ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,c_2Erelation_2EWF($o),c_2Emarker_2EAC)) | (~spl854_43 | ~spl854_622)),
% 92.92/13.70 inference(superposition,[],[f60412,f22109])).
% 92.92/13.70 thf(f22109,plain,(
% 92.92/13.70 ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,$true),$true)) | ~spl854_43),
% 92.92/13.70 inference(avatar_component_clause,[],[f22107])).
% 92.92/13.70 thf(f68272,plain,(
% 92.92/13.70 ~spl854_693 | ~spl854_251 | ~spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f61513,f60411,f23725,f68269])).
% 92.92/13.70 thf(f23725,plain,(
% 92.92/13.70 spl854_251 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_251])])).
% 92.92/13.70 thf(f61513,plain,(
% 92.92/13.70 ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61)) | (~spl854_251 | ~spl854_622)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61482])).
% 92.92/13.70 thf(f61482,plain,(
% 92.92/13.70 ($true != $true) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),sP61)) | (~spl854_251 | ~spl854_622)),
% 92.92/13.70 inference(superposition,[],[f60412,f23727])).
% 92.92/13.70 thf(f23727,plain,(
% 92.92/13.70 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_251),
% 92.92/13.70 inference(avatar_component_clause,[],[f23725])).
% 92.92/13.70 thf(f66983,plain,(
% 92.92/13.70 spl854_692),
% 92.92/13.70 inference(avatar_split_clause,[],[f18349,f66980])).
% 92.92/13.70 thf(f66980,plain,(
% 92.92/13.70 spl854_692 <=> (vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,$true) = vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_692])])).
% 92.92/13.70 thf(f18349,plain,(
% 92.92/13.70 (vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,$true) = vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))))),
% 92.92/13.70 inference(forward_demodulation,[],[f15669,f18174])).
% 92.92/13.70 thf(f15669,plain,(
% 92.92/13.70 (vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,$true))),
% 92.92/13.70 inference(equality_resolution,[],[f13753])).
% 92.92/13.70 thf(f13753,plain,(
% 92.92/13.70 ( ! [X0 : $o] : ((vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0) = vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) | ($true != X0)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9428,f13522])).
% 92.92/13.70 thf(f9428,plain,(
% 92.92/13.70 ( ! [X0 : $o] : ((vAPP(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME(tyop_2Eone_2Eone),c_2Eone_2Eone) = vAPP($o,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD,X0)) | ($true != X0)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6613])).
% 92.92/13.70 thf(f66978,plain,(
% 92.92/13.70 ~spl854_691 | ~spl854_39 | ~spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f61511,f60411,f22091,f66975])).
% 92.92/13.70 thf(f22091,plain,(
% 92.92/13.70 spl854_39 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_39])])).
% 92.92/13.70 thf(f61511,plain,(
% 92.92/13.70 ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides)) | (~spl854_39 | ~spl854_622)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61484])).
% 92.92/13.70 thf(f61484,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true != $true) | (X0 != X0) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Edivides_2Edivides))) ) | (~spl854_39 | ~spl854_622)),
% 92.92/13.70 inference(superposition,[],[f60412,f22092])).
% 92.92/13.70 thf(f22092,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X0))) ) | ~spl854_39),
% 92.92/13.70 inference(avatar_component_clause,[],[f22091])).
% 92.92/13.70 thf(f66973,plain,(
% 92.92/13.70 spl854_690),
% 92.92/13.70 inference(avatar_split_clause,[],[f17216,f66971])).
% 92.92/13.70 thf(f66971,plain,(
% 92.92/13.70 spl854_690 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_690])])).
% 92.92/13.70 thf(f17216,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17215])).
% 92.92/13.70 thf(f17215,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f11907])).
% 92.92/13.70 thf(f11907,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8026])).
% 92.92/13.70 thf(f8026,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X2),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X0),X2),X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X0),X1),X2))) & (((($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X2),X0)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X0),X2),X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X0),X1),X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8025])).
% 92.92/13.70 thf(f8025,plain,(
% 92.92/13.70 ! [X2 : $o,X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))) & (((($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X0)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2))))),
% 92.92/13.70 inference(flattening,[],[f8024])).
% 92.92/13.70 thf(f8024,plain,(
% 92.92/13.70 ! [X2 : $o,X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2)) | ((($true != vAPP($o,$o,vNOT,X2)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)))) & (((($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X0)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6459])).
% 92.92/13.70 thf(f6459,plain,(
% 92.92/13.70 ! [X2 : $o,X1 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2)) <=> ((($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X0)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66969,plain,(
% 92.92/13.70 spl854_689),
% 92.92/13.70 inference(avatar_split_clause,[],[f17212,f66967])).
% 92.92/13.70 thf(f66967,plain,(
% 92.92/13.70 spl854_689 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_689])])).
% 92.92/13.70 thf(f17212,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17211])).
% 92.92/13.70 thf(f17211,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f11911])).
% 92.92/13.70 thf(f11911,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8029])).
% 92.92/13.70 thf(f8029,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8028])).
% 92.92/13.70 thf(f8028,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != vAPP($o,$o,vNOT,X0)) & ($true != X1))) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2))))),
% 92.92/13.70 inference(flattening,[],[f8027])).
% 92.92/13.70 thf(f8027,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != vAPP($o,$o,vNOT,X0)) & ($true != X1))) & ((($true = vAPP($o,$o,vNOT,X2)) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6458])).
% 92.92/13.70 thf(f6458,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X1),X0),X2)) <=> (($true = vAPP($o,$o,vNOT,X2)) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X1)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66965,plain,(
% 92.92/13.70 spl854_688),
% 92.92/13.70 inference(avatar_split_clause,[],[f17208,f66963])).
% 92.92/13.70 thf(f66963,plain,(
% 92.92/13.70 spl854_688 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_688])])).
% 92.92/13.70 thf(f17208,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17207])).
% 92.92/13.70 thf(f17207,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f11915])).
% 92.92/13.70 thf(f11915,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8032])).
% 92.92/13.70 thf(f8032,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8031])).
% 92.92/13.70 thf(f8031,plain,(
% 92.92/13.70 ! [X1 : $o,X0 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != vAPP($o,$o,vNOT,X0)) & ($true != X2))) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1))))),
% 92.92/13.70 inference(flattening,[],[f8030])).
% 92.92/13.70 thf(f8030,plain,(
% 92.92/13.70 ! [X1 : $o,X0 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != vAPP($o,$o,vNOT,X0)) & ($true != X2))) & (((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6457])).
% 92.92/13.70 thf(f6457,plain,(
% 92.92/13.70 ! [X1 : $o,X0 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X0),X1)) <=> ((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66961,plain,(
% 92.92/13.70 spl854_687),
% 92.92/13.70 inference(avatar_split_clause,[],[f17194,f66959])).
% 92.92/13.70 thf(f66959,plain,(
% 92.92/13.70 spl854_687 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_687])])).
% 92.92/13.70 thf(f17194,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17193])).
% 92.92/13.70 thf(f17193,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f11940])).
% 92.92/13.70 thf(f11940,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8042])).
% 92.92/13.70 thf(f8042,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))))),
% 92.92/13.70 inference(flattening,[],[f8041])).
% 92.92/13.70 thf(f8041,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & ((($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6461])).
% 92.92/13.70 thf(f6461,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) <=> (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66957,plain,(
% 92.92/13.70 spl854_686),
% 92.92/13.70 inference(avatar_split_clause,[],[f17184,f66955])).
% 92.92/13.70 thf(f66955,plain,(
% 92.92/13.70 spl854_686 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_686])])).
% 92.92/13.70 thf(f17184,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f11959])).
% 92.92/13.70 thf(f11959,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8051])).
% 92.92/13.70 thf(f8051,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X1) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8050])).
% 92.92/13.70 thf(f8050,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X0) & ($true != X1))) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2))))),
% 92.92/13.70 inference(flattening,[],[f8049])).
% 92.92/13.70 thf(f8049,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X0) & ($true != X1))) & ((($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6465])).
% 92.92/13.70 thf(f6465,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) <=> (($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | ($true = X1)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66953,plain,(
% 92.92/13.70 spl854_685),
% 92.92/13.70 inference(avatar_split_clause,[],[f17177,f66951])).
% 92.92/13.70 thf(f66951,plain,(
% 92.92/13.70 spl854_685 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_685])])).
% 92.92/13.70 thf(f17177,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17176])).
% 92.92/13.70 thf(f17176,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f11978])).
% 92.92/13.70 thf(f11978,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8060])).
% 92.92/13.70 thf(f8060,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X1) & ($true != vAPP($o,$o,vNOT,X2)))) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8059])).
% 92.92/13.70 thf(f8059,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X0) & (vAPP($o,$o,vNOT,X1) != $true))) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2))))),
% 92.92/13.70 inference(flattening,[],[f8058])).
% 92.92/13.70 thf(f8058,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X0) & (vAPP($o,$o,vNOT,X1) != $true))) & ((($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | (vAPP($o,$o,vNOT,X1) = $true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6469])).
% 92.92/13.70 thf(f6469,plain,(
% 92.92/13.70 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) <=> (($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | (vAPP($o,$o,vNOT,X1) = $true)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66949,plain,(
% 92.92/13.70 spl854_684),
% 92.92/13.70 inference(avatar_split_clause,[],[f17040,f66947])).
% 92.92/13.70 thf(f66947,plain,(
% 92.92/13.70 spl854_684 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_684])])).
% 92.92/13.70 thf(f17040,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17039])).
% 92.92/13.70 thf(f17039,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12755])).
% 92.92/13.70 thf(f12755,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8601])).
% 92.92/13.70 thf(f8601,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X1) & ($true != vAPP($o,$o,vNOT,X2)))) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8600])).
% 92.92/13.70 thf(f8600,plain,(
% 92.92/13.70 ! [X3 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X3)) | (($true != vAPP($o,$o,vNOT,X3)) & ($true != X1) & ($true != vAPP($o,$o,vNOT,X2)))) & (($true = vAPP($o,$o,vNOT,X3)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X3))))),
% 92.92/13.70 inference(flattening,[],[f8599])).
% 92.92/13.70 thf(f8599,plain,(
% 92.92/13.70 ! [X3 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X3)) | (($true != vAPP($o,$o,vNOT,X3)) & ($true != X1) & ($true != vAPP($o,$o,vNOT,X2)))) & ((($true = vAPP($o,$o,vNOT,X3)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6550])).
% 92.92/13.70 thf(f6550,plain,(
% 92.92/13.70 ! [X3 : $o,X1 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X3)) <=> (($true = vAPP($o,$o,vNOT,X3)) | ($true = X1) | ($true = vAPP($o,$o,vNOT,X2))))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66945,plain,(
% 92.92/13.70 spl854_683),
% 92.92/13.70 inference(avatar_split_clause,[],[f17036,f66943])).
% 92.92/13.70 thf(f66943,plain,(
% 92.92/13.70 spl854_683 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_683])])).
% 92.92/13.70 thf(f17036,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17035])).
% 92.92/13.70 thf(f17035,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12759])).
% 92.92/13.70 thf(f12759,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8604])).
% 92.92/13.70 thf(f8604,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8603])).
% 92.92/13.70 thf(f8603,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X3 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X3),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X3))) & (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X3),X1),X0))))),
% 92.92/13.70 inference(flattening,[],[f8602])).
% 92.92/13.70 thf(f8602,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X3 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X3),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X3))) & ((($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X3)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X3),X1),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6549])).
% 92.92/13.70 thf(f6549,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X3),X1),X0)) <=> (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X3)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66941,plain,(
% 92.92/13.70 spl854_682),
% 92.92/13.70 inference(avatar_split_clause,[],[f17032,f66939])).
% 92.92/13.70 thf(f66939,plain,(
% 92.92/13.70 spl854_682 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_682])])).
% 92.92/13.70 thf(f17032,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f17031])).
% 92.92/13.70 thf(f17031,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12763])).
% 92.92/13.70 thf(f12763,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8607])).
% 92.92/13.70 thf(f8607,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8606])).
% 92.92/13.70 thf(f8606,plain,(
% 92.92/13.70 ! [X2 : $o,X1 : $o,X3 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X3),X1),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X3))) & (($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X3),X1),X2))))),
% 92.92/13.70 inference(flattening,[],[f8605])).
% 92.92/13.70 thf(f8605,plain,(
% 92.92/13.70 ! [X2 : $o,X1 : $o,X3 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X3),X1),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & (vAPP($o,$o,vNOT,X1) != $true) & ($true != X3))) & ((($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X3)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X3),X1),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6548])).
% 92.92/13.70 thf(f6548,plain,(
% 92.92/13.70 ! [X2 : $o,X1 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X3),X1),X2)) <=> (($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X3)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66937,plain,(
% 92.92/13.70 spl854_681),
% 92.92/13.70 inference(avatar_split_clause,[],[f17029,f66935])).
% 92.92/13.70 thf(f66935,plain,(
% 92.92/13.70 spl854_681 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_681])])).
% 92.92/13.70 thf(f17029,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12767])).
% 92.92/13.70 thf(f12767,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8610])).
% 92.92/13.70 thf(f8610,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X1) & ($true != X2))) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0))))),
% 92.92/13.70 inference(rectify,[],[f8609])).
% 92.92/13.70 thf(f8609,plain,(
% 92.92/13.70 ! [X0 : $o,X2 : $o,X3 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X3),X2),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2) & ($true != X3))) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2) | ($true = X3) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X3),X2),X0))))),
% 92.92/13.70 inference(flattening,[],[f8608])).
% 92.92/13.70 thf(f8608,plain,(
% 92.92/13.70 ! [X0 : $o,X2 : $o,X3 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X3),X2),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2) & ($true != X3))) & ((($true = vAPP($o,$o,vNOT,X0)) | ($true = X2) | ($true = X3)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X3),X2),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6547])).
% 92.92/13.70 thf(f6547,plain,(
% 92.92/13.70 ! [X0 : $o,X2 : $o,X3 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X3),X2),X0)) <=> (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2) | ($true = X3)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66933,plain,(
% 92.92/13.70 ~spl854_680 | ~spl854_46 | ~spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f61510,f60411,f22121,f66930])).
% 92.92/13.70 thf(f22121,plain,(
% 92.92/13.70 spl854_46 <=> ! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X1),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_46])])).
% 92.92/13.70 thf(f61510,plain,(
% 92.92/13.70 ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D)) | (~spl854_46 | ~spl854_622)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61485])).
% 92.92/13.70 thf(f61485,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true != $true) | (X0 != X0) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),$o,c_2Erelation_2EWF(tyop_2Enum_2Enum),c_2Earithmetic_2E_3E_3D))) ) | (~spl854_46 | ~spl854_622)),
% 92.92/13.70 inference(superposition,[],[f60412,f22122])).
% 92.92/13.70 thf(f22122,plain,(
% 92.92/13.70 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X1),X1))) ) | ~spl854_46),
% 92.92/13.70 inference(avatar_component_clause,[],[f22121])).
% 92.92/13.70 thf(f66928,plain,(
% 92.92/13.70 spl854_679),
% 92.92/13.70 inference(avatar_split_clause,[],[f15505,f66926])).
% 92.92/13.70 thf(f66926,plain,(
% 92.92/13.70 spl854_679 <=> ! [X0 : $tType,X4 : X0,X3 : tyop_2Enum_2Enum > X0 > X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X3),X4),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X4)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_679])])).
% 92.92/13.70 thf(f15505,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X3 : tyop_2Enum_2Enum > X0 > X0,X4 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X3),X4),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X4)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f13068,f9122])).
% 92.92/13.70 thf(f13068,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X3 : tyop_2Enum_2Enum > X0 > X0,X4 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X3),X4),c_2Enum_2E0) = X4)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5345])).
% 92.92/13.70 thf(f5345,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum > X0 > X0,X4 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X3),X4),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X2),X1)) = vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X3),vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X3,X2),X4)),X1)) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X3),X4),c_2Enum_2E0) = X4))),
% 92.92/13.70 inference(rectify,[],[f1690])).
% 92.92/13.70 thf(f1690,axiom,(
% 92.92/13.70 ! [X0 : $tType,X6 : tyop_2Enum_2Enum,X462 : tyop_2Enum_2Enum,X114 : tyop_2Enum_2Enum > X0 > X0,X123 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X114),X123),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X462),X6)) = vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X114),vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X114,X462),X123)),X6)) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),c_2Enumpair_2Enfoldl(X0),X114),X123),c_2Enum_2E0) = X123))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enfoldl__thm)).
% 92.92/13.70 thf(f66924,plain,(
% 92.92/13.70 spl854_678),
% 92.92/13.70 inference(avatar_split_clause,[],[f15298,f66922])).
% 92.92/13.70 thf(f66922,plain,(
% 92.92/13.70 spl854_678 <=> ! [X0 : $tType,X2 : tyop_2Enum_2Enum > X0 > X0,X1 : X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_678])])).
% 92.92/13.70 thf(f15298,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : tyop_2Enum_2Enum > X0 > X0,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f12363,f9122])).
% 92.92/13.70 thf(f12363,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : tyop_2Enum_2Enum > X0 > X0,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),c_2Enum_2E0) = X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8431])).
% 92.92/13.70 thf(f8431,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : tyop_2Enum_2Enum > X0 > X0] : (! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X4)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X2,X4),vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),X4))) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),c_2Enum_2E0) = X1))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK635])],[f5254,f8430])).
% 92.92/13.70 thf(f8430,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : tyop_2Enum_2Enum > X0 > X0] : (? [X3 : tyop_2Enum_2Enum > X0] : (! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,X3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X4)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X2,X4),vAPP(tyop_2Enum_2Enum,X0,X3,X4))) & (vAPP(tyop_2Enum_2Enum,X0,X3,c_2Enum_2E0) = X1)) => (! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X4)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X2,X4),vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),X4))) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(X0,sTfun(tyop_2Enum_2Enum,X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),sTfun(X0,sTfun(tyop_2Enum_2Enum,X0)),sK635(X0),X2),X1),c_2Enum_2E0) = X1)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f5254,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : tyop_2Enum_2Enum > X0 > X0] : ? [X3 : tyop_2Enum_2Enum > X0] : (! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,X3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X4)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X2,X4),vAPP(tyop_2Enum_2Enum,X0,X3,X4))) & (vAPP(tyop_2Enum_2Enum,X0,X3,c_2Enum_2E0) = X1))),
% 92.92/13.70 inference(rectify,[],[f901])).
% 92.92/13.70 thf(f901,axiom,(
% 92.92/13.70 ! [X0 : $tType,X90 : X0,X25 : tyop_2Enum_2Enum > X0 > X0] : ? [X78 : tyop_2Enum_2Enum > X0] : (! [X298 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,X78,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X298)) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),X25,X298),vAPP(tyop_2Enum_2Enum,X0,X78,X298))) & (vAPP(tyop_2Enum_2Enum,X0,X78,c_2Enum_2E0) = X90))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2Enum__Axiom)).
% 92.92/13.70 thf(f66920,plain,(
% 92.92/13.70 spl854_677),
% 92.92/13.70 inference(avatar_split_clause,[],[f14976,f66918])).
% 92.92/13.70 thf(f66918,plain,(
% 92.92/13.70 spl854_677 <=> ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X1),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_677])])).
% 92.92/13.70 thf(f14976,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X1),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X1)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11348,f9122])).
% 92.92/13.70 thf(f11348,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > X0,X1 : X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X1),X2),c_2Enum_2E0) = X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5215])).
% 92.92/13.70 thf(f5215,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : X0 > X0] : (! [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X1),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)) = vAPP(X0,X0,X2,vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X1),X2),X3))) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X1),X2),c_2Enum_2E0) = X1))),
% 92.92/13.70 inference(rectify,[],[f896])).
% 92.92/13.70 thf(f896,axiom,(
% 92.92/13.70 ! [X0 : $tType,X8 : X0,X25 : X0 > X0] : (! [X104 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X8),X25),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X104)) = vAPP(X0,X0,X25,vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X8),X25),X104))) & (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eprim__rec_2ESIMP__REC(X0),X8),X25),c_2Enum_2E0) = X8))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ESIMP__REC__THM)).
% 92.92/13.70 thf(f66916,plain,(
% 92.92/13.70 spl854_676),
% 92.92/13.70 inference(avatar_split_clause,[],[f13810,f66914])).
% 92.92/13.70 thf(f66914,plain,(
% 92.92/13.70 spl854_676 <=> ! [X0 : $tType,X4 : X0,X5 : tyop_2Enum_2Enum > X0] : (vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X4),X5),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X4)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_676])])).
% 92.92/13.70 thf(f13810,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X4 : X0,X5 : tyop_2Enum_2Enum > X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X4),X5),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X4)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9504,f9122])).
% 92.92/13.70 thf(f9504,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X4 : X0,X5 : tyop_2Enum_2Enum > X0] : ((vAPP(tyop_2Enum_2Enum,X0,vAPP(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0),vAPP(X0,sTfun(sTfun(tyop_2Enum_2Enum,X0),sTfun(tyop_2Enum_2Enum,X0)),c_2Eind__type_2EFCONS(X0),X4),X5),c_2Enum_2E0) = X4)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4942])).
% 92.92/13.70 thf(f66912,plain,(
% 92.92/13.70 spl854_675),
% 92.92/13.70 inference(avatar_split_clause,[],[f12173,f66910])).
% 92.92/13.70 thf(f66910,plain,(
% 92.92/13.70 spl854_675 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > X0] : (($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_675])])).
% 92.92/13.70 thf(f12173,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > X0] : (($true = vAPP(sTfun(X0,sTfun(X0,X0)),$o,c_2Ecombin_2EASSOC(X0),X1)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,$o),c_2Ecombin_2EMONOID(X0),X1),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8287])).
% 92.92/13.70 thf(f66908,plain,(
% 92.92/13.70 spl854_674),
% 92.92/13.70 inference(avatar_split_clause,[],[f11999,f66906])).
% 92.92/13.70 thf(f66906,plain,(
% 92.92/13.70 spl854_674 <=> ! [X0 : $tType,X5 : X0,X2 : X0 > $o,X1 : $o] : (($true = X1) | ($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK542(X0),X2),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_674])])).
% 92.92/13.70 thf(f11999,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X5 : X0] : (($true = X1) | ($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK542(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8089])).
% 92.92/13.70 thf(f8089,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = X1) | ($true = vAPP(X0,$o,X2,X3))) | (($true != X1) & ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK541(X0),X2))))) & (($true = X1) | ! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | (($true != X1) & ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK542(X0),X2),X1))))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK541,sK542])],[f8086,f8088,f8087])).
% 92.92/13.70 thf(f8087,plain,(
% 92.92/13.70 ! [X0 : $tType,X2 : X0 > $o] : (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) => ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK541(X0),X2))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8088,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X6 : X0] : (($true != X1) & ($true != vAPP(X0,$o,X2,X6))) => (($true != X1) & ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK542(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8086,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = X1) | ($true = vAPP(X0,$o,X2,X3))) | (($true != X1) & ? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)))) & (($true = X1) | ! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ? [X6 : X0] : (($true != X1) & ($true != vAPP(X0,$o,X2,X6)))))),
% 92.92/13.70 inference(rectify,[],[f8085])).
% 92.92/13.70 thf(f8085,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = X1) | ($true = vAPP(X0,$o,X2,X3))) | (($true != X1) & ? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)))) & (($true = X1) | ! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ? [X3 : X0] : (($true != X1) & ($true != vAPP(X0,$o,X2,X3)))))),
% 92.92/13.70 inference(flattening,[],[f8084])).
% 92.92/13.70 thf(f8084,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = X1) | ($true = vAPP(X0,$o,X2,X3))) | (($true != X1) & ? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)))) & ((($true = X1) | ! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4))) | ? [X3 : X0] : (($true != X1) & ($true != vAPP(X0,$o,X2,X3)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3980])).
% 92.92/13.70 thf(f3980,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = X1) | ($true = vAPP(X0,$o,X2,X3))) <=> (($true = X1) | ! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4))))),
% 92.92/13.70 inference(fool_elimination,[],[f3979])).
% 92.92/13.70 thf(f3979,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (X1 | vAPP(X0,$o,X2,X3)) <=> (X1 | ! [X4 : X0] : vAPP(X0,$o,X2,X4)))),
% 92.92/13.70 inference(rectify,[],[f100])).
% 92.92/13.70 thf(f100,axiom,(
% 92.92/13.70 ! [X0 : $tType,X42 : $o,X43 : X0 > $o] : (! [X19 : X0] : (X42 | vAPP(X0,$o,X43,X19)) <=> (X42 | ! [X15 : X0] : vAPP(X0,$o,X43,X15)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__OR__THM)).
% 92.92/13.70 thf(f66904,plain,(
% 92.92/13.70 spl854_673),
% 92.92/13.70 inference(avatar_split_clause,[],[f11996,f66902])).
% 92.92/13.70 thf(f66902,plain,(
% 92.92/13.70 spl854_673 <=> ! [X0 : $tType,X5 : X0,X2 : X0 > $o,X1 : $o] : (($true = vAPP(X0,$o,X2,X5)) | ($true = X1) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK540(X0),X2),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_673])])).
% 92.92/13.70 thf(f11996,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true = X1) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK540(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8083])).
% 92.92/13.70 thf(f8083,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK539(X0),X2))) & ($true != X1))) & (! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ($true = X1) | (($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK540(X0),X2),X1))) & ($true != X1))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK539,sK540])],[f8080,f8082,f8081])).
% 92.92/13.70 thf(f8081,plain,(
% 92.92/13.70 ! [X0 : $tType,X2 : X0 > $o] : (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) => ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK539(X0),X2))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8082,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true != X1)) => (($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK540(X0),X2),X1))) & ($true != X1)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8080,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & (! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ($true = X1) | ? [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true != X1))))),
% 92.92/13.70 inference(rectify,[],[f8079])).
% 92.92/13.70 thf(f8079,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & (! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true = X1) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true != X1))))),
% 92.92/13.70 inference(flattening,[],[f8078])).
% 92.92/13.70 thf(f8078,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & ((! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true = X1)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true != X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3978])).
% 92.92/13.70 thf(f3978,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) <=> (! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true = X1)))),
% 92.92/13.70 inference(fool_elimination,[],[f3977])).
% 92.92/13.70 thf(f3977,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X2,X3) | X1) <=> (! [X4 : X0] : vAPP(X0,$o,X2,X4) | X1))),
% 92.92/13.70 inference(rectify,[],[f101])).
% 92.92/13.70 thf(f101,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : $o,X41 : X0 > $o] : (! [X19 : X0] : (vAPP(X0,$o,X41,X19) | X7) <=> (! [X15 : X0] : vAPP(X0,$o,X41,X15) | X7))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__OR__THM)).
% 92.92/13.70 thf(f66900,plain,(
% 92.92/13.70 spl854_672),
% 92.92/13.70 inference(avatar_split_clause,[],[f11956,f66898])).
% 92.92/13.70 thf(f66898,plain,(
% 92.92/13.70 spl854_672 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) | ($true = X0) | ($true = X1) | ($true = X2))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_672])])).
% 92.92/13.70 thf(f11956,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) | ($true = X0) | ($true = X1) | ($true = X2)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8048])).
% 92.92/13.70 thf(f8048,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) | (((($true != X0) & ($true != X1)) | ($true != X2)) & (($true = X0) | ($true = X1) | ($true = X2)))) & (((($true = X2) | (($true != X0) & ($true != X1))) & (($true = X0) | ($true = X1) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0))))),
% 92.92/13.70 inference(flattening,[],[f8047])).
% 92.92/13.70 thf(f8047,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) | (((($true != X0) & ($true != X1)) | ($true != X2)) & ((($true = X0) | ($true = X1)) | ($true = X2)))) & (((($true = X2) | (($true != X0) & ($true != X1))) & ((($true = X0) | ($true = X1)) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6466])).
% 92.92/13.70 thf(f6466,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) <=> (($true = X2) <=> (($true = X0) | ($true = X1))))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66896,plain,(
% 92.92/13.70 spl854_671),
% 92.92/13.70 inference(avatar_split_clause,[],[f11919,f66894])).
% 92.92/13.70 thf(f66894,plain,(
% 92.92/13.70 spl854_671 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_671])])).
% 92.92/13.70 thf(f11919,plain,(
% 92.92/13.70 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8034])).
% 92.92/13.70 thf(f8034,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)) | (($true != X0) & ($true != X1) & ($true != X2))) & (($true = X0) | ($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))))),
% 92.92/13.70 inference(flattening,[],[f8033])).
% 92.92/13.70 thf(f8033,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)) | (($true != X0) & ($true != X1) & ($true != X2))) & ((($true = X0) | ($true = X1) | ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6456])).
% 92.92/13.70 thf(f6456,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)) <=> (($true = X0) | ($true = X1) | ($true = X2)))),
% 92.92/13.70 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.70 thf(f66892,plain,(
% 92.92/13.70 spl854_670),
% 92.92/13.70 inference(avatar_split_clause,[],[f11863,f66890])).
% 92.92/13.70 thf(f66890,plain,(
% 92.92/13.70 spl854_670 <=> ! [X0 : $tType,X6 : X0,X2 : X0 > $o,X1 : $o] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK532(X0),X2),X1))) | ($true = X1) | ($true != vAPP(X0,$o,X2,X6)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_670])])).
% 92.92/13.70 thf(f11863,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X6 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK532(X0),X2),X1))) | ($true = X1) | ($true != vAPP(X0,$o,X2,X6))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8007])).
% 92.92/13.70 thf(f8007,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK531(X0),X2))) | ($true = X1) | ! [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & ((($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK532(X0),X2),X1))) | ($true = X1)) | (! [X6 : X0] : ($true != vAPP(X0,$o,X2,X6)) & ($true != X1))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK531,sK532])],[f8004,f8006,f8005])).
% 92.92/13.70 thf(f8005,plain,(
% 92.92/13.70 ! [X0 : $tType,X2 : X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) => ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK531(X0),X2))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8006,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true = X1)) => (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK532(X0),X2),X1))) | ($true = X1)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8004,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) | ($true = X1) | ! [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & (? [X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true = X1)) | (! [X6 : X0] : ($true != vAPP(X0,$o,X2,X6)) & ($true != X1))))),
% 92.92/13.70 inference(rectify,[],[f8003])).
% 92.92/13.70 thf(f8003,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) | ($true = X1) | ! [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & (? [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true = X1)) | (! [X3 : X0] : ($true != vAPP(X0,$o,X2,X3)) & ($true != X1))))),
% 92.92/13.70 inference(flattening,[],[f8002])).
% 92.92/13.70 thf(f8002,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((? [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true != X1))) & (? [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true = X1)) | (! [X3 : X0] : ($true != vAPP(X0,$o,X2,X3)) & ($true != X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3954])).
% 92.92/13.70 thf(f3954,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) | ($true = X1)) <=> ? [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true = X1)))),
% 92.92/13.70 inference(fool_elimination,[],[f3953])).
% 92.92/13.70 thf(f3953,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : vAPP(X0,$o,X2,X3) | X1) <=> ? [X4 : X0] : (vAPP(X0,$o,X2,X4) | X1))),
% 92.92/13.70 inference(rectify,[],[f95])).
% 92.92/13.70 thf(f95,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : $o,X41 : X0 > $o] : ((? [X19 : X0] : vAPP(X0,$o,X41,X19) | X7) <=> ? [X15 : X0] : (vAPP(X0,$o,X41,X15) | X7))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__EXISTS__THM)).
% 92.92/13.70 thf(f66835,plain,(
% 92.92/13.70 spl854_669),
% 92.92/13.70 inference(avatar_split_clause,[],[f10795,f66833])).
% 92.92/13.70 thf(f66833,plain,(
% 92.92/13.70 spl854_669 <=> ! [X0 : $tType,X1 : X0 > X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_669])])).
% 92.92/13.70 thf(f10795,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7401])).
% 92.92/13.70 thf(f7401,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK362(X0),X1)))) & (! [X3 : X0] : ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK362])],[f7399,f7400])).
% 92.92/13.70 thf(f7400,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0] : ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) => ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK362(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7399,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ? [X2 : X0] : ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2))) & (! [X3 : X0] : ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))))),
% 92.92/13.70 inference(rectify,[],[f7398])).
% 92.92/13.70 thf(f7398,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ? [X2 : X0] : ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2))) & (! [X2 : X0] : ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3194])).
% 92.92/13.70 thf(f3194,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ! [X2 : X0] : ($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f3193])).
% 92.92/13.70 thf(f3193,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) <=> ! [X2 : X0] : vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X1),X2))),
% 92.92/13.70 inference(rectify,[],[f577])).
% 92.92/13.70 thf(f577,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) <=> ! [X4 : X0] : vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),c_2Erelation_2EWFP(X0),X143),X4))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__EQ__WFP)).
% 92.92/13.70 thf(f66831,plain,(
% 92.92/13.70 spl854_668),
% 92.92/13.70 inference(avatar_split_clause,[],[f10205,f66829])).
% 92.92/13.70 thf(f66829,plain,(
% 92.92/13.70 spl854_668 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_668])])).
% 92.92/13.70 thf(f10205,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5555])).
% 92.92/13.70 thf(f5555,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.70 inference(flattening,[],[f5554])).
% 92.92/13.70 thf(f5554,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))))),
% 92.92/13.70 inference(ennf_transformation,[],[f2654])).
% 92.92/13.70 thf(f2654,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))) => (X0 = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2653])).
% 92.92/13.70 thf(f2653,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1) & vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1) & vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) => (X0 = X1))),
% 92.92/13.70 inference(rectify,[],[f1486])).
% 92.92/13.70 thf(f1486,axiom,(
% 92.92/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X134),X137) & vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X137) & vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X134)) => (X134 = X137))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2Eprime__divides__only__self)).
% 92.92/13.70 thf(f66628,plain,(
% 92.92/13.70 spl854_667 | ~spl854_580 | ~spl854_615),
% 92.92/13.70 inference(avatar_split_clause,[],[f61178,f60316,f57833,f66625])).
% 92.92/13.70 thf(f66625,plain,(
% 92.92/13.70 spl854_667 <=> ($false = vAPP(sTfun($o,$o),$o,sK378($o),vNOT))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_667])])).
% 92.92/13.70 thf(f57833,plain,(
% 92.92/13.70 spl854_580 <=> ($false = vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_580])])).
% 92.92/13.70 thf(f60316,plain,(
% 92.92/13.70 spl854_615 <=> ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK378(X0),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_615])])).
% 92.92/13.70 thf(f61178,plain,(
% 92.92/13.70 ($false = vAPP(sTfun($o,$o),$o,sK378($o),vNOT)) | (~spl854_580 | ~spl854_615)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61177])).
% 92.92/13.70 thf(f61177,plain,(
% 92.92/13.70 ($true = $false) | ($false = vAPP(sTfun($o,$o),$o,sK378($o),vNOT)) | (~spl854_580 | ~spl854_615)),
% 92.92/13.70 inference(forward_demodulation,[],[f61163,f57835])).
% 92.92/13.70 thf(f57835,plain,(
% 92.92/13.70 ($false = vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT)) | ~spl854_580),
% 92.92/13.70 inference(avatar_component_clause,[],[f57833])).
% 92.92/13.70 thf(f61163,plain,(
% 92.92/13.70 ($true = vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT)) | ($false = vAPP(sTfun($o,$o),$o,sK378($o),vNOT)) | ~spl854_615),
% 92.92/13.70 inference(not_proxy_clausification,[],[f61162])).
% 92.92/13.70 thf(f61162,plain,(
% 92.92/13.70 ($true = vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK378($o),vNOT))) | ~spl854_615),
% 92.92/13.70 inference(not_proxy_clausification,[],[f60882])).
% 92.92/13.70 thf(f60882,plain,(
% 92.92/13.70 ($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT))) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK378($o),vNOT))) | ~spl854_615),
% 92.92/13.70 inference(primitive_instantiation,[],[f60317])).
% 92.92/13.70 thf(f60317,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK378(X0),X1)))) ) | ~spl854_615),
% 92.92/13.70 inference(avatar_component_clause,[],[f60316])).
% 92.92/13.70 thf(f62384,plain,(
% 92.92/13.70 ~spl854_666 | ~spl854_44 | ~spl854_628),
% 92.92/13.70 inference(avatar_split_clause,[],[f62084,f60436,f22112,f62381])).
% 92.92/13.70 thf(f62381,plain,(
% 92.92/13.70 spl854_666 <=> (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) = vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$false))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_666])])).
% 92.92/13.70 thf(f60436,plain,(
% 92.92/13.70 spl854_628 <=> ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_628])])).
% 92.92/13.70 thf(f62084,plain,(
% 92.92/13.70 (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$false)) | (~spl854_44 | ~spl854_628)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f62005])).
% 92.92/13.70 thf(f62005,plain,(
% 92.92/13.70 ($true = $false) | (vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124) != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$false)) | (~spl854_44 | ~spl854_628)),
% 92.92/13.70 inference(constrained_superposition,[],[f60437,f22114])).
% 92.92/13.70 thf(f60437,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))) ) | ~spl854_628),
% 92.92/13.70 inference(avatar_component_clause,[],[f60436])).
% 92.92/13.70 thf(f62321,plain,(
% 92.92/13.70 spl854_665 | ~spl854_70 | ~spl854_146),
% 92.92/13.70 inference(avatar_split_clause,[],[f31296,f22890,f22294,f62319])).
% 92.92/13.70 thf(f62319,plain,(
% 92.92/13.70 spl854_665 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_665])])).
% 92.92/13.70 thf(f22294,plain,(
% 92.92/13.70 spl854_70 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_70])])).
% 92.92/13.70 thf(f22890,plain,(
% 92.92/13.70 spl854_146 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_146])])).
% 92.92/13.70 thf(f31296,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) ) | (~spl854_70 | ~spl854_146)),
% 92.92/13.70 inference(forward_demodulation,[],[f18311,f23002])).
% 92.92/13.70 thf(f23002,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) ) | (~spl854_70 | ~spl854_146)),
% 92.92/13.70 inference(superposition,[],[f22891,f22295])).
% 92.92/13.70 thf(f22295,plain,(
% 92.92/13.70 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) ) | ~spl854_70),
% 92.92/13.70 inference(avatar_component_clause,[],[f22294])).
% 92.92/13.70 thf(f22891,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) ) | ~spl854_146),
% 92.92/13.70 inference(avatar_component_clause,[],[f22890])).
% 92.92/13.70 thf(f18311,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18310,f9370])).
% 92.92/13.70 thf(f18310,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f9397,f9165])).
% 92.92/13.70 thf(f9397,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4925])).
% 92.92/13.70 thf(f62317,plain,(
% 92.92/13.70 spl854_664),
% 92.92/13.70 inference(avatar_split_clause,[],[f19948,f62315])).
% 92.92/13.70 thf(f62315,plain,(
% 92.92/13.70 spl854_664 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_664])])).
% 92.92/13.70 thf(f19948,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19947,f18124])).
% 92.92/13.70 thf(f19947,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f19946,f13563])).
% 92.92/13.70 thf(f19946,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f16488,f13548])).
% 92.92/13.70 thf(f16488,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1),X0))) )),
% 92.92/13.70 inference(equality_resolution,[],[f15247])).
% 92.92/13.70 thf(f15247,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X2)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f12294,f13512])).
% 92.92/13.70 thf(f12294,plain,(
% 92.92/13.70 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP62,X2),X1),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X2)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8373])).
% 92.92/13.70 thf(f62313,plain,(
% 92.92/13.70 spl854_663),
% 92.92/13.70 inference(avatar_split_clause,[],[f19565,f62311])).
% 92.92/13.70 thf(f62311,plain,(
% 92.92/13.70 spl854_663 <=> ! [X0 : $tType,X1 : X0] : (vAPP(tyop_2Eone_2Eone,X0,vAPP(X0,sTfun(tyop_2Eone_2Eone,X0),sK387(X0),X1),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))) = X1)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_663])])).
% 92.92/13.70 thf(f19565,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(tyop_2Eone_2Eone,X0,vAPP(X0,sTfun(tyop_2Eone_2Eone,X0),sK387(X0),X1),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),$true))) = X1)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14864,f18174])).
% 92.92/13.70 thf(f14864,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(tyop_2Eone_2Eone,X0,vAPP(X0,sTfun(tyop_2Eone_2Eone,X0),sK387(X0),X1),vAPP(sTfun(tyop_2Eone_2Eone,$o),tyop_2Eone_2Eone,c_2Emin_2E_40(tyop_2Eone_2Eone),vAPP($o,sTfun(tyop_2Eone_2Eone,$o),c_2Ecombin_2EK($o,tyop_2Eone_2Eone),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) = X1)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11178,f13522])).
% 92.92/13.70 thf(f11178,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0] : ((vAPP(tyop_2Eone_2Eone,X0,vAPP(X0,sTfun(tyop_2Eone_2Eone,X0),sK387(X0),X1),c_2Eone_2Eone) = X1)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7680])).
% 92.92/13.70 thf(f7680,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0] : (vAPP(tyop_2Eone_2Eone,X0,vAPP(X0,sTfun(tyop_2Eone_2Eone,X0),sK387(X0),X1),c_2Eone_2Eone) = X1)),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK387])],[f5129,f7679])).
% 92.92/13.70 thf(f7679,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0] : (? [X2 : tyop_2Eone_2Eone > X0] : (vAPP(tyop_2Eone_2Eone,X0,X2,c_2Eone_2Eone) = X1) => (vAPP(tyop_2Eone_2Eone,X0,vAPP(X0,sTfun(tyop_2Eone_2Eone,X0),sK387(X0),X1),c_2Eone_2Eone) = X1))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f5129,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0] : ? [X2 : tyop_2Eone_2Eone > X0] : (vAPP(tyop_2Eone_2Eone,X0,X2,c_2Eone_2Eone) = X1)),
% 92.92/13.70 inference(rectify,[],[f397])).
% 92.92/13.70 thf(f397,axiom,(
% 92.92/13.70 ! [X0 : $tType,X90 : X0] : ? [X138 : tyop_2Eone_2Eone > X0] : (vAPP(tyop_2Eone_2Eone,X0,X138,c_2Eone_2Eone) = X90)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eone_2Eone__prim__rec)).
% 92.92/13.70 thf(f62309,plain,(
% 92.92/13.70 spl854_662),
% 92.92/13.70 inference(avatar_split_clause,[],[f18573,f62307])).
% 92.92/13.70 thf(f62307,plain,(
% 92.92/13.70 spl854_662 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_662])])).
% 92.92/13.70 thf(f18573,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0)) )),
% 92.92/13.70 inference(forward_demodulation,[],[f17825,f18124])).
% 92.92/13.70 thf(f17825,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.70 inference(equality_proxy_clausification,[],[f17824])).
% 92.92/13.70 thf(f17824,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f14000])).
% 92.92/13.70 thf(f14000,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9752,f13512])).
% 92.92/13.70 thf(f9752,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK185,X0) != X0) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6794])).
% 92.92/13.70 thf(f62305,plain,(
% 92.92/13.70 spl854_661),
% 92.92/13.70 inference(avatar_split_clause,[],[f18341,f62302])).
% 92.92/13.70 thf(f62302,plain,(
% 92.92/13.70 spl854_661 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),$true)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_661])])).
% 92.92/13.70 thf(f18341,plain,(
% 92.92/13.70 (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),$true)))),
% 92.92/13.70 inference(forward_demodulation,[],[f13735,f13591])).
% 92.92/13.70 thf(f13735,plain,(
% 92.92/13.70 (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.70 inference(definition_unfolding,[],[f9412,f9122,f9976,f13514])).
% 92.92/13.70 thf(f9412,plain,(
% 92.92/13.70 (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),c_2Enum_2E0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),kCOMB,c_2Ebool_2ET)))),
% 92.92/13.70 inference(cnf_transformation,[],[f2112])).
% 92.92/13.70 thf(f2112,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),c_2Enum_2E0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),kCOMB,c_2Ebool_2ET))) & (c_2Eoption_2ENONE(tyop_2Enum_2Enum) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),kCOMB,c_2Ebool_2EF))) & (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Emin_2E_3D(tyop_2Enum_2Enum)),X0))))),
% 92.92/13.70 inference(fool_elimination,[],[f2111])).
% 92.92/13.70 thf(f2111,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X1 : tyop_2Enum_2Enum] : (c_2Ebool_2ET))) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),c_2Enum_2E0)) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X2 : tyop_2Enum_2Enum] : (c_2Ebool_2EF))) = c_2Eoption_2ENONE(tyop_2Enum_2Enum)) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0),X3)))) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0)) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X4),X0)))) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0)))),
% 92.92/13.70 inference(rectify,[],[f1432])).
% 92.92/13.70 thf(f1432,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X303 : tyop_2Enum_2Enum] : (c_2Ebool_2ET))) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),c_2Enum_2E0)) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X298 : tyop_2Enum_2Enum] : (c_2Ebool_2EF))) = c_2Eoption_2ENONE(tyop_2Enum_2Enum)) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X8),X135)))) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X8)) & (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,(^[X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X137),X8)))) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X8)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2EOLEAST__EQNS)).
% 92.92/13.70 thf(f62300,plain,(
% 92.92/13.70 spl854_660),
% 92.92/13.70 inference(avatar_split_clause,[],[f18340,f62298])).
% 92.92/13.70 thf(f62298,plain,(
% 92.92/13.70 spl854_660 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_660])])).
% 92.92/13.70 thf(f18340,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18339,f18124])).
% 92.92/13.70 thf(f18339,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18338,f13563])).
% 92.92/13.70 thf(f18338,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f13734,f13548])).
% 92.92/13.70 thf(f13734,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9405,f13512,f13512])).
% 92.92/13.70 thf(f9405,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4928])).
% 92.92/13.70 thf(f4928,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))),
% 92.92/13.70 inference(rectify,[],[f1201])).
% 92.92/13.70 thf(f1201,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X136) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X136)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEXP__1)).
% 92.92/13.70 thf(f62296,plain,(
% 92.92/13.70 spl854_659),
% 92.92/13.70 inference(avatar_split_clause,[],[f18334,f62294])).
% 92.92/13.70 thf(f62294,plain,(
% 92.92/13.70 spl854_659 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_659])])).
% 92.92/13.70 thf(f18334,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18333,f18124])).
% 92.92/13.70 thf(f18333,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18332,f13563])).
% 92.92/13.70 thf(f18332,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f13732,f13548])).
% 92.92/13.70 thf(f13732,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9403,f13512,f13512])).
% 92.92/13.70 thf(f9403,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4927])).
% 92.92/13.70 thf(f4927,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))),
% 92.92/13.70 inference(rectify,[],[f1581])).
% 92.92/13.70 thf(f1581,axiom,(
% 92.92/13.70 ! [X8 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X8),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X8)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__1)).
% 92.92/13.70 thf(f62292,plain,(
% 92.92/13.70 spl854_658),
% 92.92/13.70 inference(avatar_split_clause,[],[f18331,f62290])).
% 92.92/13.70 thf(f62290,plain,(
% 92.92/13.70 spl854_658 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_658])])).
% 92.92/13.70 thf(f18331,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18330,f18124])).
% 92.92/13.70 thf(f18330,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18329,f13563])).
% 92.92/13.70 thf(f18329,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f13731,f13548])).
% 92.92/13.70 thf(f13731,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9404,f13512,f13512])).
% 92.92/13.70 thf(f9404,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4927])).
% 92.92/13.70 thf(f62288,plain,(
% 92.92/13.70 spl854_657),
% 92.92/13.70 inference(avatar_split_clause,[],[f18313,f62286])).
% 92.92/13.70 thf(f62286,plain,(
% 92.92/13.70 spl854_657 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_657])])).
% 92.92/13.70 thf(f18313,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18312,f9385])).
% 92.92/13.70 thf(f9385,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4923])).
% 92.92/13.70 thf(f4923,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0))))),
% 92.92/13.70 inference(rectify,[],[f1388])).
% 92.92/13.70 thf(f1388,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO)) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X136))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiDUB__removal)).
% 92.92/13.70 thf(f18312,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f9396,f9164])).
% 92.92/13.70 thf(f9164,plain,(
% 92.92/13.70 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4841])).
% 92.92/13.70 thf(f9396,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4925])).
% 92.92/13.70 thf(f62284,plain,(
% 92.92/13.70 spl854_656),
% 92.92/13.70 inference(avatar_split_clause,[],[f18309,f62282])).
% 92.92/13.70 thf(f62282,plain,(
% 92.92/13.70 spl854_656 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_656])])).
% 92.92/13.70 thf(f18309,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f9398,f9164])).
% 92.92/13.70 thf(f9398,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4925])).
% 92.92/13.70 thf(f62280,plain,(
% 92.92/13.70 spl854_655),
% 92.92/13.70 inference(avatar_split_clause,[],[f17000,f62278])).
% 92.92/13.70 thf(f62278,plain,(
% 92.92/13.70 spl854_655 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : ((X2 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_655])])).
% 92.92/13.70 thf(f17000,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : ((X2 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3))) )),
% 92.92/13.70 inference(equality_proxy_clausification,[],[f16999])).
% 92.92/13.70 thf(f16999,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12856])).
% 92.92/13.70 thf(f12856,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8706])).
% 92.92/13.70 thf(f8706,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) & ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3))))),
% 92.92/13.70 inference(flattening,[],[f8705])).
% 92.92/13.70 thf(f8705,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3)) | (($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4478])).
% 92.92/13.70 thf(f4478,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3)) <=> (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.70 inference(fool_elimination,[],[f4477])).
% 92.92/13.70 thf(f4477,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X1),X2),X3) <=> (vAPP($o,$o,vNOT,(X2 = X3)) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))),
% 92.92/13.70 inference(rectify,[],[f443])).
% 92.92/13.70 thf(f443,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o,X73 : X0,X79 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESTRORD(X0),X143),X73),X79) <=> (vAPP($o,$o,vNOT,(X73 = X79)) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X73),X79)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ESTRORD)).
% 92.92/13.70 thf(f62276,plain,(
% 92.92/13.70 spl854_654),
% 92.92/13.70 inference(avatar_split_clause,[],[f16425,f62274])).
% 92.92/13.70 thf(f62274,plain,(
% 92.92/13.70 spl854_654 <=> ! [X0 : $tType,X4 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK572(X0),$true),X1))) | ($true != vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_654])])).
% 92.92/13.70 thf(f16425,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK572(X0),$true),X1))) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.92/13.70 inference(equality_resolution,[],[f12050])).
% 92.92/13.70 thf(f12050,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK572(X0),X2),X1))) | ($true != X2) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8166])).
% 92.92/13.70 thf(f8166,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK572(X0),X2),X1)))) | ($true != X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) & ((($true = X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK573(X0),X1)))) | ! [X6 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK572,sK573])],[f8163,f8165,f8164])).
% 92.92/13.70 thf(f8164,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X3))) => (($true = X2) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK572(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8165,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK573(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8163,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((? [X3 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X3))) | ($true != X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) & ((($true = X2) & ? [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ! [X6 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X6)))))),
% 92.92/13.70 inference(rectify,[],[f8162])).
% 92.92/13.70 thf(f8162,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((? [X3 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X3))) | ($true != X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) & ((($true = X2) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4))) | ! [X3 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(flattening,[],[f8161])).
% 92.92/13.70 thf(f8161,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((? [X3 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X3))) | (($true != X2) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4)))) & ((($true = X2) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4))) | ! [X3 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4012])).
% 92.92/13.70 thf(f4012,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X3))) <=> (($true = X2) & ? [X4 : X0] : ($true = vAPP(X0,$o,X1,X4))))),
% 92.92/13.70 inference(fool_elimination,[],[f4011])).
% 92.92/13.70 thf(f4011,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X3 : X0] : (X2 & vAPP(X0,$o,X1,X3)) <=> (X2 & ? [X4 : X0] : vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 inference(rectify,[],[f97])).
% 92.92/13.70 thf(f97,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : (? [X19 : X0] : (X41 & vAPP(X0,$o,X7,X19)) <=> (X41 & ? [X15 : X0] : vAPP(X0,$o,X7,X15)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__AND__THM)).
% 92.92/13.70 thf(f62272,plain,(
% 92.92/13.70 spl854_653),
% 92.92/13.70 inference(avatar_split_clause,[],[f16230,f62270])).
% 92.92/13.70 thf(f62270,plain,(
% 92.92/13.70 spl854_653 <=> ! [X0 : $tType,X1 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK525(X0),$true),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_653])])).
% 92.92/13.70 thf(f16230,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK525(X0),$true),X1)))) )),
% 92.92/13.70 inference(equality_resolution,[],[f11813])).
% 92.92/13.70 thf(f11813,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK525(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7970])).
% 92.92/13.70 thf(f7970,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) & ! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) | (($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK525(X0),X2),X1))))) & (! [X5 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X5))) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK526(X0),X1)))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK525,sK526])],[f7967,f7969,f7968])).
% 92.92/13.70 thf(f7968,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X4 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X4))) => (($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK525(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7969,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK526(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7967,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) & ! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) | ? [X4 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X4)))) & (! [X5 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X5))) | ($true != X2) | ? [X6 : X0] : ($true != vAPP(X0,$o,X1,X6))))),
% 92.92/13.70 inference(rectify,[],[f7966])).
% 92.92/13.70 thf(f7966,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) & ! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) | ? [X4 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X4)))) & (! [X4 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X4))) | ($true != X2) | ? [X3 : X0] : ($true != vAPP(X0,$o,X1,X3))))),
% 92.92/13.70 inference(flattening,[],[f7965])).
% 92.92/13.70 thf(f7965,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((($true = X2) & ! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) | ? [X4 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X4)))) & (! [X4 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X4))) | (($true != X2) | ? [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3938])).
% 92.92/13.70 thf(f3938,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((($true = X2) & ! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3))) <=> ! [X4 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X4))))),
% 92.92/13.70 inference(fool_elimination,[],[f3937])).
% 92.92/13.70 thf(f3937,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((X2 & ! [X3 : X0] : vAPP(X0,$o,X1,X3)) <=> ! [X4 : X0] : (X2 & vAPP(X0,$o,X1,X4)))),
% 92.92/13.70 inference(rectify,[],[f91])).
% 92.92/13.70 thf(f91,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : ((X41 & ! [X19 : X0] : vAPP(X0,$o,X7,X19)) <=> ! [X15 : X0] : (X41 & vAPP(X0,$o,X7,X15)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__FORALL__THM)).
% 92.92/13.70 thf(f62268,plain,(
% 92.92/13.70 spl854_652),
% 92.92/13.70 inference(avatar_split_clause,[],[f16162,f62266])).
% 92.92/13.70 thf(f62266,plain,(
% 92.92/13.70 spl854_652 <=> ! [X0 : $tType,X11 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X11)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK400(X0),$true),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_652])])).
% 92.92/13.70 thf(f16162,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X11 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X11)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK400(X0),$true),X1)))) )),
% 92.92/13.70 inference(equality_resolution,[],[f11443])).
% 92.92/13.70 thf(f11443,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X11 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X11)) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK400(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7714])).
% 92.92/13.70 thf(f7714,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK396(X0),X2),X1))) | ($true != X2))) & (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) & ($true = X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK397(X0),X1))) | ($true != X2)) & ((($true = X2) & ! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) | (($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK398(X0),X2),X1))))) & (! [X9 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X9))) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK399(X0),X1)))) & (! [X11 : X0] : ($true = vAPP(X0,$o,X1,X11)) | ($true != X2) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK400(X0),X2),X1))) & ($true = X2))) & (! [X13 : X0] : (($true = vAPP(X0,$o,X1,X13)) | ($true != X2)) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK401(X0),X1))) & ($true = X2))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK396,sK397,sK398,sK399,sK400,sK401])],[f7707,f7713,f7712,f7711,f7710,f7709,f7708])).
% 92.92/13.70 thf(f7708,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2)) => (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK396(X0),X2),X1))) | ($true != X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7709,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK397(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7710,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X8 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X8))) => (($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK398(X0),X2),X1)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7711,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X10 : X0] : ($true != vAPP(X0,$o,X1,X10)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK399(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7712,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (? [X12 : X0] : (($true != vAPP(X0,$o,X1,X12)) & ($true = X2)) => (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK400(X0),X2),X1))) & ($true = X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7713,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X14 : X0] : ($true != vAPP(X0,$o,X1,X14)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK401(X0),X1))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f7707,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) & ($true = X2)) | ? [X6 : X0] : ($true != vAPP(X0,$o,X1,X6)) | ($true != X2)) & ((($true = X2) & ! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) | ? [X8 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X8)))) & (! [X9 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X9))) | ($true != X2) | ? [X10 : X0] : ($true != vAPP(X0,$o,X1,X10))) & (! [X11 : X0] : ($true = vAPP(X0,$o,X1,X11)) | ($true != X2) | ? [X12 : X0] : (($true != vAPP(X0,$o,X1,X12)) & ($true = X2))) & (! [X13 : X0] : (($true = vAPP(X0,$o,X1,X13)) | ($true != X2)) | (? [X14 : X0] : ($true != vAPP(X0,$o,X1,X14)) & ($true = X2))))),
% 92.92/13.70 inference(rectify,[],[f7706])).
% 92.92/13.70 thf(f7706,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & (! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2)) | ? [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)) | ($true != X2)) & ((($true = X2) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ? [X6 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X6)))) & (! [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6))) | ($true != X2) | ? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5))) & (! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) | ($true != X2) | ? [X8 : X0] : (($true != vAPP(X0,$o,X1,X8)) & ($true = X2))) & (! [X8 : X0] : (($true = vAPP(X0,$o,X1,X8)) | ($true != X2)) | (? [X7 : X0] : ($true != vAPP(X0,$o,X1,X7)) & ($true = X2))))),
% 92.92/13.70 inference(flattening,[],[f7705])).
% 92.92/13.70 thf(f7705,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : ((((! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true != X2))) & (! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2)) | (? [X3 : X0] : ($true != vAPP(X0,$o,X1,X3)) | ($true != X2)))) & (((($true = X2) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) | ? [X6 : X0] : (($true != X2) | ($true != vAPP(X0,$o,X1,X6)))) & (! [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6))) | (($true != X2) | ? [X5 : X0] : ($true != vAPP(X0,$o,X1,X5))))) & (((! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) | ($true != X2)) | ? [X8 : X0] : (($true != vAPP(X0,$o,X1,X8)) & ($true = X2))) & (! [X8 : X0] : (($true = vAPP(X0,$o,X1,X8)) | ($true != X2)) | (? [X7 : X0] : ($true != vAPP(X0,$o,X1,X7)) & ($true = X2)))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5827])).
% 92.92/13.70 thf(f5827,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) <=> ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2))) & ((($true = X2) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) <=> ! [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6)))) & ((! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7)) | ($true != X2)) <=> ! [X8 : X0] : (($true = vAPP(X0,$o,X1,X8)) | ($true != X2))))),
% 92.92/13.70 inference(ennf_transformation,[],[f3632])).
% 92.92/13.70 thf(f3632,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) & ($true = X2)) <=> ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) & ($true = X2))) & ((($true = X2) & ! [X5 : X0] : ($true = vAPP(X0,$o,X1,X5))) <=> ! [X6 : X0] : (($true = X2) & ($true = vAPP(X0,$o,X1,X6)))) & ((($true = X2) => ! [X7 : X0] : ($true = vAPP(X0,$o,X1,X7))) <=> ! [X8 : X0] : (($true = X2) => ($true = vAPP(X0,$o,X1,X8)))))),
% 92.92/13.70 inference(fool_elimination,[],[f3631])).
% 92.92/13.70 thf(f3631,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : $o] : (((! [X3 : X0] : vAPP(X0,$o,X1,X3) & X2) <=> ! [X4 : X0] : (vAPP(X0,$o,X1,X4) & X2)) & ((X2 & ! [X5 : X0] : vAPP(X0,$o,X1,X5)) <=> ! [X6 : X0] : (X2 & vAPP(X0,$o,X1,X6))) & ((X2 => ! [X7 : X0] : vAPP(X0,$o,X1,X7)) <=> ! [X8 : X0] : (X2 => vAPP(X0,$o,X1,X8))))),
% 92.92/13.70 inference(rectify,[],[f195])).
% 92.92/13.70 thf(f195,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X41 : $o] : (((! [X33 : X0] : vAPP(X0,$o,X7,X33) & X41) <=> ! [X93 : X0] : (vAPP(X0,$o,X7,X93) & X41)) & ((X41 & ! [X23 : X0] : vAPP(X0,$o,X7,X23)) <=> ! [X92 : X0] : (X41 & vAPP(X0,$o,X7,X92))) & ((X41 => ! [X19 : X0] : vAPP(X0,$o,X7,X19)) <=> ! [X15 : X0] : (X41 => vAPP(X0,$o,X7,X15))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EPULL__FORALL)).
% 92.92/13.70 thf(f62264,plain,(
% 92.92/13.70 spl854_651),
% 92.92/13.70 inference(avatar_split_clause,[],[f16159,f62262])).
% 92.92/13.70 thf(f62262,plain,(
% 92.92/13.70 spl854_651 <=> ! [X0 : $tType,X1 : X0 > $o,X7 : X0] : (($true = vAPP(X0,$o,X1,X7)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK398(X0),$true),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_651])])).
% 92.92/13.70 thf(f16159,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X7 : X0] : (($true = vAPP(X0,$o,X1,X7)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK398(X0),$true),X1)))) )),
% 92.92/13.70 inference(equality_resolution,[],[f11446])).
% 92.92/13.70 thf(f11446,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X7 : X0] : (($true = vAPP(X0,$o,X1,X7)) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK398(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7714])).
% 92.92/13.70 thf(f62260,plain,(
% 92.92/13.70 spl854_650),
% 92.92/13.70 inference(avatar_split_clause,[],[f16154,f62258])).
% 92.92/13.70 thf(f62258,plain,(
% 92.92/13.70 spl854_650 <=> ! [X0 : $tType,X1 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK396(X0),$true),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_650])])).
% 92.92/13.70 thf(f16154,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK396(X0),$true),X1)))) )),
% 92.92/13.70 inference(equality_resolution,[],[f11451])).
% 92.92/13.70 thf(f11451,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK396(X0),X2),X1))) | ($true != X2)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7714])).
% 92.92/13.70 thf(f62256,plain,(
% 92.92/13.70 spl854_649),
% 92.92/13.70 inference(avatar_split_clause,[],[f16151,f62254])).
% 92.92/13.70 thf(f62254,plain,(
% 92.92/13.70 spl854_649 <=> ! [X0 : $tType,X1 : X0 > $o,X10 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK393(X0),$true),X1))) | ($true != vAPP(X0,$o,X1,X10)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_649])])).
% 92.92/13.70 thf(f16151,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X10 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK393(X0),$true),X1))) | ($true != vAPP(X0,$o,X1,X10))) )),
% 92.92/13.70 inference(equality_resolution,[],[f11432])).
% 92.92/13.70 thf(f11432,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X10 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK393(X0),X2),X1))) | ($true != X2) | ($true != vAPP(X0,$o,X1,X10))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7704])).
% 92.92/13.70 thf(f62252,plain,(
% 92.92/13.70 spl854_648 | ~spl854_5 | spl854_631),
% 92.92/13.70 inference(avatar_split_clause,[],[f62206,f62001,f21881,f62250])).
% 92.92/13.70 thf(f62250,plain,(
% 92.92/13.70 spl854_648 <=> ! [X0 : $o] : ((sK124 != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),X0)) | ($false = X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_648])])).
% 92.92/13.70 thf(f62001,plain,(
% 92.92/13.70 spl854_631 <=> (sK124 = vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$true))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_631])])).
% 92.92/13.70 thf(f62206,plain,(
% 92.92/13.70 ( ! [X0 : $o] : ((sK124 != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),X0)) | ($false = X0)) ) | (~spl854_5 | spl854_631)),
% 92.92/13.70 inference(superposition,[],[f62003,f21882])).
% 92.92/13.70 thf(f62003,plain,(
% 92.92/13.70 (sK124 != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$true)) | spl854_631),
% 92.92/13.70 inference(avatar_component_clause,[],[f62001])).
% 92.92/13.70 thf(f62248,plain,(
% 92.92/13.70 spl854_647),
% 92.92/13.70 inference(avatar_split_clause,[],[f16146,f62246])).
% 92.92/13.70 thf(f62246,plain,(
% 92.92/13.70 spl854_647 <=> ! [X0 : $tType,X6 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK391(X0),$true),X1))) | ($true != vAPP(X0,$o,X1,X6)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_647])])).
% 92.92/13.70 thf(f16146,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X6 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK391(X0),$true),X1))) | ($true != vAPP(X0,$o,X1,X6))) )),
% 92.92/13.70 inference(equality_resolution,[],[f11437])).
% 92.92/13.70 thf(f11437,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X6 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK391(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X6)) | ($true != X2)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7704])).
% 92.92/13.70 thf(f62244,plain,(
% 92.92/13.70 spl854_646),
% 92.92/13.70 inference(avatar_split_clause,[],[f14082,f62242])).
% 92.92/13.70 thf(f62242,plain,(
% 92.92/13.70 spl854_646 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_646])])).
% 92.92/13.70 thf(f14082,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9863,f9122,f9122])).
% 92.92/13.70 thf(f9863,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X1),c_2Enum_2E0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4966])).
% 92.92/13.70 thf(f4966,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X0),X1),c_2Enum_2E0))),
% 92.92/13.70 inference(rectify,[],[f1742])).
% 92.92/13.70 thf(f1742,axiom,(
% 92.92/13.70 ! [X254 : tyop_2Enum_2Enum,X461 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITS,X254),X461),c_2Enum_2E0))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBITS__ZERO2)).
% 92.92/13.70 thf(f62240,plain,(
% 92.92/13.70 spl854_645),
% 92.92/13.70 inference(avatar_split_clause,[],[f14081,f62238])).
% 92.92/13.70 thf(f62238,plain,(
% 92.92/13.70 spl854_645 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X1),X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_645])])).
% 92.92/13.70 thf(f14081,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X1),X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9862,f9122,f9122])).
% 92.92/13.70 thf(f9862,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X1),X0),c_2Enum_2E0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4965])).
% 92.92/13.70 thf(f4965,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X1),X0),c_2Enum_2E0))),
% 92.92/13.70 inference(rectify,[],[f1768])).
% 92.92/13.70 thf(f1768,axiom,(
% 92.92/13.70 ! [X466 : tyop_2Enum_2Enum,X462 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESLICE,X462),X466),c_2Enum_2E0))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ESLICE__ZERO2)).
% 92.92/13.70 thf(f62236,plain,(
% 92.92/13.70 spl854_644),
% 92.92/13.70 inference(avatar_split_clause,[],[f13639,f62234])).
% 92.92/13.70 thf(f62234,plain,(
% 92.92/13.70 spl854_644 <=> ! [X6 : $o,X7 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X6),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X7))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_644])])).
% 92.92/13.70 thf(f13639,plain,(
% 92.92/13.70 ( ! [X6 : $o,X7 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X6),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X7))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9254,f13512,f13512])).
% 92.92/13.70 thf(f9254,plain,(
% 92.92/13.70 ( ! [X6 : $o,X7 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X6),c_2Earithmetic_2EZERO),X7))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4854])).
% 92.92/13.70 thf(f4854,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X0),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1)))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X1))))) & ! [X3 : $o,X4 : tyop_2Enum_2Enum,X5 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X3),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X4)),X5) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X3),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X5),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X4)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X4))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X4)))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X5),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X4)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X4))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X4))))) & ! [X6 : $o,X7 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X6),c_2Earithmetic_2EZERO),X7))),
% 92.92/13.70 inference(rectify,[],[f2044])).
% 92.92/13.70 thf(f2044,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X0),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1)))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X1))))) & ! [X7 : $o,X8 : tyop_2Enum_2Enum,X9 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X7),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X8)),X9) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X7),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X9),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X8)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X8))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X8)))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X9),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X8)),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Earithmetic_2EBIT1),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X8))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),bCOMB,c_2Enumeral_2EiDUB),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X8))))) & ! [X14 : $o,X15 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X14),c_2Earithmetic_2EZERO),X15))),
% 92.92/13.70 inference(fool_elimination,[],[f2043])).
% 92.92/13.70 thf(f2043,plain,(
% 92.92/13.70 ! [X0 : $o,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X0),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)),(^[X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1),X3))))),(^[X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1),X4)))))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)),(^[X5 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X1),X5))))),(^[X6 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X1),X6))))))) & ! [X7 : $o,X8 : tyop_2Enum_2Enum,X9 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X7),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X8)),X9) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X7),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X9),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X8)),(^[X10 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X8),X10))))),(^[X11 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X8),X11)))))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X9),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X8)),(^[X12 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X8),X12))))),(^[X13 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X8),X13))))))) & ! [X14 : $o,X15 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X14),c_2Earithmetic_2EZERO),X15))),
% 92.92/13.70 inference(rectify,[],[f1370])).
% 92.92/13.70 thf(f1370,axiom,(
% 92.92/13.70 ! [X291 : $o,X352 : tyop_2Enum_2Enum,X220 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X291),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X352)),X220) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X291),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X220),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X352)),(^[X353 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X352),X353))))),(^[X354 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X352),X354)))))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X220),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X352)),(^[X355 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X352),X355))))),(^[X356 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X352),X356))))))) & ! [X79 : $o,X298 : tyop_2Enum_2Enum,X23 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X79),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X298)),X23) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),X79),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X23),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X298)),(^[X309 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X298),X309))))),(^[X349 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X298),X349)))))),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases(tyop_2Enum_2Enum),X23),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X298)),(^[X350 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X298),X350))))),(^[X351 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2EF),X298),X351))))))) & ! [X35 : $o,X4 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,X35),c_2Earithmetic_2EZERO),X4))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiSUB__DEF)).
% 92.92/13.70 thf(f62232,plain,(
% 92.92/13.70 spl854_643),
% 92.92/13.70 inference(avatar_split_clause,[],[f13568,f62230])).
% 92.92/13.70 thf(f62230,plain,(
% 92.92/13.70 spl854_643 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_643])])).
% 92.92/13.70 thf(f13568,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,X0)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9171,f9121])).
% 92.92/13.70 thf(f9171,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4842])).
% 92.92/13.70 thf(f62225,plain,(
% 92.92/13.70 spl854_642 | ~spl854_24 | ~spl854_641),
% 92.92/13.70 inference(avatar_split_clause,[],[f62220,f62216,f22014,f62222])).
% 92.92/13.70 thf(f62222,plain,(
% 92.92/13.70 spl854_642 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),$true)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_642])])).
% 92.92/13.70 thf(f22014,plain,(
% 92.92/13.70 spl854_24 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_24])])).
% 92.92/13.70 thf(f62216,plain,(
% 92.92/13.70 spl854_641 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_641])])).
% 92.92/13.70 thf(f62220,plain,(
% 92.92/13.70 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),$true))) | (~spl854_24 | ~spl854_641)),
% 92.92/13.70 inference(forward_demodulation,[],[f62218,f22016])).
% 92.92/13.70 thf(f22016,plain,(
% 92.92/13.70 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_24),
% 92.92/13.70 inference(avatar_component_clause,[],[f22014])).
% 92.92/13.70 thf(f62218,plain,(
% 92.92/13.70 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) | ~spl854_641),
% 92.92/13.70 inference(avatar_component_clause,[],[f62216])).
% 92.92/13.70 thf(f62219,plain,(
% 92.92/13.70 spl854_641),
% 92.92/13.70 inference(avatar_split_clause,[],[f13551,f62216])).
% 92.92/13.70 thf(f13551,plain,(
% 92.92/13.70 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),c_2Ecombin_2EK($o,tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.70 inference(definition_unfolding,[],[f9140,f9122,f9976,f13514])).
% 92.92/13.70 thf(f9140,plain,(
% 92.92/13.70 (c_2Enum_2E0 = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),kCOMB,c_2Ebool_2ET)))),
% 92.92/13.70 inference(cnf_transformation,[],[f2026])).
% 92.92/13.70 thf(f2026,plain,(
% 92.92/13.70 (c_2Enum_2E0 = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP($o,sTfun(tyop_2Enum_2Enum,$o),kCOMB,c_2Ebool_2ET)))),
% 92.92/13.70 inference(fool_elimination,[],[f2025])).
% 92.92/13.70 thf(f2025,plain,(
% 92.92/13.70 (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X0 : tyop_2Enum_2Enum] : (c_2Ebool_2ET))) = c_2Enum_2E0)),
% 92.92/13.70 inference(rectify,[],[f1430])).
% 92.92/13.70 thf(f1430,axiom,(
% 92.92/13.70 (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,(^[X8 : tyop_2Enum_2Enum] : (c_2Ebool_2ET))) = c_2Enum_2E0)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2ELEAST__T)).
% 92.92/13.70 thf(f62214,plain,(
% 92.92/13.70 spl854_640),
% 92.92/13.70 inference(avatar_split_clause,[],[f12039,f62212])).
% 92.92/13.70 thf(f62212,plain,(
% 92.92/13.70 spl854_640 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_640])])).
% 92.92/13.70 thf(f12039,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8152])).
% 92.92/13.70 thf(f8152,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1) = X2)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | (X2 != X4))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK569])],[f8150,f8151])).
% 92.92/13.70 thf(f8151,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) => (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1) = X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8150,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | (X2 != X4))))),
% 92.92/13.70 inference(rectify,[],[f8149])).
% 92.92/13.70 thf(f8149,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ! [X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) | (X2 != X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4006])).
% 92.92/13.70 thf(f4006,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) <=> ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f4005])).
% 92.92/13.70 thf(f4005,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (vAPP(X0,$o,X1,X3) & (X2 = X3)) <=> vAPP(X0,$o,X1,X2))),
% 92.92/13.70 inference(rectify,[],[f159])).
% 92.92/13.70 thf(f159,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X73 : X0] : (? [X19 : X0] : (vAPP(X0,$o,X7,X19) & (X19 = X73)) <=> vAPP(X0,$o,X7,X73))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__THM1)).
% 92.92/13.70 thf(f62210,plain,(
% 92.92/13.70 spl854_639),
% 92.92/13.70 inference(avatar_split_clause,[],[f12036,f62208])).
% 92.92/13.70 thf(f62208,plain,(
% 92.92/13.70 spl854_639 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_639])])).
% 92.92/13.70 thf(f12036,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8148])).
% 92.92/13.70 thf(f8148,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1) = X2)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | (X2 != X4))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK568])],[f8146,f8147])).
% 92.92/13.70 thf(f8147,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) => (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1) = X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8146,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | (X2 != X4))))),
% 92.92/13.70 inference(rectify,[],[f8145])).
% 92.92/13.70 thf(f8145,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ! [X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) | (X2 != X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f4004])).
% 92.92/13.70 thf(f4004,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) & (X2 = X3)) <=> ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f4003])).
% 92.92/13.70 thf(f4003,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X3 : X0] : (vAPP(X0,$o,X1,X3) & (X2 = X3)) <=> vAPP(X0,$o,X1,X2))),
% 92.92/13.70 inference(rectify,[],[f160])).
% 92.92/13.70 thf(f160,axiom,(
% 92.92/13.70 ! [X0 : $tType,X7 : X0 > $o,X73 : X0] : (? [X19 : X0] : (vAPP(X0,$o,X7,X19) & (X19 = X73)) <=> vAPP(X0,$o,X7,X73))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__THM2)).
% 92.92/13.70 thf(f62205,plain,(
% 92.92/13.70 spl854_638),
% 92.92/13.70 inference(avatar_split_clause,[],[f12007,f62203])).
% 92.92/13.70 thf(f62203,plain,(
% 92.92/13.70 spl854_638 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_638])])).
% 92.92/13.70 thf(f12007,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8097])).
% 92.92/13.70 thf(f8097,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1) = X2))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK544])],[f8095,f8096])).
% 92.92/13.70 thf(f8096,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) & (X2 = X4)) => (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1) = X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8095,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) & (X2 = X4))))),
% 92.92/13.70 inference(rectify,[],[f8094])).
% 92.92/13.70 thf(f8094,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) & (X2 = X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6053])).
% 92.92/13.70 thf(f6053,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) <=> ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 inference(ennf_transformation,[],[f3984])).
% 92.92/13.70 thf(f3984,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : ((X2 = X3) => ($true = vAPP(X0,$o,X1,X3))) <=> ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f3983])).
% 92.92/13.70 thf(f3983,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : ((X2 = X3) => vAPP(X0,$o,X1,X3)) <=> vAPP(X0,$o,X1,X2))),
% 92.92/13.70 inference(rectify,[],[f161])).
% 92.92/13.70 thf(f161,axiom,(
% 92.92/13.70 ! [X0 : $tType,X3 : X0 > $o,X74 : X0] : (! [X19 : X0] : ((X19 = X74) => vAPP(X0,$o,X3,X19)) <=> vAPP(X0,$o,X3,X74))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__FORALL__THM1)).
% 92.92/13.70 thf(f62201,plain,(
% 92.92/13.70 spl854_637),
% 92.92/13.70 inference(avatar_split_clause,[],[f12004,f62199])).
% 92.92/13.70 thf(f62199,plain,(
% 92.92/13.70 spl854_637 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_637])])).
% 92.92/13.70 thf(f12004,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f8093])).
% 92.92/13.70 thf(f8093,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1) = X2))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK543])],[f8091,f8092])).
% 92.92/13.70 thf(f8092,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) & (X2 = X4)) => (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1))) & (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1) = X2)))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f8091,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) & (X2 = X4))))),
% 92.92/13.70 inference(rectify,[],[f8090])).
% 92.92/13.70 thf(f8090,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) | ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) & (X2 = X3))))),
% 92.92/13.70 inference(nnf_transformation,[],[f6052])).
% 92.92/13.70 thf(f6052,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (X2 != X3)) <=> ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 inference(ennf_transformation,[],[f3982])).
% 92.92/13.70 thf(f3982,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : ((X2 = X3) => ($true = vAPP(X0,$o,X1,X3))) <=> ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.70 inference(fool_elimination,[],[f3981])).
% 92.92/13.70 thf(f3981,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : ((X2 = X3) => vAPP(X0,$o,X1,X3)) <=> vAPP(X0,$o,X1,X2))),
% 92.92/13.70 inference(rectify,[],[f162])).
% 92.92/13.70 thf(f162,axiom,(
% 92.92/13.70 ! [X0 : $tType,X3 : X0 > $o,X74 : X0] : (! [X19 : X0] : ((X19 = X74) => vAPP(X0,$o,X3,X19)) <=> vAPP(X0,$o,X3,X74))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__FORALL__THM2)).
% 92.92/13.70 thf(f62197,plain,(
% 92.92/13.70 spl854_636),
% 92.92/13.70 inference(avatar_split_clause,[],[f11478,f62195])).
% 92.92/13.70 thf(f62195,plain,(
% 92.92/13.70 spl854_636 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : ($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),c_2Erelation_2ERUNIV(X0,X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_636])])).
% 92.92/13.70 thf(f11478,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),c_2Erelation_2ERUNIV(X0,X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7724])).
% 92.92/13.70 thf(f62193,plain,(
% 92.92/13.70 spl854_635),
% 92.92/13.70 inference(avatar_split_clause,[],[f11040,f62191])).
% 92.92/13.70 thf(f62191,plain,(
% 92.92/13.70 spl854_635 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_635])])).
% 92.92/13.70 thf(f11040,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7570])).
% 92.92/13.70 thf(f7570,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)) | ((X0 != X1) & ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)))) & ((X0 = X1) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1))))),
% 92.92/13.70 inference(flattening,[],[f7569])).
% 92.92/13.70 thf(f7569,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)) | ((X0 != X1) & ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)))) & (((X0 = X1) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3360])).
% 92.92/13.70 thf(f3360,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)) <=> ((X0 = X1) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1))))),
% 92.92/13.70 inference(fool_elimination,[],[f3359])).
% 92.92/13.70 thf(f3359,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1) <=> ((X0 = X1) | vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)))),
% 92.92/13.70 inference(rectify,[],[f925])).
% 92.92/13.70 thf(f925,axiom,(
% 92.92/13.70 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X134),X137) <=> ((X134 = X137) | vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X134),X137)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EGREATER__OR__EQ)).
% 92.92/13.70 thf(f62189,plain,(
% 92.92/13.70 spl854_634),
% 92.92/13.70 inference(avatar_split_clause,[],[f10233,f62187])).
% 92.92/13.70 thf(f62187,plain,(
% 92.92/13.70 spl854_634 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_634])])).
% 92.92/13.70 thf(f10233,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f5599])).
% 92.92/13.70 thf(f5599,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)))),
% 92.92/13.70 inference(flattening,[],[f5598])).
% 92.92/13.70 thf(f5598,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))))),
% 92.92/13.70 inference(ennf_transformation,[],[f2698])).
% 92.92/13.70 thf(f2698,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1))) => (X0 = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f2697])).
% 92.92/13.70 thf(f2697,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) => (X0 = X1))),
% 92.92/13.70 inference(rectify,[],[f1475])).
% 92.92/13.70 thf(f1475,axiom,(
% 92.92/13.70 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X49),X72) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X72),X49)) => (X49 = X72))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EDIVIDES__ANTISYM)).
% 92.92/13.70 thf(f62185,plain,(
% 92.92/13.70 spl854_633),
% 92.92/13.70 inference(avatar_split_clause,[],[f10133,f62183])).
% 92.92/13.70 thf(f62183,plain,(
% 92.92/13.70 spl854_633 <=> ! [X1 : $tType,X0 : $tType,X3 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),X3)) = X3)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_633])])).
% 92.92/13.70 thf(f10133,plain,(
% 92.92/13.70 ( ! [X1 : $tType,X0 : $tType,X3 : tyop_2Epair_2Eprod(X0,X1)] : ((vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),X3)) = X3)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6847])).
% 92.92/13.70 thf(f6847,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0 > X1 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),bCOMB,c_2Ebool_2E_3F(X0)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),bCOMB,c_2Ebool_2E_3F(X1))),vAPP(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o)))),cCOMB,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o))))),bCOMB,bCOMB),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),vAPP(sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),$o),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)))),bCOMB,bCOMB),c_2Emin_2E_3D(sTfun(X0,sTfun(X1,$o)))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o))))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),vAPP(sTfun(sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o)))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))))),bCOMB,vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),bCOMB,bCOMB)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,c_2Ebool_2E_2F_5C)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0))))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X1,$o)),cCOMB,c_2Emin_2E_3D(X1)))))),X2)) | (vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),X2)) != X2)) & ((vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),X2)) = X2) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),bCOMB,c_2Ebool_2E_3F(X0)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),bCOMB,c_2Ebool_2E_3F(X1))),vAPP(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o)))),cCOMB,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o))))),bCOMB,bCOMB),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),vAPP(sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),$o),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)))),bCOMB,bCOMB),c_2Emin_2E_3D(sTfun(X0,sTfun(X1,$o)))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o))))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),vAPP(sTfun(sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o)))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))))),bCOMB,vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),bCOMB,bCOMB)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,c_2Ebool_2E_2F_5C)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0))))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X1,$o)),cCOMB,c_2Emin_2E_3D(X1)))))),X2)))) & ! [X3 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),X3)) = X3))),
% 92.92/13.70 inference(nnf_transformation,[],[f5093])).
% 92.92/13.70 thf(f5093,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),bCOMB,c_2Ebool_2E_3F(X0)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),bCOMB,c_2Ebool_2E_3F(X1))),vAPP(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o)))),cCOMB,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o))))),bCOMB,bCOMB),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),vAPP(sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),$o),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)))),bCOMB,bCOMB),c_2Emin_2E_3D(sTfun(X0,sTfun(X1,$o)))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o))))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),vAPP(sTfun(sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o)))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))))),bCOMB,vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),bCOMB,bCOMB)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,c_2Ebool_2E_2F_5C)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0))))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X1,$o)),cCOMB,c_2Emin_2E_3D(X1)))))),X2)) <=> (vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),X2)) = X2)) & ! [X3 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),X3)) = X3))),
% 92.92/13.70 inference(rectify,[],[f2598])).
% 92.92/13.70 thf(f2598,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),bCOMB,c_2Ebool_2E_3F(X0)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,$o)),bCOMB,c_2Ebool_2E_3F(X1))),vAPP(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o))),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(X0,sTfun(X1,$o)))),cCOMB,vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(X1,$o))))),bCOMB,bCOMB),vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),vAPP(sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),$o),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o))),sTfun(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X1,sTfun(X0,sTfun(X1,$o))),sTfun(X1,$o)))),bCOMB,bCOMB),c_2Emin_2E_3D(sTfun(X0,sTfun(X1,$o)))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X0,sTfun(X1,sTfun(X0,sTfun(X1,$o))))),cCOMB,vAPP(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),vAPP(sTfun(sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))),sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o))))),sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X0,sTfun(X1,$o)))))),bCOMB,bCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X0,sTfun(X1,$o))))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o))))),bCOMB,vAPP(sTfun(sTfun($o,$o),sTfun(sTfun(X1,$o),sTfun(X1,$o))),sTfun(sTfun(X0,sTfun($o,$o)),sTfun(X0,sTfun(sTfun(X1,$o),sTfun(X1,$o)))),bCOMB,bCOMB)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,c_2Ebool_2E_2F_5C)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0))))))),vAPP(sTfun(X1,sTfun(X1,$o)),sTfun(X1,sTfun(X1,$o)),cCOMB,c_2Emin_2E_3D(X1)))))),X2)) <=> (vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),X2)) = X2)) & ! [X8 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),X8)) = X8))),
% 92.92/13.70 inference(fool_elimination,[],[f2597])).
% 92.92/13.70 thf(f2597,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0 > X1 > $o] : (vAPP(sTfun(X0,sTfun(X1,$o)),$o,(^[X3 : X0 > X1 > $o] : (vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),(^[X4 : X0] : (vAPP(sTfun(X1,$o),$o,c_2Ebool_2E_3F(X1),(^[X5 : X1] : (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Emin_2E_3D(sTfun(X0,sTfun(X1,$o))),X3),(^[X6 : X0, X7 : X1] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X6),X4)),vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),c_2Emin_2E_3D(X1),X7),X5))))))))))))),X2) <=> (vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),X2)) = X2)) & ! [X8 : tyop_2Epair_2Eprod(X0,X1)] : (vAPP(sTfun(X0,sTfun(X1,$o)),tyop_2Epair_2Eprod(X0,X1),c_2Epair_2EABS__prod(X0,X1),vAPP(tyop_2Epair_2Eprod(X0,X1),sTfun(X0,sTfun(X1,$o)),c_2Epair_2EREP__prod(X0,X1),X8)) = X8))),
% 92.92/13.70 inference(rectify,[],[f788])).
% 92.92/13.70 thf(f788,axiom,(
% 92.92/13.70 ! [X0 : $tType,X5 : $tType] : (! [X112 : X0 > X5 > $o] : (vAPP(sTfun(X0,sTfun(X5,$o)),$o,(^[X108 : X0 > X5 > $o] : (vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),(^[X15 : X0] : (vAPP(sTfun(X5,$o),$o,c_2Ebool_2E_3F(X5),(^[X28 : X5] : (vAPP(sTfun(X0,sTfun(X5,$o)),$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o),c_2Emin_2E_3D(sTfun(X0,sTfun(X5,$o))),X108),(^[X261 : X0, X167 : X5] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X261),X15)),vAPP(X5,$o,vAPP(X5,sTfun(X5,$o),c_2Emin_2E_3D(X5),X167),X28))))))))))))),X112) <=> (vAPP(tyop_2Epair_2Eprod(X0,X5),sTfun(X0,sTfun(X5,$o)),c_2Epair_2EREP__prod(X0,X5),vAPP(sTfun(X0,sTfun(X5,$o)),tyop_2Epair_2Eprod(X0,X5),c_2Epair_2EABS__prod(X0,X5),X112)) = X112)) & ! [X72 : tyop_2Epair_2Eprod(X0,X5)] : (vAPP(sTfun(X0,sTfun(X5,$o)),tyop_2Epair_2Eprod(X0,X5),c_2Epair_2EABS__prod(X0,X5),vAPP(tyop_2Epair_2Eprod(X0,X5),sTfun(X0,sTfun(X5,$o)),c_2Epair_2EREP__prod(X0,X5),X72)) = X72))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2EABS__REP__prod)).
% 92.92/13.70 thf(f62181,plain,(
% 92.92/13.70 spl854_632),
% 92.92/13.70 inference(avatar_split_clause,[],[f9157,f62179])).
% 92.92/13.70 thf(f62179,plain,(
% 92.92/13.70 spl854_632 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_632])])).
% 92.92/13.70 thf(f9157,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4838])).
% 92.92/13.70 thf(f4838,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,c_2Enum_2E0))),
% 92.92/13.70 inference(rectify,[],[f1646])).
% 92.92/13.70 thf(f1646,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X136))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,c_2Enum_2E0))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Etri__def)).
% 92.92/13.70 thf(f62004,plain,(
% 92.92/13.70 ~spl854_631 | ~spl854_44 | ~spl854_627),
% 92.92/13.70 inference(avatar_split_clause,[],[f61996,f60432,f22112,f62001])).
% 92.92/13.70 thf(f60432,plain,(
% 92.92/13.70 spl854_627 <=> ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_627])])).
% 92.92/13.70 thf(f61996,plain,(
% 92.92/13.70 (sK124 != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$true)) | (~spl854_44 | ~spl854_627)),
% 92.92/13.70 inference(trivial_inequality_removal,[],[f61921])).
% 92.92/13.70 thf(f61921,plain,(
% 92.92/13.70 ($true = $false) | (sK124 != vAPP($o,sTfun(sK123,$o),c_2Ecombin_2EK($o,sK123),$true)) | (~spl854_44 | ~spl854_627)),
% 92.92/13.70 inference(constrained_superposition,[],[f60433,f22114])).
% 92.92/13.70 thf(f60433,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)))) ) | ~spl854_627),
% 92.92/13.70 inference(avatar_component_clause,[],[f60432])).
% 92.92/13.70 thf(f60446,plain,(
% 92.92/13.70 spl854_630),
% 92.92/13.70 inference(avatar_split_clause,[],[f19575,f60444])).
% 92.92/13.70 thf(f60444,plain,(
% 92.92/13.70 spl854_630 <=> ! [X0 : $tType,X1 : X0 > $o] : ($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_630])])).
% 92.92/13.70 thf(f19575,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)),X1))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f17349,f13591])).
% 92.92/13.70 thf(f17349,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f14878])).
% 92.92/13.70 thf(f14878,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11195,f13544])).
% 92.92/13.70 thf(f11195,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),c_2Epred__set_2EUNIV(X0)),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f3500])).
% 92.92/13.70 thf(f3500,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),c_2Epred__set_2EUNIV(X0)),X1)))),
% 92.92/13.70 inference(fool_elimination,[],[f3499])).
% 92.92/13.70 thf(f3499,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),c_2Epred__set_2EUNIV(X0)),X1))),
% 92.92/13.70 inference(rectify,[],[f1896])).
% 92.92/13.70 thf(f1896,axiom,(
% 92.92/13.70 ! [X0 : $tType,X111 : X0 > $o] : vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),c_2Epred__set_2EUNIV(X0)),X111))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__UNIV__PSUBSET)).
% 92.92/13.70 thf(f60442,plain,(
% 92.92/13.70 spl854_629),
% 92.92/13.70 inference(avatar_split_clause,[],[f19574,f60440])).
% 92.92/13.70 thf(f60440,plain,(
% 92.92/13.70 spl854_629 <=> ! [X0 : $tType,X1 : X0 > $o] : ($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_629])])).
% 92.92/13.70 thf(f19574,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f17350,f17793])).
% 92.92/13.70 thf(f17350,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f14877])).
% 92.92/13.70 thf(f14877,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11194,f13541])).
% 92.92/13.70 thf(f11194,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),c_2Epred__set_2EEMPTY(X0))))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f3498])).
% 92.92/13.70 thf(f3498,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),c_2Epred__set_2EEMPTY(X0))))),
% 92.92/13.70 inference(fool_elimination,[],[f3497])).
% 92.92/13.70 thf(f3497,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),c_2Epred__set_2EEMPTY(X0)))),
% 92.92/13.70 inference(rectify,[],[f1895])).
% 92.92/13.70 thf(f1895,axiom,(
% 92.92/13.70 ! [X0 : $tType,X111 : X0 > $o] : vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X111),c_2Epred__set_2EEMPTY(X0)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__PSUBSET__EMPTY)).
% 92.92/13.70 thf(f60438,plain,(
% 92.92/13.70 spl854_628),
% 92.92/13.70 inference(avatar_split_clause,[],[f19571,f60436])).
% 92.92/13.70 thf(f19571,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14870,f17793])).
% 92.92/13.70 thf(f14870,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11186,f13541])).
% 92.92/13.70 thf(f11186,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EEMPTY(X0)),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f3482])).
% 92.92/13.70 thf(f3482,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EEMPTY(X0)),X1))),
% 92.92/13.70 inference(fool_elimination,[],[f3481])).
% 92.92/13.70 thf(f3481,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EEMPTY(X0)),X1)),
% 92.92/13.70 inference(rectify,[],[f1884])).
% 92.92/13.70 thf(f1884,axiom,(
% 92.92/13.70 ! [X0 : $tType,X111 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),c_2Epred__set_2EEMPTY(X0)),X111)),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__SUBSET)).
% 92.92/13.70 thf(f60434,plain,(
% 92.92/13.70 spl854_627),
% 92.92/13.70 inference(avatar_split_clause,[],[f19570,f60432])).
% 92.92/13.70 thf(f19570,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true)))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14869,f13591])).
% 92.92/13.70 thf(f14869,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11185,f13544])).
% 92.92/13.70 thf(f11185,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),c_2Epred__set_2EUNIV(X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f3480])).
% 92.92/13.70 thf(f3480,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),c_2Epred__set_2EUNIV(X0)))),
% 92.92/13.70 inference(fool_elimination,[],[f3479])).
% 92.92/13.70 thf(f3479,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),c_2Epred__set_2EUNIV(X0))),
% 92.92/13.70 inference(rectify,[],[f1886])).
% 92.92/13.70 thf(f1886,axiom,(
% 92.92/13.70 ! [X0 : $tType,X111 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X111),c_2Epred__set_2EUNIV(X0))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__UNIV)).
% 92.92/13.70 thf(f60430,plain,(
% 92.92/13.70 spl854_498 | spl854_626 | ~spl854_217),
% 92.92/13.70 inference(avatar_split_clause,[],[f24562,f23581,f60427,f48711])).
% 92.92/13.70 thf(f60427,plain,(
% 92.92/13.70 spl854_626 <=> ($true = vAPP(sTfun($o,$o),$o,sK399($o),vNOT))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_626])])).
% 92.92/13.70 thf(f23581,plain,(
% 92.92/13.70 spl854_217 <=> ! [X0 : $tType,X9 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X9)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK399(X0),X1))))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_217])])).
% 92.92/13.70 thf(f24562,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK399($o),vNOT)) | ($false = X0)) ) | ~spl854_217),
% 92.92/13.70 inference(not_proxy_clausification,[],[f24561])).
% 92.92/13.70 thf(f24561,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK399($o),vNOT)) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_217),
% 92.92/13.70 inference(not_proxy_clausification,[],[f24501])).
% 92.92/13.70 thf(f24501,plain,(
% 92.92/13.70 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK399($o),vNOT))) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_217),
% 92.92/13.70 inference(primitive_instantiation,[],[f23582])).
% 92.92/13.70 thf(f23582,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o,X9 : X0] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK399(X0),X1))) | ($true = vAPP(X0,$o,X1,X9))) ) | ~spl854_217),
% 92.92/13.70 inference(avatar_component_clause,[],[f23581])).
% 92.92/13.70 thf(f60425,plain,(
% 92.92/13.70 spl854_625),
% 92.92/13.70 inference(avatar_split_clause,[],[f18948,f60423])).
% 92.92/13.70 thf(f60423,plain,(
% 92.92/13.70 spl854_625 <=> ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_625])])).
% 92.92/13.70 thf(f18948,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)),X1))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14233,f17793])).
% 92.92/13.70 thf(f14233,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10164,f13541])).
% 92.92/13.70 thf(f10164,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),c_2Epred__set_2EEMPTY(X0)),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f2614])).
% 92.92/13.70 thf(f2614,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),c_2Epred__set_2EEMPTY(X0))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),c_2Epred__set_2EEMPTY(X0)),X1)))),
% 92.92/13.70 inference(fool_elimination,[],[f2613])).
% 92.92/13.70 thf(f2613,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),c_2Epred__set_2EEMPTY(X0)) & vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),c_2Epred__set_2EEMPTY(X0)),X1))),
% 92.92/13.70 inference(rectify,[],[f1927])).
% 92.92/13.70 thf(f1927,axiom,(
% 92.92/13.70 ! [X0 : $tType,X111 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X111),c_2Epred__set_2EEMPTY(X0)) & vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),c_2Epred__set_2EEMPTY(X0)),X111))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__EMPTY)).
% 92.92/13.70 thf(f60421,plain,(
% 92.92/13.70 spl854_624),
% 92.92/13.70 inference(avatar_split_clause,[],[f18947,f60419])).
% 92.92/13.70 thf(f60419,plain,(
% 92.92/13.70 spl854_624 <=> ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_624])])).
% 92.92/13.70 thf(f18947,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false)))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f14232,f17793])).
% 92.92/13.70 thf(f14232,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f10165,f13541])).
% 92.92/13.70 thf(f10165,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EDISJOINT(X0),X1),c_2Epred__set_2EEMPTY(X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f2614])).
% 92.92/13.70 thf(f60417,plain,(
% 92.92/13.70 spl854_623),
% 92.92/13.70 inference(avatar_split_clause,[],[f18491,f60415])).
% 92.92/13.70 thf(f60415,plain,(
% 92.92/13.70 spl854_623 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_623])])).
% 92.92/13.70 thf(f18491,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18490,f18124])).
% 92.92/13.70 thf(f18490,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f18489,f13563])).
% 92.92/13.70 thf(f18489,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0))) )),
% 92.92/13.70 inference(forward_demodulation,[],[f17956,f13548])).
% 92.92/13.70 thf(f17956,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.70 inference(equality_proxy_clausification,[],[f17955])).
% 92.92/13.70 thf(f17955,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f13907])).
% 92.92/13.70 thf(f13907,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9625,f13512])).
% 92.92/13.70 thf(f9625,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6687])).
% 92.92/13.70 thf(f6687,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f5498,f6686])).
% 92.92/13.70 thf(f6686,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1))) => (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)))))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f5498,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))))),
% 92.92/13.70 inference(ennf_transformation,[],[f2274])).
% 92.92/13.70 thf(f2274,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))) => ? [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1))))),
% 92.92/13.70 inference(fool_elimination,[],[f2273])).
% 92.92/13.70 thf(f2273,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0)) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0) & vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)))),
% 92.92/13.70 inference(rectify,[],[f1487])).
% 92.92/13.70 thf(f1487,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X136)) => ? [X110 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X110),X136) & vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X110)))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EPRIME__FACTOR)).
% 92.92/13.70 thf(f60413,plain,(
% 92.92/13.70 spl854_622),
% 92.92/13.70 inference(avatar_split_clause,[],[f17059,f60411])).
% 92.92/13.70 thf(f17059,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : ((X2 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.70 inference(equality_proxy_clausification,[],[f17058])).
% 92.92/13.70 thf(f17058,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.70 inference(not_proxy_clausification,[],[f12692])).
% 92.92/13.70 thf(f12692,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6178])).
% 92.92/13.70 thf(f6178,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.70 inference(flattening,[],[f6177])).
% 92.92/13.70 thf(f6177,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.70 inference(ennf_transformation,[],[f4384])).
% 92.92/13.70 thf(f4384,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) => ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))))),
% 92.92/13.70 inference(fool_elimination,[],[f4383])).
% 92.92/13.70 thf(f4383,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3) => vAPP($o,$o,vNOT,(X2 = X3))))),
% 92.92/13.70 inference(rectify,[],[f555])).
% 92.92/13.70 thf(f555,axiom,(
% 92.92/13.70 ! [X0 : $tType,X143 : X0 > X0 > $o,X4 : X0,X12 : X0] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12) => vAPP($o,$o,vNOT,(X4 = X12))))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__NOT__REFL)).
% 92.92/13.70 thf(f60409,plain,(
% 92.92/13.70 spl854_621),
% 92.92/13.70 inference(avatar_split_clause,[],[f15879,f60407])).
% 92.92/13.70 thf(f60407,plain,(
% 92.92/13.70 spl854_621 <=> ! [X0 : tyop_2Enum_2Enum > $o,X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_621])])).
% 92.92/13.70 thf(f15879,plain,(
% 92.92/13.70 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3)),X0))) )),
% 92.92/13.70 inference(equality_resolution,[],[f10693])).
% 92.92/13.70 thf(f10693,plain,(
% 92.92/13.70 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3) != X1) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7303])).
% 92.92/13.70 thf(f60405,plain,(
% 92.92/13.70 spl854_620),
% 92.92/13.70 inference(avatar_split_clause,[],[f14800,f60403])).
% 92.92/13.70 thf(f60403,plain,(
% 92.92/13.70 spl854_620 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X1),X0)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_620])])).
% 92.92/13.70 thf(f14800,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X1),X0))) )),
% 92.92/13.70 inference(definition_unfolding,[],[f11098,f9122])).
% 92.92/13.70 thf(f11098,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,c_2Enum_2E0),X1),X0))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7614])).
% 92.92/13.70 thf(f7614,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,c_2Enum_2E0),X1),X0)) | (X0 != X1)) & ((X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,c_2Enum_2E0),X1),X0))))),
% 92.92/13.70 inference(nnf_transformation,[],[f3412])).
% 92.92/13.70 thf(f3412,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,c_2Enum_2E0),X1),X0)) <=> (X0 = X1))),
% 92.92/13.70 inference(fool_elimination,[],[f3411])).
% 92.92/13.70 thf(f3411,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,c_2Enum_2E0),X1),X0) <=> (X0 = X1))),
% 92.92/13.70 inference(rectify,[],[f1302])).
% 92.92/13.70 thf(f1302,axiom,(
% 92.92/13.70 ! [X211 : tyop_2Enum_2Enum,X253 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,c_2Enum_2E0),X253),X211) <=> (X211 = X253))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__0__CONG)).
% 92.92/13.70 thf(f60401,plain,(
% 92.92/13.70 spl854_619),
% 92.92/13.70 inference(avatar_split_clause,[],[f13825,f60399])).
% 92.92/13.70 thf(f60399,plain,(
% 92.92/13.70 spl854_619 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK131,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK132,X0)) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_619])])).
% 92.92/13.70 thf(f13825,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK131,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK132,X0)) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9532,f9122])).
% 92.92/13.70 thf(f9532,plain,(
% 92.92/13.70 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK131,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK132,X0)) = X0) | (c_2Enum_2E0 = X0)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f6631])).
% 92.92/13.70 thf(f6631,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK131,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK132,X0)) = X0) | (c_2Enum_2E0 = X0))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK131,sK132])],[f4947,f6630])).
% 92.92/13.70 thf(f6630,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X2) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK131,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK132,X0)) = X0))),
% 92.92/13.70 introduced(choice_axiom,[])).
% 92.92/13.70 thf(f4947,plain,(
% 92.92/13.70 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X2) = X0) | (c_2Enum_2E0 = X0))),
% 92.92/13.70 inference(rectify,[],[f1692])).
% 92.92/13.70 thf(f1692,axiom,(
% 92.92/13.70 ! [X136 : tyop_2Enum_2Enum] : (? [X462 : tyop_2Enum_2Enum,X11 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X462),X11) = X136) | (c_2Enum_2E0 = X136))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases)).
% 92.92/13.70 thf(f60397,plain,(
% 92.92/13.70 spl854_618),
% 92.92/13.70 inference(avatar_split_clause,[],[f13809,f60395])).
% 92.92/13.70 thf(f60395,plain,(
% 92.92/13.70 spl854_618 <=> ! [X0 : $tType,X4 : X0 > X0,X5 : X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X4),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X5) = X5)),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_618])])).
% 92.92/13.70 thf(f13809,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X4 : X0 > X0,X5 : X0] : ((vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X4),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X5) = X5)) )),
% 92.92/13.70 inference(definition_unfolding,[],[f9502,f9122])).
% 92.92/13.70 thf(f9502,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X4 : X0 > X0,X5 : X0] : ((vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X4),c_2Enum_2E0),X5) = X5)) )),
% 92.92/13.70 inference(cnf_transformation,[],[f4941])).
% 92.92/13.70 thf(f4941,plain,(
% 92.92/13.70 ! [X0 : $tType] : (! [X1 : X0 > X0,X2 : tyop_2Enum_2Enum,X3 : X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),X3) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X1),X2),vAPP(X0,X0,X1,X3))) & ! [X4 : X0 > X0,X5 : X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X4),c_2Enum_2E0),X5) = X5))),
% 92.92/13.70 inference(rectify,[],[f929])).
% 92.92/13.70 thf(f929,axiom,(
% 92.92/13.70 ! [X0 : $tType] : (! [X114 : X0 > X0,X298 : tyop_2Enum_2Enum,X23 : X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X114),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X298)),X23) = vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X114),X298),vAPP(X0,X0,X114,X23))) & ! [X3 : X0 > X0,X4 : X0] : (vAPP(X0,X0,vAPP(tyop_2Enum_2Enum,sTfun(X0,X0),vAPP(sTfun(X0,X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,X0)),c_2Earithmetic_2EFUNPOW(X0),X3),c_2Enum_2E0),X4) = X4))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EFUNPOW)).
% 92.92/13.70 thf(f60393,plain,(
% 92.92/13.70 spl854_617),
% 92.92/13.70 inference(avatar_split_clause,[],[f11786,f60391])).
% 92.92/13.70 thf(f60391,plain,(
% 92.92/13.70 spl854_617 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X1) != vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_617])])).
% 92.92/13.70 thf(f11786,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X1) != vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7952])).
% 92.92/13.70 thf(f7952,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : X0] : (((vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X1) = vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X2)) | (X1 != X2)) & ((X1 = X2) | (vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X1) != vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5238])).
% 92.92/13.70 thf(f5238,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0,X2 : X0] : ((vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X1) = vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X2)) <=> (X1 = X2))),
% 92.92/13.70 inference(rectify,[],[f1532])).
% 92.92/13.70 thf(f1532,axiom,(
% 92.92/13.70 ! [X0 : $tType,X425 : X0,X426 : X0] : ((vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X425) = vAPP(X0,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJA(X0),X426)) <=> (X425 = X426))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EINJA__INJ)).
% 92.92/13.70 thf(f60389,plain,(
% 92.92/13.70 spl854_616),
% 92.92/13.70 inference(avatar_split_clause,[],[f11784,f60387])).
% 92.92/13.70 thf(f60387,plain,(
% 92.92/13.70 spl854_616 <=> ! [X0 : $tType,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X1) != vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X2)))),
% 92.92/13.70 introduced(avatar_definition,[new_symbols(naming,[spl854_616])])).
% 92.92/13.70 thf(f11784,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X1) != vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X2))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7951])).
% 92.92/13.70 thf(f7951,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X1) = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X2)) | (X1 != X2)) & ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X1) != vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X2))))),
% 92.92/13.70 inference(nnf_transformation,[],[f5237])).
% 92.92/13.70 thf(f5237,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X1) = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X2)) <=> (X1 = X2))),
% 92.92/13.70 inference(rectify,[],[f1531])).
% 92.92/13.70 thf(f1531,axiom,(
% 92.92/13.70 ! [X0 : $tType,X325 : tyop_2Enum_2Enum,X326 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X325) = vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2EINJN(X0),X326)) <=> (X325 = X326))),
% 92.92/13.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EINJN__INJ)).
% 92.92/13.70 thf(f60318,plain,(
% 92.92/13.70 spl854_615),
% 92.92/13.70 inference(avatar_split_clause,[],[f11151,f60316])).
% 92.92/13.70 thf(f11151,plain,(
% 92.92/13.70 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK378(X0),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1)))) )),
% 92.92/13.70 inference(cnf_transformation,[],[f7650])).
% 92.92/13.70 thf(f7650,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) | ! [X2 : X0] : ($true != vAPP(X0,$o,X1,X2))) & (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK378(X0),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1)))))),
% 92.92/13.70 inference(skolemisation,[status(esa),new_symbols(skolem,[sK378])],[f7648,f7649])).
% 92.92/13.70 thf(f7649,plain,(
% 92.92/13.70 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK378(X0),X1))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7648,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) | ! [X2 : X0] : ($true != vAPP(X0,$o,X1,X2))) & (? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1)))))),
% 92.92/13.71 inference(rectify,[],[f7647])).
% 92.92/13.71 thf(f7647,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) | ! [X2 : X0] : ($true != vAPP(X0,$o,X1,X2))) & (? [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5123])).
% 92.92/13.71 thf(f5123,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) <=> ? [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.71 inference(rectify,[],[f3450])).
% 92.92/13.71 thf(f3450,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) <=> ? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)))),
% 92.92/13.71 inference(fool_elimination,[],[f3449])).
% 92.92/13.71 thf(f3449,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),(^[X2 : X0] : (vAPP(X0,$o,X1,X2))))) <=> ? [X3 : X0] : vAPP(X0,$o,X1,X3))),
% 92.92/13.71 inference(rectify,[],[f83])).
% 92.92/13.71 thf(f83,axiom,(
% 92.92/13.71 ! [X0 : $tType,X7 : X0 > $o] : (vAPP(X0,$o,X7,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),(^[X4 : X0] : (vAPP(X0,$o,X7,X4))))) <=> ? [X19 : X0] : vAPP(X0,$o,X7,X19))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESELECT__THM)).
% 92.92/13.71 thf(f60314,plain,(
% 92.92/13.71 spl854_614),
% 92.92/13.71 inference(avatar_split_clause,[],[f11064,f60312])).
% 92.92/13.71 thf(f60312,plain,(
% 92.92/13.71 spl854_614 <=> ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK373(X0),X1))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_614])])).
% 92.92/13.71 thf(f11064,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK373(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7593])).
% 92.92/13.71 thf(f7593,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK373(X0),X1)))) & (! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1)))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK373])],[f7591,f7592])).
% 92.92/13.71 thf(f7592,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ($true != vAPP(X0,$o,X1,X2)) => ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK373(X0),X1))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7591,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) | ? [X2 : X0] : ($true != vAPP(X0,$o,X1,X2))) & (! [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1)))))),
% 92.92/13.71 inference(rectify,[],[f7590])).
% 92.92/13.71 thf(f7590,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) | ? [X2 : X0] : ($true != vAPP(X0,$o,X1,X2))) & (! [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3376])).
% 92.92/13.71 thf(f3376,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) <=> ! [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.71 inference(fool_elimination,[],[f3375])).
% 92.92/13.71 thf(f3375,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1)) <=> ! [X2 : X0] : vAPP(X0,$o,X1,X2))),
% 92.92/13.71 inference(rectify,[],[f275])).
% 92.92/13.71 thf(f275,axiom,(
% 92.92/13.71 ! [X0 : $tType,X26 : X0 > $o] : (vAPP(X0,$o,X26,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X26)) <=> ! [X4 : X0] : vAPP(X0,$o,X26,X4))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EnormalForms_2EUNIV__POINT)).
% 92.92/13.71 thf(f60310,plain,(
% 92.92/13.71 spl854_613),
% 92.92/13.71 inference(avatar_split_clause,[],[f10699,f60308])).
% 92.92/13.71 thf(f60308,plain,(
% 92.92/13.71 spl854_613 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_613])])).
% 92.92/13.71 thf(f10699,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7304])).
% 92.92/13.71 thf(f7304,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1))) & (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6408])).
% 92.92/13.71 thf(f6408,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))) <=> ($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f5781,f6407])).
% 92.92/13.71 thf(f5781,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))) <=> ! [X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,X1,X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) != X0)) & (($true = vAPP(tyop_2Enum_2Enum,$o,X1,c_2Enum_2E0)) | (c_2Enum_2E0 != X0))))),
% 92.92/13.71 inference(ennf_transformation,[],[f3144])).
% 92.92/13.71 thf(f3144,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))) <=> ! [X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) = X0) => ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ((c_2Enum_2E0 = X0) => ($true = vAPP(tyop_2Enum_2Enum,$o,X1,c_2Enum_2E0)))))),
% 92.92/13.71 inference(fool_elimination,[],[f3143])).
% 92.92/13.71 thf(f3143,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0)) <=> ! [X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) = X0) => vAPP(tyop_2Enum_2Enum,$o,X1,X2)) & ((c_2Enum_2E0 = X0) => vAPP(tyop_2Enum_2Enum,$o,X1,c_2Enum_2E0))))),
% 92.92/13.71 inference(rectify,[],[f1196])).
% 92.92/13.71 thf(f1196,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X43 : tyop_2Enum_2Enum > $o] : (vAPP(tyop_2Enum_2Enum,$o,X43,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X136)) <=> ! [X104 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X104) = X136) => vAPP(tyop_2Enum_2Enum,$o,X43,X104)) & ((c_2Enum_2E0 = X136) => vAPP(tyop_2Enum_2Enum,$o,X43,c_2Enum_2E0))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EPRE__ELIM__THM)).
% 92.92/13.71 thf(f60306,plain,(
% 92.92/13.71 spl854_612),
% 92.92/13.71 inference(avatar_split_clause,[],[f10698,f60304])).
% 92.92/13.71 thf(f60304,plain,(
% 92.92/13.71 spl854_612 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_612])])).
% 92.92/13.71 thf(f10698,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(tyop_2Enum_2Enum,sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),sP16,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7304])).
% 92.92/13.71 thf(f60302,plain,(
% 92.92/13.71 spl854_611),
% 92.92/13.71 inference(avatar_split_clause,[],[f10172,f60300])).
% 92.92/13.71 thf(f60300,plain,(
% 92.92/13.71 spl854_611 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_611])])).
% 92.92/13.71 thf(f10172,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),$o),c_2Erelation_2ERSUBSET(X0,X0),c_2Erelation_2EEMPTY__REL(X0)),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6853])).
% 92.92/13.71 thf(f60228,plain,(
% 92.92/13.71 spl854_498 | spl854_610 | ~spl854_216),
% 92.92/13.71 inference(avatar_split_clause,[],[f24479,f23577,f60225,f48711])).
% 92.92/13.71 thf(f60225,plain,(
% 92.92/13.71 spl854_610 <=> ($true = vAPP(sTfun($o,$o),$o,sK397($o),vNOT))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_610])])).
% 92.92/13.71 thf(f23577,plain,(
% 92.92/13.71 spl854_216 <=> ! [X0 : $tType,X5 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK397(X0),X1))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_216])])).
% 92.92/13.71 thf(f24479,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK397($o),vNOT)) | ($false = X0)) ) | ~spl854_216),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24478])).
% 92.92/13.71 thf(f24478,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK397($o),vNOT)) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_216),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24418])).
% 92.92/13.71 thf(f24418,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK397($o),vNOT))) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_216),
% 92.92/13.71 inference(primitive_instantiation,[],[f23578])).
% 92.92/13.71 thf(f23578,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o,X5 : X0] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK397(X0),X1))) | ($true = vAPP(X0,$o,X1,X5))) ) | ~spl854_216),
% 92.92/13.71 inference(avatar_component_clause,[],[f23577])).
% 92.92/13.71 thf(f58431,plain,(
% 92.92/13.71 spl854_609 | spl854_305 | ~spl854_215),
% 92.92/13.71 inference(avatar_split_clause,[],[f24397,f23573,f29086,f58428])).
% 92.92/13.71 thf(f58428,plain,(
% 92.92/13.71 spl854_609 <=> ($false = vAPP(sTfun($o,$o),$o,sK392($o),vNOT))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_609])])).
% 92.92/13.71 thf(f29086,plain,(
% 92.92/13.71 spl854_305 <=> ! [X0 : $o] : ($true = X0)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_305])])).
% 92.92/13.71 thf(f23573,plain,(
% 92.92/13.71 spl854_215 <=> ! [X0 : $tType,X1 : X0 > $o,X8 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK392(X0),X1))) | ($true != vAPP(X0,$o,X1,X8)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_215])])).
% 92.92/13.71 thf(f24397,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,sK392($o),vNOT))) ) | ~spl854_215),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24396])).
% 92.92/13.71 thf(f24396,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK392($o),vNOT)))) ) | ~spl854_215),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24297])).
% 92.92/13.71 thf(f24297,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK392($o),vNOT)))) ) | ~spl854_215),
% 92.92/13.71 inference(primitive_instantiation,[],[f23574])).
% 92.92/13.71 thf(f23574,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o,X8 : X0] : (($true != vAPP(X0,$o,X1,X8)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK392(X0),X1)))) ) | ~spl854_215),
% 92.92/13.71 inference(avatar_component_clause,[],[f23573])).
% 92.92/13.71 thf(f57987,plain,(
% 92.92/13.71 spl854_608),
% 92.92/13.71 inference(avatar_split_clause,[],[f17198,f57985])).
% 92.92/13.71 thf(f57985,plain,(
% 92.92/13.71 spl854_608 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_608])])).
% 92.92/13.71 thf(f17198,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11929])).
% 92.92/13.71 thf(f11929,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8038])).
% 92.92/13.71 thf(f8038,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X1)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X0),X2),X1))) & (((($true = vAPP($o,$o,vNOT,X0)) | ($true = X1)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X0),X2),X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8037])).
% 92.92/13.71 thf(f8037,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X0)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))) & (((($true = vAPP($o,$o,vNOT,X2)) | ($true = X0)) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8036])).
% 92.92/13.71 thf(f8036,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X1),X0),X2)) | ((($true != vAPP($o,$o,vNOT,X2)) & ($true != X0)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)))) & (((($true = vAPP($o,$o,vNOT,X2)) | ($true = X0)) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6463])).
% 92.92/13.71 thf(f6463,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X1),X0),X2)) <=> ((($true = vAPP($o,$o,vNOT,X2)) | ($true = X0)) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = X1)) & ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57983,plain,(
% 92.92/13.71 spl854_607),
% 92.92/13.71 inference(avatar_split_clause,[],[f17197,f57981])).
% 92.92/13.71 thf(f57981,plain,(
% 92.92/13.71 spl854_607 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_607])])).
% 92.92/13.71 thf(f17197,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11928])).
% 92.92/13.71 thf(f11928,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP47,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8038])).
% 92.92/13.71 thf(f57979,plain,(
% 92.92/13.71 spl854_606),
% 92.92/13.71 inference(avatar_split_clause,[],[f17187,f57977])).
% 92.92/13.71 thf(f57977,plain,(
% 92.92/13.71 spl854_606 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_606])])).
% 92.92/13.71 thf(f17187,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11947])).
% 92.92/13.71 thf(f11947,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8046])).
% 92.92/13.71 thf(f8046,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != X0)) | (($true != vAPP($o,$o,vNOT,X2)) & ($true != X0))) & ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X0)) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8045])).
% 92.92/13.71 thf(f8045,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X1),X0),X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != X2))) & ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8044])).
% 92.92/13.71 thf(f8044,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X1),X0),X2)) | (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != X2)))) & ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6467])).
% 92.92/13.71 thf(f6467,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X1),X0),X2)) <=> (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X1),X0),X2)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X2))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57975,plain,(
% 92.92/13.71 spl854_605),
% 92.92/13.71 inference(avatar_split_clause,[],[f17186,f57973])).
% 92.92/13.71 thf(f57973,plain,(
% 92.92/13.71 spl854_605 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_605])])).
% 92.92/13.71 thf(f17186,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11946])).
% 92.92/13.71 thf(f11946,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP50,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8046])).
% 92.92/13.71 thf(f57971,plain,(
% 92.92/13.71 spl854_604),
% 92.92/13.71 inference(avatar_split_clause,[],[f17180,f57969])).
% 92.92/13.71 thf(f57969,plain,(
% 92.92/13.71 spl854_604 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_604])])).
% 92.92/13.71 thf(f17180,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11966])).
% 92.92/13.71 thf(f11966,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8055])).
% 92.92/13.71 thf(f8055,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != X0)) | (($true != X2) & ($true != X0))) & ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X0)) & (($true = X2) | ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8054])).
% 92.92/13.71 thf(f8054,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X1),X0),X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2)) | (($true != X1) & ($true != X2))) & ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & (($true = X1) | ($true = X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8053])).
% 92.92/13.71 thf(f8053,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X1),X0),X2)) | (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) | (($true != vAPP($o,$o,vNOT,X0)) & ($true != X2)) | (($true != X1) & ($true != X2)))) & ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & (($true = X1) | ($true = X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6471])).
% 92.92/13.71 thf(f6471,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X1),X0),X2)) <=> (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X1),X0),X2)) & (($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & (($true = X1) | ($true = X2))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57967,plain,(
% 92.92/13.71 spl854_603),
% 92.92/13.71 inference(avatar_split_clause,[],[f17143,f57965])).
% 92.92/13.71 thf(f57965,plain,(
% 92.92/13.71 spl854_603 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($false = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_603])])).
% 92.92/13.71 thf(f17143,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($false = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12232])).
% 92.92/13.71 thf(f12232,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | (vAPP($o,$o,vNOT,X1) = $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8341])).
% 92.92/13.71 thf(f8341,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0)) | (($true != X0) & ($true != X1)) | (($true != X2) & (vAPP($o,$o,vNOT,X1) != $true))) & (((($true = X0) | ($true = X1)) & (($true = X2) | (vAPP($o,$o,vNOT,X1) = $true))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8340])).
% 92.92/13.71 thf(f8340,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X1),X0),X2)) | (($true != X2) & ($true != X0)) | (($true != X1) & ($true != vAPP($o,$o,vNOT,X0)))) & (((($true = X2) | ($true = X0)) & (($true = X1) | ($true = vAPP($o,$o,vNOT,X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8339])).
% 92.92/13.71 thf(f8339,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X1),X0),X2)) | ((($true != X2) & ($true != X0)) | (($true != X1) & ($true != vAPP($o,$o,vNOT,X0))))) & (((($true = X2) | ($true = X0)) & (($true = X1) | ($true = vAPP($o,$o,vNOT,X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6481])).
% 92.92/13.71 thf(f6481,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X1),X0),X2)) <=> ((($true = X2) | ($true = X0)) & (($true = X1) | ($true = vAPP($o,$o,vNOT,X0)))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57963,plain,(
% 92.92/13.71 spl854_602),
% 92.92/13.71 inference(avatar_split_clause,[],[f17140,f57961])).
% 92.92/13.71 thf(f57961,plain,(
% 92.92/13.71 spl854_602 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_602])])).
% 92.92/13.71 thf(f17140,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12241])).
% 92.92/13.71 thf(f12241,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | (vAPP($o,$o,vNOT,X1) != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8345])).
% 92.92/13.71 thf(f8345,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0)) | (($true != X0) & (vAPP($o,$o,vNOT,X1) = $true)) | (($true != X2) & ($true = X1))) & (((($true = X0) | (vAPP($o,$o,vNOT,X1) != $true)) & (($true = X2) | ($true != X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8344])).
% 92.92/13.71 thf(f8344,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X1),X0),X2)) | (($true != X2) & ($true = vAPP($o,$o,vNOT,X0))) | (($true != X1) & ($true = X0))) & (((($true = X2) | ($true != vAPP($o,$o,vNOT,X0))) & (($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8343])).
% 92.92/13.71 thf(f8343,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X1),X0),X2)) | ((($true != X2) & ($true = vAPP($o,$o,vNOT,X0))) | (($true != X1) & ($true = X0)))) & (((($true = X2) | ($true != vAPP($o,$o,vNOT,X0))) & (($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6483])).
% 92.92/13.71 thf(f6483,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X1),X0),X2)) <=> ((($true = X2) | ($true != vAPP($o,$o,vNOT,X0))) & (($true = X1) | ($true != X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57959,plain,(
% 92.92/13.71 spl854_601 | spl854_305 | ~spl854_214),
% 92.92/13.71 inference(avatar_split_clause,[],[f24271,f23569,f29086,f57956])).
% 92.92/13.71 thf(f57956,plain,(
% 92.92/13.71 spl854_601 <=> ($false = vAPP(sTfun($o,$o),$o,sK390($o),vNOT))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_601])])).
% 92.92/13.71 thf(f23569,plain,(
% 92.92/13.71 spl854_214 <=> ! [X0 : $tType,X4 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK390(X0),X1))) | ($true != vAPP(X0,$o,X1,X4)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_214])])).
% 92.92/13.71 thf(f24271,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,sK390($o),vNOT))) ) | ~spl854_214),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24270])).
% 92.92/13.71 thf(f24270,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK390($o),vNOT)))) ) | ~spl854_214),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24171])).
% 92.92/13.71 thf(f24171,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK390($o),vNOT)))) ) | ~spl854_214),
% 92.92/13.71 inference(primitive_instantiation,[],[f23570])).
% 92.92/13.71 thf(f23570,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o,X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK390(X0),X1)))) ) | ~spl854_214),
% 92.92/13.71 inference(avatar_component_clause,[],[f23569])).
% 92.92/13.71 thf(f57954,plain,(
% 92.92/13.71 spl854_600),
% 92.92/13.71 inference(avatar_split_clause,[],[f17138,f57952])).
% 92.92/13.71 thf(f57952,plain,(
% 92.92/13.71 spl854_600 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_600])])).
% 92.92/13.71 thf(f17138,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12249])).
% 92.92/13.71 thf(f12249,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8349])).
% 92.92/13.71 thf(f8349,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0)) | ((($true != X0) | (vAPP($o,$o,vNOT,X1) != $true)) & (($true != X2) | ($true != X1)))) & ((($true = X0) & (vAPP($o,$o,vNOT,X1) = $true)) | (($true = X2) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8348])).
% 92.92/13.71 thf(f8348,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X1),X0),X2)) | ((($true != X2) | ($true != vAPP($o,$o,vNOT,X0))) & (($true != X1) | ($true != X0)))) & ((($true = X2) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8347])).
% 92.92/13.71 thf(f8347,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X1),X0),X2)) | ((($true != X2) | ($true != vAPP($o,$o,vNOT,X0))) & (($true != X1) | ($true != X0)))) & (((($true = X2) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6485])).
% 92.92/13.71 thf(f6485,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X1),X0),X2)) <=> ((($true = X2) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57950,plain,(
% 92.92/13.71 spl854_599),
% 92.92/13.71 inference(avatar_split_clause,[],[f17004,f57948])).
% 92.92/13.71 thf(f57948,plain,(
% 92.92/13.71 spl854_599 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : ((X2 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_599])])).
% 92.92/13.71 thf(f17004,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : ((X2 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2))) )),
% 92.92/13.71 inference(equality_proxy_clausification,[],[f17003])).
% 92.92/13.71 thf(f17003,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12850])).
% 92.92/13.71 thf(f12850,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8702])).
% 92.92/13.71 thf(f8702,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1))) & ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2))))),
% 92.92/13.71 inference(flattening,[],[f8701])).
% 92.92/13.71 thf(f8701,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2)) | (($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)))) & ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4474])).
% 92.92/13.71 thf(f4474,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2)) <=> (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1))))),
% 92.92/13.71 inference(fool_elimination,[],[f4473])).
% 92.92/13.71 thf(f4473,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X1),X3),X2) <=> (vAPP($o,$o,vNOT,(X2 = X3)) & vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)))),
% 92.92/13.71 inference(rectify,[],[f1974])).
% 92.92/13.71 thf(f1974,axiom,(
% 92.92/13.71 ! [X0 : $tType,X111 : X0 > $o,X4 : X0,X12 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Epred__set_2EDELETE(X0),X111),X12),X4) <=> (vAPP($o,$o,vNOT,(X4 = X12)) & vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X4),X111)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__applied)).
% 92.92/13.71 thf(f57946,plain,(
% 92.92/13.71 spl854_598),
% 92.92/13.71 inference(avatar_split_clause,[],[f16636,f57944])).
% 92.92/13.71 thf(f57944,plain,(
% 92.92/13.71 spl854_598 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1 > $o] : ($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X3))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_598])])).
% 92.92/13.71 thf(f16636,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X3 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X3))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12737])).
% 92.92/13.71 thf(f12737,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0 > X1 > $o] : (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2)) | (X2 != X3)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8585])).
% 92.92/13.71 thf(f8585,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0 > X1 > $o] : (((X2 = X3) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),X3))) & ((($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2)) & ($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),X3))) | (X2 != X3)))),
% 92.92/13.71 inference(flattening,[],[f8584])).
% 92.92/13.71 thf(f8584,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0 > X1 > $o] : (((X2 = X3) | (($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),X3)))) & ((($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2)) & ($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),X3))) | (X2 != X3)))),
% 92.92/13.71 inference(nnf_transformation,[],[f4442])).
% 92.92/13.71 thf(f4442,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0 > X1 > $o] : ((X2 = X3) <=> (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2)) & ($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),X3))))),
% 92.92/13.71 inference(fool_elimination,[],[f4441])).
% 92.92/13.71 thf(f4441,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0 > X1 > $o] : ((X2 = X3) <=> (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X3),X2) & vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),c_2Erelation_2ERSUBSET(X0,X1),X2),X3)))),
% 92.92/13.71 inference(rectify,[],[f619])).
% 92.92/13.71 thf(f619,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X70 : X0 > X5 > $o,X182 : X0 > X5 > $o] : ((X70 = X182) <=> (vAPP(sTfun(X0,sTfun(X5,$o)),$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o),c_2Erelation_2ERSUBSET(X0,X5),X182),X70) & vAPP(sTfun(X0,sTfun(X5,$o)),$o,vAPP(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o),c_2Erelation_2ERSUBSET(X0,X5),X70),X182)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EEqIsBothRSUBSET)).
% 92.92/13.71 thf(f57942,plain,(
% 92.92/13.71 spl854_597),
% 92.92/13.71 inference(avatar_split_clause,[],[f16434,f57940])).
% 92.92/13.71 thf(f57940,plain,(
% 92.92/13.71 spl854_597 <=> ! [X0 : $tType,X2 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK577(X0),X2),$true))) | ($true != vAPP(X0,$o,X2,X4)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_597])])).
% 92.92/13.71 thf(f16434,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK577(X0),X2),$true))) | ($true != vAPP(X0,$o,X2,X4))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12063])).
% 92.92/13.71 thf(f12063,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK577(X0),X2),X1))) | ($true != X1) | ($true != vAPP(X0,$o,X2,X4))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8181])).
% 92.92/13.71 thf(f8181,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK577(X0),X2),X1))) | ($true != X1)) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK578(X0),X2))) | ($true != X1) | ! [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true = X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK577,sK578])],[f8178,f8180,f8179])).
% 92.92/13.71 thf(f8179,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) => (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK577(X0),X2),X1))) | ($true != X1)))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f8180,plain,(
% 92.92/13.71 ! [X0 : $tType,X2 : X0 > $o] : (? [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) => ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK578(X0),X2))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f8178,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & (? [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ($true != X1) | ! [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true = X1))))),
% 92.92/13.71 inference(rectify,[],[f8177])).
% 92.92/13.71 thf(f8177,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & (? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true != X1) | ! [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = X1))))),
% 92.92/13.71 inference(flattening,[],[f8176])).
% 92.92/13.71 thf(f8176,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & ((? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true != X1)) | ! [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6058])).
% 92.92/13.71 thf(f6058,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) <=> (? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true != X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f4018])).
% 92.92/13.71 thf(f4018,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = X1) => ($true = vAPP(X0,$o,X2,X3))) <=> (($true = X1) => ? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4))))),
% 92.92/13.71 inference(fool_elimination,[],[f4017])).
% 92.92/13.71 thf(f4017,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (X1 => vAPP(X0,$o,X2,X3)) <=> (X1 => ? [X4 : X0] : vAPP(X0,$o,X2,X4)))),
% 92.92/13.71 inference(rectify,[],[f107])).
% 92.92/13.71 thf(f107,axiom,(
% 92.92/13.71 ! [X0 : $tType,X7 : $o,X41 : X0 > $o] : (? [X19 : X0] : (X7 => vAPP(X0,$o,X41,X19)) <=> (X7 => ? [X15 : X0] : vAPP(X0,$o,X41,X15)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__IMP__THM)).
% 92.92/13.71 thf(f57938,plain,(
% 92.92/13.71 spl854_596),
% 92.92/13.71 inference(avatar_split_clause,[],[f16420,f57936])).
% 92.92/13.71 thf(f57936,plain,(
% 92.92/13.71 spl854_596 <=> ! [X0 : $tType,X2 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK570(X0),X2),$true))) | ($true != vAPP(X0,$o,X2,X4)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_596])])).
% 92.92/13.71 thf(f16420,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK570(X0),X2),$true))) | ($true != vAPP(X0,$o,X2,X4))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12047])).
% 92.92/13.71 thf(f12047,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK570(X0),X2),X1))) | ($true != vAPP(X0,$o,X2,X4)) | ($true != X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8160])).
% 92.92/13.71 thf(f8160,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK570(X0),X2),X1))) & ($true = X1)) | ! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ($true != X1)) & ((($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK571(X0),X2))) & ($true = X1)) | ! [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) | ($true != X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK570,sK571])],[f8157,f8159,f8158])).
% 92.92/13.71 thf(f8158,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) => (($true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK570(X0),X2),X1))) & ($true = X1)))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f8159,plain,(
% 92.92/13.71 ! [X0 : $tType,X2 : X0 > $o] : (? [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) => ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK571(X0),X2))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f8157,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | ! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ($true != X1)) & ((? [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) & ($true = X1)) | ! [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) | ($true != X1))))),
% 92.92/13.71 inference(rectify,[],[f8156])).
% 92.92/13.71 thf(f8156,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | ! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ($true != X1)) & ((? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) & ($true = X1)) | ! [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) | ($true != X1))))),
% 92.92/13.71 inference(flattening,[],[f8155])).
% 92.92/13.71 thf(f8155,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | (! [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) | ($true != X1))) & ((? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) & ($true = X1)) | ! [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) | ($true != X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4010])).
% 92.92/13.71 thf(f4010,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) <=> (? [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) & ($true = X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f4009])).
% 92.92/13.71 thf(f4009,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X3 : X0] : (vAPP(X0,$o,X2,X3) & X1) <=> (? [X4 : X0] : vAPP(X0,$o,X2,X4) & X1))),
% 92.92/13.71 inference(rectify,[],[f98])).
% 92.92/13.71 thf(f98,axiom,(
% 92.92/13.71 ! [X0 : $tType,X7 : $o,X41 : X0 > $o] : (? [X19 : X0] : (vAPP(X0,$o,X41,X19) & X7) <=> (? [X15 : X0] : vAPP(X0,$o,X41,X15) & X7))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__AND__THM)).
% 92.92/13.71 thf(f57934,plain,(
% 92.92/13.71 spl854_595),
% 92.92/13.71 inference(avatar_split_clause,[],[f16406,f57932])).
% 92.92/13.71 thf(f57932,plain,(
% 92.92/13.71 spl854_595 <=> ! [X0 : $tType,X2 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK546(X0),X2),$true))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_595])])).
% 92.92/13.71 thf(f16406,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK546(X0),X2),$true)))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12014])).
% 92.92/13.71 thf(f12014,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true != X1) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK546(X0),X2),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8105])).
% 92.92/13.71 thf(f8105,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK545(X0),X2))) & ($true = X1))) & (! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ($true != X1) | (($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK546(X0),X2),X1))) & ($true = X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK545,sK546])],[f8102,f8104,f8103])).
% 92.92/13.71 thf(f8103,plain,(
% 92.92/13.71 ! [X0 : $tType,X2 : X0 > $o] : (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) => ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK545(X0),X2))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f8104,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true = X1)) => (($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK546(X0),X2),X1))) & ($true = X1)))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f8102,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & (! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ($true != X1) | ? [X6 : X0] : (($true != vAPP(X0,$o,X2,X6)) & ($true = X1))))),
% 92.92/13.71 inference(rectify,[],[f8101])).
% 92.92/13.71 thf(f8101,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & (! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true != X1) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = X1))))),
% 92.92/13.71 inference(flattening,[],[f8100])).
% 92.92/13.71 thf(f8100,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) | (? [X4 : X0] : ($true != vAPP(X0,$o,X2,X4)) & ($true = X1))) & ((! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true != X1)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6055])).
% 92.92/13.71 thf(f6055,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1)) <=> (! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4)) | ($true != X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f3988])).
% 92.92/13.71 thf(f3988,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = X1) => ($true = vAPP(X0,$o,X2,X3))) <=> (($true = X1) => ! [X4 : X0] : ($true = vAPP(X0,$o,X2,X4))))),
% 92.92/13.71 inference(fool_elimination,[],[f3987])).
% 92.92/13.71 thf(f3987,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (! [X3 : X0] : (X1 => vAPP(X0,$o,X2,X3)) <=> (X1 => ! [X4 : X0] : vAPP(X0,$o,X2,X4)))),
% 92.92/13.71 inference(rectify,[],[f104])).
% 92.92/13.71 thf(f104,axiom,(
% 92.92/13.71 ! [X0 : $tType,X7 : $o,X41 : X0 > $o] : (! [X19 : X0] : (X7 => vAPP(X0,$o,X41,X19)) <=> (X7 => ! [X15 : X0] : vAPP(X0,$o,X41,X15)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__IMP__THM)).
% 92.92/13.71 thf(f57930,plain,(
% 92.92/13.71 spl854_594),
% 92.92/13.71 inference(avatar_split_clause,[],[f16383,f57928])).
% 92.92/13.71 thf(f57928,plain,(
% 92.92/13.71 spl854_594 <=> ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),$true),X0)) | ($true = X0) | ($true = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_594])])).
% 92.92/13.71 thf(f16383,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),$true),X0)) | ($true = X0) | ($true = X2)) )),
% 92.92/13.71 inference(equality_resolution,[],[f11975])).
% 92.92/13.71 thf(f11975,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)) | ($true = X0) | ($true != X1) | ($true = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8057])).
% 92.92/13.71 thf(f8057,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)) | (((($true != X0) & ($true = X1)) | ($true != X2)) & (($true = X0) | ($true != X1) | ($true = X2)))) & (((($true = X2) | (($true != X0) & ($true = X1))) & (($true = X0) | ($true != X1) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0))))),
% 92.92/13.71 inference(flattening,[],[f8056])).
% 92.92/13.71 thf(f8056,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)) | (((($true != X0) & ($true = X1)) | ($true != X2)) & ((($true = X0) | ($true != X1)) | ($true = X2)))) & (((($true = X2) | (($true != X0) & ($true = X1))) & ((($true = X0) | ($true != X1)) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6470])).
% 92.92/13.71 thf(f6470,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)) <=> (($true = X2) <=> (($true = X0) | ($true != X1))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57926,plain,(
% 92.92/13.71 spl854_593),
% 92.92/13.71 inference(avatar_split_clause,[],[f16372,f57924])).
% 92.92/13.71 thf(f57924,plain,(
% 92.92/13.71 spl854_593 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,$true),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_593])])).
% 92.92/13.71 thf(f16372,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,$true),X1),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11953])).
% 92.92/13.71 thf(f11953,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8048])).
% 92.92/13.71 thf(f57922,plain,(
% 92.92/13.71 spl854_592),
% 92.92/13.71 inference(avatar_split_clause,[],[f16241,f57920])).
% 92.92/13.71 thf(f57920,plain,(
% 92.92/13.71 spl854_592 <=> ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK527(X0),X2),$true))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_592])])).
% 92.92/13.71 thf(f16241,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK527(X0),X2),$true)))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11828])).
% 92.92/13.71 thf(f11828,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : $o] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK527(X0),X2),X1))) | ($true != X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7981])).
% 92.92/13.71 thf(f7981,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | (($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK527(X0),X2),X1))) | ($true != X1))) & (! [X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) & ($true = X1)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK528(X0),X2))) | ($true != X1)))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK527,sK528])],[f7978,f7980,f7979])).
% 92.92/13.71 thf(f7979,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) | ($true != X1)) => (($true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK527(X0),X2),X1))) | ($true != X1)))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7980,plain,(
% 92.92/13.71 ! [X0 : $tType,X2 : X0 > $o] : (? [X6 : X0] : ($true != vAPP(X0,$o,X2,X6)) => ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK528(X0),X2))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7978,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) | ($true != X1))) & (! [X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) & ($true = X1)) | ? [X6 : X0] : ($true != vAPP(X0,$o,X2,X6)) | ($true != X1)))),
% 92.92/13.71 inference(rectify,[],[f7977])).
% 92.92/13.71 thf(f7977,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) | ($true != X1))) & (! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) & ($true = X1)) | ? [X3 : X0] : ($true != vAPP(X0,$o,X2,X3)) | ($true != X1)))),
% 92.92/13.71 inference(flattening,[],[f7976])).
% 92.92/13.71 thf(f7976,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : (((! [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) | ($true != X1))) & (! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) & ($true = X1)) | (? [X3 : X0] : ($true != vAPP(X0,$o,X2,X3)) | ($true != X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3942])).
% 92.92/13.71 thf(f3942,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) & ($true = X1)) <=> ! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) & ($true = X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3941])).
% 92.92/13.71 thf(f3941,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $o,X2 : X0 > $o] : ((! [X3 : X0] : vAPP(X0,$o,X2,X3) & X1) <=> ! [X4 : X0] : (vAPP(X0,$o,X2,X4) & X1))),
% 92.92/13.71 inference(rectify,[],[f92])).
% 92.92/13.71 thf(f92,axiom,(
% 92.92/13.71 ! [X0 : $tType,X7 : $o,X41 : X0 > $o] : ((! [X19 : X0] : vAPP(X0,$o,X41,X19) & X7) <=> ! [X15 : X0] : (vAPP(X0,$o,X41,X15) & X7))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__FORALL__THM)).
% 92.92/13.71 thf(f57918,plain,(
% 92.92/13.71 spl854_591),
% 92.92/13.71 inference(avatar_split_clause,[],[f14450,f57916])).
% 92.92/13.71 thf(f57916,plain,(
% 92.92/13.71 spl854_591 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_591])])).
% 92.92/13.71 thf(f14450,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10482,f9122,f9122])).
% 92.92/13.71 thf(f10482,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7007])).
% 92.92/13.71 thf(f57876,plain,(
% 92.92/13.71 spl854_590),
% 92.92/13.71 inference(avatar_split_clause,[],[f14432,f57874])).
% 92.92/13.71 thf(f57874,plain,(
% 92.92/13.71 spl854_590 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_590])])).
% 92.92/13.71 thf(f14432,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X0)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10463,f9122,f9122])).
% 92.92/13.71 thf(f10463,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6992])).
% 92.92/13.71 thf(f6992,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X0) | ((c_2Enum_2E0 != X1) & (c_2Enum_2E0 != X0))) & ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X0)))),
% 92.92/13.71 inference(flattening,[],[f6991])).
% 92.92/13.71 thf(f6991,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X0) | ((c_2Enum_2E0 != X1) & (c_2Enum_2E0 != X0))) & (((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X0)))),
% 92.92/13.71 inference(nnf_transformation,[],[f5114])).
% 92.92/13.71 thf(f5114,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X0) <=> ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 = X0)))),
% 92.92/13.71 inference(rectify,[],[f1043])).
% 92.92/13.71 thf(f1043,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X134),X137) = X134) <=> ((c_2Enum_2E0 = X137) | (c_2Enum_2E0 = X134)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQ__EQ__0)).
% 92.92/13.71 thf(f57872,plain,(
% 92.92/13.71 spl854_589),
% 92.92/13.71 inference(avatar_split_clause,[],[f13067,f57870])).
% 92.92/13.71 thf(f57870,plain,(
% 92.92/13.71 spl854_589 <=> ! [X2 : $tType,X0 : $tType,X4 : tyop_2Eoption_2Eoption(X0),X3 : X2] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X2),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__IGNORE__BIND(X0,X2),vAPP(X2,tyop_2Eoption_2Eoption(X2),c_2Eoption_2ESOME(X2),X3)),X4) = X4)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_589])])).
% 92.92/13.71 thf(f13067,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : $tType,X3 : X2,X4 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X2),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__IGNORE__BIND(X0,X2),vAPP(X2,tyop_2Eoption_2Eoption(X2),c_2Eoption_2ESOME(X2),X3)),X4) = X4)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5344])).
% 92.92/13.71 thf(f5344,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2,X4 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X2),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__IGNORE__BIND(X0,X2),vAPP(X2,tyop_2Eoption_2Eoption(X2),c_2Eoption_2ESOME(X2),X3)),X4) = X4) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__IGNORE__BIND(X0,X1),c_2Eoption_2ENONE(X1)),X4)))),
% 92.92/13.71 inference(rectify,[],[f755])).
% 92.92/13.71 thf(f755,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X57 : $tType,X29 : X57,X27 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X57),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__IGNORE__BIND(X0,X57),vAPP(X57,tyop_2Eoption_2Eoption(X57),c_2Eoption_2ESOME(X57),X29)),X27) = X27) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X5),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X0)),c_2Eoption_2EOPTION__IGNORE__BIND(X0,X5),c_2Eoption_2ENONE(X5)),X27)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__IGNORE__BIND__thm)).
% 92.92/13.71 thf(f57868,plain,(
% 92.92/13.71 spl854_588),
% 92.92/13.71 inference(avatar_split_clause,[],[f12846,f57866])).
% 92.92/13.71 thf(f57866,plain,(
% 92.92/13.71 spl854_588 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : ((X2 = X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_588])])).
% 92.92/13.71 thf(f12846,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : ((X2 = X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8700])).
% 92.92/13.71 thf(f8700,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)) | (X2 != X3)) & ((($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)) & (X2 = X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f8699])).
% 92.92/13.71 thf(f8699,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3)) | (($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)) | (X2 != X3))) & ((($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)) & (X2 = X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4472])).
% 92.92/13.71 thf(f4472,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3)) <=> (($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1)) & (X2 = X3)))),
% 92.92/13.71 inference(fool_elimination,[],[f4471])).
% 92.92/13.71 thf(f4471,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X1),X2),X3) <=> (vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X2),X1) & (X2 = X3)))),
% 92.92/13.71 inference(rectify,[],[f447])).
% 92.92/13.71 thf(f447,axiom,(
% 92.92/13.71 ! [X0 : $tType,X44 : X0 > $o,X4 : X0,X12 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Ediag(X0),X44),X4),X12) <=> (vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X4),X44) & (X4 = X12)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ediag__def)).
% 92.92/13.71 thf(f57864,plain,(
% 92.92/13.71 spl854_587),
% 92.92/13.71 inference(avatar_split_clause,[],[f12393,f57862])).
% 92.92/13.71 thf(f57862,plain,(
% 92.92/13.71 spl854_587 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : (vAPP(tyop_2Epair_2Eprod(X0,X1),X0,c_2Epair_2EFST(X0,X1),vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X2),X3)) = X2)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_587])])).
% 92.92/13.71 thf(f12393,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : ((vAPP(tyop_2Epair_2Eprod(X0,X1),X0,c_2Epair_2EFST(X0,X1),vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X2),X3)) = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5265])).
% 92.92/13.71 thf(f5265,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : (vAPP(tyop_2Epair_2Eprod(X0,X1),X0,c_2Epair_2EFST(X0,X1),vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X2),X3)) = X2)),
% 92.92/13.71 inference(rectify,[],[f803])).
% 92.92/13.71 thf(f803,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X8 : X0,X18 : X5] : (vAPP(tyop_2Epair_2Eprod(X0,X5),X0,c_2Epair_2EFST(X0,X5),vAPP(X5,tyop_2Epair_2Eprod(X0,X5),vAPP(X0,sTfun(X5,tyop_2Epair_2Eprod(X0,X5)),c_2Epair_2E_2C(X0,X5),X8),X18)) = X8)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2EFST)).
% 92.92/13.71 thf(f57860,plain,(
% 92.92/13.71 spl854_586),
% 92.92/13.71 inference(avatar_split_clause,[],[f12392,f57858])).
% 92.92/13.71 thf(f57858,plain,(
% 92.92/13.71 spl854_586 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : (vAPP(tyop_2Epair_2Eprod(X0,X1),X1,c_2Epair_2ESND(X0,X1),vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X2),X3)) = X3)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_586])])).
% 92.92/13.71 thf(f12392,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : ((vAPP(tyop_2Epair_2Eprod(X0,X1),X1,c_2Epair_2ESND(X0,X1),vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X2),X3)) = X3)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5264])).
% 92.92/13.71 thf(f5264,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : (vAPP(tyop_2Epair_2Eprod(X0,X1),X1,c_2Epair_2ESND(X0,X1),vAPP(X1,tyop_2Epair_2Eprod(X0,X1),vAPP(X0,sTfun(X1,tyop_2Epair_2Eprod(X0,X1)),c_2Epair_2E_2C(X0,X1),X2),X3)) = X3)),
% 92.92/13.71 inference(rectify,[],[f804])).
% 92.92/13.71 thf(f804,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X8 : X0,X18 : X5] : (vAPP(tyop_2Epair_2Eprod(X0,X5),X5,c_2Epair_2ESND(X0,X5),vAPP(X5,tyop_2Epair_2Eprod(X0,X5),vAPP(X0,sTfun(X5,tyop_2Epair_2Eprod(X0,X5)),c_2Epair_2E_2C(X0,X5),X8),X18)) = X18)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epair_2ESND)).
% 92.92/13.71 thf(f57856,plain,(
% 92.92/13.71 spl854_585),
% 92.92/13.71 inference(avatar_split_clause,[],[f12251,f57854])).
% 92.92/13.71 thf(f57854,plain,(
% 92.92/13.71 spl854_585 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_585])])).
% 92.92/13.71 thf(f12251,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8349])).
% 92.92/13.71 thf(f57852,plain,(
% 92.92/13.71 spl854_584),
% 92.92/13.71 inference(avatar_split_clause,[],[f12250,f57850])).
% 92.92/13.71 thf(f57850,plain,(
% 92.92/13.71 spl854_584 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_584])])).
% 92.92/13.71 thf(f12250,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8349])).
% 92.92/13.71 thf(f57848,plain,(
% 92.92/13.71 spl854_583),
% 92.92/13.71 inference(avatar_split_clause,[],[f12233,f57846])).
% 92.92/13.71 thf(f57846,plain,(
% 92.92/13.71 spl854_583 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_583])])).
% 92.92/13.71 thf(f12233,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8341])).
% 92.92/13.71 thf(f57844,plain,(
% 92.92/13.71 spl854_582),
% 92.92/13.71 inference(avatar_split_clause,[],[f11973,f57842])).
% 92.92/13.71 thf(f57842,plain,(
% 92.92/13.71 spl854_582 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_582])])).
% 92.92/13.71 thf(f11973,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8057])).
% 92.92/13.71 thf(f57840,plain,(
% 92.92/13.71 spl854_581),
% 92.92/13.71 inference(avatar_split_clause,[],[f11965,f57838])).
% 92.92/13.71 thf(f57838,plain,(
% 92.92/13.71 spl854_581 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_581])])).
% 92.92/13.71 thf(f11965,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP53,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8055])).
% 92.92/13.71 thf(f57836,plain,(
% 92.92/13.71 spl854_580 | spl854_305 | ~spl854_199),
% 92.92/13.71 inference(avatar_split_clause,[],[f24111,f23508,f29086,f57833])).
% 92.92/13.71 thf(f23508,plain,(
% 92.92/13.71 spl854_199 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) | ($true != vAPP(X0,$o,X1,X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_199])])).
% 92.92/13.71 thf(f24111,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT))) ) | ~spl854_199),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24110])).
% 92.92/13.71 thf(f24110,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT)))) ) | ~spl854_199),
% 92.92/13.71 inference(not_proxy_clausification,[],[f24015])).
% 92.92/13.71 thf(f24015,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,c_2Emin_2E_40($o),vNOT)))) ) | ~spl854_199),
% 92.92/13.71 inference(primitive_instantiation,[],[f23509])).
% 92.92/13.71 thf(f23509,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1)))) ) | ~spl854_199),
% 92.92/13.71 inference(avatar_component_clause,[],[f23508])).
% 92.92/13.71 thf(f57831,plain,(
% 92.92/13.71 spl854_579),
% 92.92/13.71 inference(avatar_split_clause,[],[f11938,f57829])).
% 92.92/13.71 thf(f57829,plain,(
% 92.92/13.71 spl854_579 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | ($true = X0) | ($true = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_579])])).
% 92.92/13.71 thf(f11938,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | ($true = X0) | ($true = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8040])).
% 92.92/13.71 thf(f8040,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | ((($true != X0) | ($true != X1) | ($true != X2)) & ((($true = X0) & ($true = X1)) | ($true = X2)))) & (((($true = X2) | ($true != X0) | ($true != X1)) & ((($true = X0) & ($true = X1)) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0))))),
% 92.92/13.71 inference(flattening,[],[f8039])).
% 92.92/13.71 thf(f8039,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | (((($true != X0) | ($true != X1)) | ($true != X2)) & ((($true = X0) & ($true = X1)) | ($true = X2)))) & (((($true = X2) | (($true != X0) | ($true != X1))) & ((($true = X0) & ($true = X1)) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6462])).
% 92.92/13.71 thf(f6462,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) <=> (($true = X2) <=> (($true = X0) & ($true = X1))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57827,plain,(
% 92.92/13.71 spl854_578),
% 92.92/13.71 inference(avatar_split_clause,[],[f11937,f57825])).
% 92.92/13.71 thf(f57825,plain,(
% 92.92/13.71 spl854_578 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | ($true = X1) | ($true = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_578])])).
% 92.92/13.71 thf(f11937,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | ($true = X1) | ($true = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8040])).
% 92.92/13.71 thf(f57823,plain,(
% 92.92/13.71 spl854_577),
% 92.92/13.71 inference(avatar_split_clause,[],[f11880,f57821])).
% 92.92/13.71 thf(f57821,plain,(
% 92.92/13.71 spl854_577 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0)) | ($true = X1) | ($true = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_577])])).
% 92.92/13.71 thf(f11880,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0)) | ($true = X1) | ($true = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8014])).
% 92.92/13.71 thf(f8014,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0)) | (($true != X0) & ($true = X1)) | (($true != X0) & ($true = X2))) & (((($true = X0) | ($true != X1)) & (($true = X0) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8013])).
% 92.92/13.71 thf(f8013,plain,(
% 92.92/13.71 ! [X2 : $o,X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X0),X1),X2)) | (($true != X2) & ($true = X1)) | (($true != X2) & ($true = X0))) & (((($true = X2) | ($true != X1)) & (($true = X2) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X0),X1),X2))))),
% 92.92/13.71 inference(flattening,[],[f8012])).
% 92.92/13.71 thf(f8012,plain,(
% 92.92/13.71 ! [X2 : $o,X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X0),X1),X2)) | ((($true != X2) & ($true = X1)) | (($true != X2) & ($true = X0)))) & (((($true = X2) | ($true != X1)) & (($true = X2) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X0),X1),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6452])).
% 92.92/13.71 thf(f6452,plain,(
% 92.92/13.71 ! [X2 : $o,X1 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X0),X1),X2)) <=> ((($true = X2) | ($true != X1)) & (($true = X2) | ($true != X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57819,plain,(
% 92.92/13.71 spl854_576),
% 92.92/13.71 inference(avatar_split_clause,[],[f11853,f57817])).
% 92.92/13.71 thf(f57817,plain,(
% 92.92/13.71 spl854_576 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_576])])).
% 92.92/13.71 thf(f11853,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7999])).
% 92.92/13.71 thf(f7999,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0)) | (($true != X0) & ($true != X1)) | (($true != X2) & ($true != X1))) & (((($true = X0) | ($true = X1)) & (($true = X2) | ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f7998])).
% 92.92/13.71 thf(f7998,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X1),X0),X2)) | (($true != X2) & ($true != X0)) | (($true != X1) & ($true != X0))) & (((($true = X2) | ($true = X0)) & (($true = X1) | ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f7997])).
% 92.92/13.71 thf(f7997,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X1),X0),X2)) | ((($true != X2) & ($true != X0)) | (($true != X1) & ($true != X0)))) & (((($true = X2) | ($true = X0)) & (($true = X1) | ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6450])).
% 92.92/13.71 thf(f6450,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X1),X0),X2)) <=> ((($true = X2) | ($true = X0)) & (($true = X1) | ($true = X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57815,plain,(
% 92.92/13.71 spl854_575),
% 92.92/13.71 inference(avatar_split_clause,[],[f11852,f57813])).
% 92.92/13.71 thf(f57813,plain,(
% 92.92/13.71 spl854_575 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_575])])).
% 92.92/13.71 thf(f11852,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7999])).
% 92.92/13.71 thf(f57811,plain,(
% 92.92/13.71 spl854_574),
% 92.92/13.71 inference(avatar_split_clause,[],[f11839,f57809])).
% 92.92/13.71 thf(f57809,plain,(
% 92.92/13.71 spl854_574 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_574])])).
% 92.92/13.71 thf(f11839,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7988])).
% 92.92/13.71 thf(f7988,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0)) | (($true != X0) & ($true != X1)) | (($true != X0) & ($true != X2))) & (((($true = X0) | ($true = X1)) & (($true = X0) | ($true = X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f7987])).
% 92.92/13.71 thf(f7987,plain,(
% 92.92/13.71 ! [X0 : $o,X2 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X1),X2),X0)) | (($true != X0) & ($true != X2)) | (($true != X0) & ($true != X1))) & (((($true = X0) | ($true = X2)) & (($true = X0) | ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X1),X2),X0))))),
% 92.92/13.71 inference(flattening,[],[f7986])).
% 92.92/13.71 thf(f7986,plain,(
% 92.92/13.71 ! [X0 : $o,X2 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X1),X2),X0)) | ((($true != X0) & ($true != X2)) | (($true != X0) & ($true != X1)))) & (((($true = X0) | ($true = X2)) & (($true = X0) | ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X1),X2),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6448])).
% 92.92/13.71 thf(f6448,plain,(
% 92.92/13.71 ! [X0 : $o,X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X1),X2),X0)) <=> ((($true = X0) | ($true = X2)) & (($true = X0) | ($true = X1))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57807,plain,(
% 92.92/13.71 spl854_573),
% 92.92/13.71 inference(avatar_split_clause,[],[f11838,f57805])).
% 92.92/13.71 thf(f57805,plain,(
% 92.92/13.71 spl854_573 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_573])])).
% 92.92/13.71 thf(f11838,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7988])).
% 92.92/13.71 thf(f57803,plain,(
% 92.92/13.71 spl854_572),
% 92.92/13.71 inference(avatar_split_clause,[],[f11818,f57801])).
% 92.92/13.71 thf(f57801,plain,(
% 92.92/13.71 spl854_572 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_572])])).
% 92.92/13.71 thf(f11818,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7973])).
% 92.92/13.71 thf(f7973,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0)) | ((($true != X0) | ($true != X1)) & (($true != X2) | ($true != X1)))) & ((($true = X0) & ($true = X1)) | (($true = X2) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f7972])).
% 92.92/13.71 thf(f7972,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X1),X0),X2)) | ((($true != X2) | ($true != X0)) & (($true != X1) | ($true != X0)))) & ((($true = X2) & ($true = X0)) | (($true = X1) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f7971])).
% 92.92/13.71 thf(f7971,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X1),X0),X2)) | ((($true != X2) | ($true != X0)) & (($true != X1) | ($true != X0)))) & (((($true = X2) & ($true = X0)) | (($true = X1) & ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6446])).
% 92.92/13.71 thf(f6446,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X1),X0),X2)) <=> ((($true = X2) & ($true = X0)) | (($true = X1) & ($true = X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57799,plain,(
% 92.92/13.71 spl854_571),
% 92.92/13.71 inference(avatar_split_clause,[],[f11801,f57797])).
% 92.92/13.71 thf(f57797,plain,(
% 92.92/13.71 spl854_571 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_571])])).
% 92.92/13.71 thf(f11801,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7962])).
% 92.92/13.71 thf(f7962,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0)) | ((($true != X0) | ($true != X1)) & (($true != X0) | ($true != X2)))) & ((($true = X0) & ($true = X1)) | (($true = X0) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f7961])).
% 92.92/13.71 thf(f7961,plain,(
% 92.92/13.71 ! [X0 : $o,X2 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X1),X2),X0)) | ((($true != X0) | ($true != X2)) & (($true != X0) | ($true != X1)))) & ((($true = X0) & ($true = X2)) | (($true = X0) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X1),X2),X0))))),
% 92.92/13.71 inference(flattening,[],[f7960])).
% 92.92/13.71 thf(f7960,plain,(
% 92.92/13.71 ! [X0 : $o,X2 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X1),X2),X0)) | ((($true != X0) | ($true != X2)) & (($true != X0) | ($true != X1)))) & (((($true = X0) & ($true = X2)) | (($true = X0) & ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X1),X2),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6444])).
% 92.92/13.71 thf(f6444,plain,(
% 92.92/13.71 ! [X0 : $o,X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X1),X2),X0)) <=> ((($true = X0) & ($true = X2)) | (($true = X0) & ($true = X1))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f57795,plain,(
% 92.92/13.71 spl854_570),
% 92.92/13.71 inference(avatar_split_clause,[],[f11171,f57793])).
% 92.92/13.71 thf(f57793,plain,(
% 92.92/13.71 spl854_570 <=> ! [X0 : $tType,X5 : X0,X6 : X0,X1 : X0 > $o] : ((X5 = X6) | ($true != vAPP(X0,$o,X1,X6)) | ($true != vAPP(X0,$o,X1,X5)) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_570])])).
% 92.92/13.71 thf(f11171,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o,X6 : X0,X5 : X0] : ((X5 = X6) | ($true != vAPP(X0,$o,X1,X6)) | ($true != vAPP(X0,$o,X1,X5)) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7675])).
% 92.92/13.71 thf(f57707,plain,(
% 92.92/13.71 spl854_569),
% 92.92/13.71 inference(avatar_split_clause,[],[f9150,f57705])).
% 92.92/13.71 thf(f57705,plain,(
% 92.92/13.71 spl854_569 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_569])])).
% 92.92/13.71 thf(f9150,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4836])).
% 92.92/13.71 thf(f4836,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2)))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Earithmetic_2EZERO))),
% 92.92/13.71 inference(rectify,[],[f1383])).
% 92.92/13.71 thf(f1383,axiom,(
% 92.92/13.71 ! [X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X135)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X135)) & ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X137))) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Earithmetic_2EZERO))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__pre)).
% 92.92/13.71 thf(f57146,plain,(
% 92.92/13.71 spl854_568),
% 92.92/13.71 inference(avatar_split_clause,[],[f18492,f57144])).
% 92.92/13.71 thf(f57144,plain,(
% 92.92/13.71 spl854_568 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_568])])).
% 92.92/13.71 thf(f18492,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f17954,f18124])).
% 92.92/13.71 thf(f17954,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.71 inference(equality_proxy_clausification,[],[f17953])).
% 92.92/13.71 thf(f17953,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0))) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f13908])).
% 92.92/13.71 thf(f13908,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9624,f13512])).
% 92.92/13.71 thf(f9624,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK161,X0))) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6687])).
% 92.92/13.71 thf(f57142,plain,(
% 92.92/13.71 spl854_567),
% 92.92/13.71 inference(avatar_split_clause,[],[f17165,f57140])).
% 92.92/13.71 thf(f57140,plain,(
% 92.92/13.71 spl854_567 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2) != X1) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_567])])).
% 92.92/13.71 thf(f17165,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2) != X1) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1))) )),
% 92.92/13.71 inference(equality_proxy_clausification,[],[f17164])).
% 92.92/13.71 thf(f17164,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12148])).
% 92.92/13.71 thf(f12148,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8264])).
% 92.92/13.71 thf(f8264,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X2))) & ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1))))),
% 92.92/13.71 inference(flattening,[],[f8263])).
% 92.92/13.71 thf(f8263,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1)) | (($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X2)))) & ((($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4098])).
% 92.92/13.71 thf(f4098,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1)) <=> (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2)),X1))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X2))))),
% 92.92/13.71 inference(fool_elimination,[],[f4097])).
% 92.92/13.71 thf(f4097,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X2),X1) <=> (vAPP($o,$o,vNOT,(vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X2) = X1)) & vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X2)))),
% 92.92/13.71 inference(rectify,[],[f1994])).
% 92.92/13.71 thf(f1994,axiom,(
% 92.92/13.71 ! [X0 : $tType,X8 : X0,X157 : X0 > $o] : (vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X157),X8) <=> (vAPP($o,$o,vNOT,(vAPP(sTfun(X0,$o),X0,c_2Epred__set_2ECHOICE(X0),X157) = X8)) & vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X8),X157)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__applied)).
% 92.92/13.71 thf(f57138,plain,(
% 92.92/13.71 spl854_566),
% 92.92/13.71 inference(avatar_split_clause,[],[f16666,f57136])).
% 92.92/13.71 thf(f57136,plain,(
% 92.92/13.71 spl854_566 <=> ! [X0 : $tType,X1 : X0 > X0 > $o,X3 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X3))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_566])])).
% 92.92/13.71 thf(f16666,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X3))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12862])).
% 92.92/13.71 thf(f12862,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3)) | (X2 != X3)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8710])).
% 92.92/13.71 thf(f8710,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) & (X2 != X3))) & (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (X2 = X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f8709])).
% 92.92/13.71 thf(f8709,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) & (X2 != X3))) & ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (X2 = X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4482])).
% 92.92/13.71 thf(f4482,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3)) <=> (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (X2 = X3)))),
% 92.92/13.71 inference(fool_elimination,[],[f4481])).
% 92.92/13.71 thf(f4481,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X2),X3) <=> (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3) | (X2 = X3)))),
% 92.92/13.71 inference(rectify,[],[f418])).
% 92.92/13.71 thf(f418,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o,X4 : X0,X12 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143),X4),X12) <=> (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12) | (X4 = X12)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERC__DEF)).
% 92.92/13.71 thf(f57134,plain,(
% 92.92/13.71 spl854_565),
% 92.92/13.71 inference(avatar_split_clause,[],[f16665,f57132])).
% 92.92/13.71 thf(f57132,plain,(
% 92.92/13.71 spl854_565 <=> ! [X0 : $tType,X2 : X0,X3 : X0 > $o] : ($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_565])])).
% 92.92/13.71 thf(f16665,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X2))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12853])).
% 92.92/13.71 thf(f12853,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1)) | (X1 != X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8704])).
% 92.92/13.71 thf(f8704,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1)) | (($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X3)) & (X1 != X2))) & (($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X3)) | (X1 = X2) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1))))),
% 92.92/13.71 inference(flattening,[],[f8703])).
% 92.92/13.71 thf(f8703,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1)) | (($true != vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X3)) & (X1 != X2))) & ((($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X3)) | (X1 = X2)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4476])).
% 92.92/13.71 thf(f4476,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1)) <=> (($true = vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X3)) | (X1 = X2)))),
% 92.92/13.71 inference(fool_elimination,[],[f4475])).
% 92.92/13.71 thf(f4475,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : (vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X2),X3),X1) <=> (vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X1),X3) | (X1 = X2)))),
% 92.92/13.71 inference(rectify,[],[f1951])).
% 92.92/13.71 thf(f1951,axiom,(
% 92.92/13.71 ! [X0 : $tType,X8 : X0,X18 : X0,X94 : X0 > $o] : (vAPP(X0,$o,vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINSERT(X0),X18),X94),X8) <=> (vAPP(sTfun(X0,$o),$o,vAPP(X0,sTfun(sTfun(X0,$o),$o),c_2Ebool_2EIN(X0),X8),X94) | (X8 = X18)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__applied)).
% 92.92/13.71 thf(f57130,plain,(
% 92.92/13.71 spl854_564),
% 92.92/13.71 inference(avatar_split_clause,[],[f12785,f57128])).
% 92.92/13.71 thf(f57128,plain,(
% 92.92/13.71 spl854_564 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((X0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_564])])).
% 92.92/13.71 thf(f12785,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8620])).
% 92.92/13.71 thf(f8620,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2)) | (X0 != X2) | (X1 != X3)) & (((X0 = X2) & (X1 = X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2))))),
% 92.92/13.71 inference(flattening,[],[f8619])).
% 92.92/13.71 thf(f8619,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2)) | ((X0 != X2) | (X1 != X3))) & (((X0 = X2) & (X1 = X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5327])).
% 92.92/13.71 thf(f5327,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2)) <=> ((X0 = X2) & (X1 = X3)))),
% 92.92/13.71 inference(rectify,[],[f1682])).
% 92.92/13.71 thf(f1682,axiom,(
% 92.92/13.71 ! [X70 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum,X11 : tyop_2Enum_2Enum,X457 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X4),X70) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X457),X11)) <=> ((X11 = X70) & (X4 = X457)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11)).
% 92.92/13.71 thf(f57067,plain,(
% 92.92/13.71 spl854_563),
% 92.92/13.71 inference(avatar_split_clause,[],[f12784,f57065])).
% 92.92/13.71 thf(f57065,plain,(
% 92.92/13.71 spl854_563 <=> ! [X0 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_563])])).
% 92.92/13.71 thf(f12784,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X3),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8620])).
% 92.92/13.71 thf(f57063,plain,(
% 92.92/13.71 spl854_562),
% 92.92/13.71 inference(avatar_split_clause,[],[f12782,f57061])).
% 92.92/13.71 thf(f57061,plain,(
% 92.92/13.71 spl854_562 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_562])])).
% 92.92/13.71 thf(f12782,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8618])).
% 92.92/13.71 thf(f8618,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0)) | (X0 != X1) | (X2 != X3)) & (((X0 = X1) & (X2 = X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0))))),
% 92.92/13.71 inference(flattening,[],[f8617])).
% 92.92/13.71 thf(f8617,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0)) | ((X0 != X1) | (X2 != X3))) & (((X0 = X1) & (X2 = X3)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5326])).
% 92.92/13.71 thf(f5326,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0)) <=> ((X0 = X1) & (X2 = X3)))),
% 92.92/13.71 inference(rectify,[],[f1679])).
% 92.92/13.71 thf(f1679,axiom,(
% 92.92/13.71 ! [X455 : tyop_2Enum_2Enum,X423 : tyop_2Enum_2Enum,X17 : tyop_2Enum_2Enum,X456 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X456),X423) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X17),X455)) <=> ((X423 = X455) & (X17 = X456)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enpair__11)).
% 92.92/13.71 thf(f57059,plain,(
% 92.92/13.71 spl854_561),
% 92.92/13.71 inference(avatar_split_clause,[],[f12781,f57057])).
% 92.92/13.71 thf(f57057,plain,(
% 92.92/13.71 spl854_561 <=> ! [X0 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X2 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_561])])).
% 92.92/13.71 thf(f12781,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X2 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X3),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X2),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8618])).
% 92.92/13.71 thf(f57055,plain,(
% 92.92/13.71 spl854_560),
% 92.92/13.71 inference(avatar_split_clause,[],[f12779,f57053])).
% 92.92/13.71 thf(f57053,plain,(
% 92.92/13.71 spl854_560 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((X1 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_560])])).
% 92.92/13.71 thf(f12779,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8616])).
% 92.92/13.71 thf(f8616,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)) | (X1 != X3) | (X0 != X2)) & (((X1 = X3) & (X0 = X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f8615])).
% 92.92/13.71 thf(f8615,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)) | ((X1 != X3) | (X0 != X2))) & (((X1 = X3) & (X0 = X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5325])).
% 92.92/13.71 thf(f5325,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)) <=> ((X1 = X3) & (X0 = X2)))),
% 92.92/13.71 inference(rectify,[],[f1529])).
% 92.92/13.71 thf(f1529,axiom,(
% 92.92/13.71 ! [X245 : tyop_2Enum_2Enum,X423 : tyop_2Enum_2Enum,X17 : tyop_2Enum_2Enum,X248 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X245),X423) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X17),X248)) <=> ((X248 = X423) & (X17 = X245)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2ENUMPAIR__INJ)).
% 92.92/13.71 thf(f57051,plain,(
% 92.92/13.71 spl854_559),
% 92.92/13.71 inference(avatar_split_clause,[],[f12776,f57049])).
% 92.92/13.71 thf(f57049,plain,(
% 92.92/13.71 spl854_559 <=> ! [X2 : $o,X0 : $o,X1 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((X1 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_559])])).
% 92.92/13.71 thf(f12776,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : tyop_2Enum_2Enum,X0 : $o,X1 : tyop_2Enum_2Enum] : ((X1 = X3) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8614])).
% 92.92/13.71 thf(f8614,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : tyop_2Enum_2Enum,X2 : $o,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3)) | (X1 != X3) | (X0 != X2)) & (((X1 = X3) & (X0 = X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f8613])).
% 92.92/13.71 thf(f8613,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : tyop_2Enum_2Enum,X2 : $o,X3 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3)) | ((X1 != X3) | (X0 != X2))) & (((X1 = X3) & (X0 = X2)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5324])).
% 92.92/13.71 thf(f5324,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : tyop_2Enum_2Enum,X2 : $o,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X2),X3)) <=> ((X1 = X3) & (X0 = X2)))),
% 92.92/13.71 inference(rectify,[],[f1530])).
% 92.92/13.71 thf(f1530,axiom,(
% 92.92/13.71 ! [X99 : $o,X16 : tyop_2Enum_2Enum,X424 : $o,X419 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X99),X16) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X424),X419)) <=> ((X16 = X419) & (X99 = X424)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2ENUMSUM__INJ)).
% 92.92/13.71 thf(f57047,plain,(
% 92.92/13.71 spl854_558),
% 92.92/13.71 inference(avatar_split_clause,[],[f12504,f57045])).
% 92.92/13.71 thf(f57045,plain,(
% 92.92/13.71 spl854_558 <=> ! [X0 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_558])])).
% 92.92/13.71 thf(f12504,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6076])).
% 92.92/13.71 thf(f6076,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((X0 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)))),
% 92.92/13.71 inference(ennf_transformation,[],[f5312])).
% 92.92/13.71 thf(f5312,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X2),X3)) => (X0 = X2))),
% 92.92/13.71 inference(rectify,[],[f1528])).
% 92.92/13.71 thf(f1528,axiom,(
% 92.92/13.71 ! [X245 : tyop_2Enum_2Enum,X423 : tyop_2Enum_2Enum,X17 : tyop_2Enum_2Enum,X248 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X245),X423) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X17),X248)) => (X17 = X245))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2ENUMPAIR__INJ__LEMMA)).
% 92.92/13.71 thf(f57043,plain,(
% 92.92/13.71 spl854_557),
% 92.92/13.71 inference(avatar_split_clause,[],[f12369,f57041])).
% 92.92/13.71 thf(f57041,plain,(
% 92.92/13.71 spl854_557 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > $o] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1),X2),X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_557])])).
% 92.92/13.71 thf(f12369,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1),X2),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4204])).
% 92.92/13.71 thf(f4204,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1),X2),X2))),
% 92.92/13.71 inference(fool_elimination,[],[f4203])).
% 92.92/13.71 thf(f4203,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1),X2),X2)),
% 92.92/13.71 inference(rectify,[],[f536])).
% 92.92/13.71 thf(f536,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o,X4 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X143),X4),X4)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__REFL)).
% 92.92/13.71 thf(f57039,plain,(
% 92.92/13.71 spl854_556),
% 92.92/13.71 inference(avatar_split_clause,[],[f11782,f57037])).
% 92.92/13.71 thf(f57037,plain,(
% 92.92/13.71 spl854_556 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_556])])).
% 92.92/13.71 thf(f11782,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7950])).
% 92.92/13.71 thf(f7950,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2)) | (X1 != X2)) & ((X1 = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5236])).
% 92.92/13.71 thf(f5236,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2)) <=> (X1 = X2))),
% 92.92/13.71 inference(rectify,[],[f1052])).
% 92.92/13.71 thf(f1052,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum,X108 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X108)) <=> (X108 = X137))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__ADD__LCANCEL)).
% 92.92/13.71 thf(f57035,plain,(
% 92.92/13.71 spl854_555),
% 92.92/13.71 inference(avatar_split_clause,[],[f11778,f57033])).
% 92.92/13.71 thf(f57033,plain,(
% 92.92/13.71 spl854_555 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_555])])).
% 92.92/13.71 thf(f11778,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7948])).
% 92.92/13.71 thf(f7948,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5234])).
% 92.92/13.71 thf(f5234,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X2)) <=> (X0 = X1))),
% 92.92/13.71 inference(rectify,[],[f1016])).
% 92.92/13.71 thf(f1016,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum,X108 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X137),X108) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X108)) <=> (X134 = X137))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MONO__ADD__EQ)).
% 92.92/13.71 thf(f57031,plain,(
% 92.92/13.71 spl854_554),
% 92.92/13.71 inference(avatar_split_clause,[],[f11209,f57029])).
% 92.92/13.71 thf(f57029,plain,(
% 92.92/13.71 spl854_554 <=> ! [X1 : $tType,X0 : $tType] : ($true = vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2Eantisymmetric(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_554])])).
% 92.92/13.71 thf(f11209,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType] : (($true = vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2Eantisymmetric(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3528])).
% 92.92/13.71 thf(f3528,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : ($true = vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2Eantisymmetric(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3527])).
% 92.92/13.71 thf(f3527,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2Eantisymmetric(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1))),
% 92.92/13.71 inference(rectify,[],[f617])).
% 92.92/13.71 thf(f617,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o)),$o,c_2Erelation_2Eantisymmetric(sTfun(X0,sTfun(X5,$o))),c_2Erelation_2ERSUBSET(X0,X5))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERSUBSET__antisymmetric)).
% 92.92/13.71 thf(f56968,plain,(
% 92.92/13.71 spl854_553),
% 92.92/13.71 inference(avatar_split_clause,[],[f11208,f56966])).
% 92.92/13.71 thf(f56966,plain,(
% 92.92/13.71 spl854_553 <=> ! [X1 : $tType,X0 : $tType] : ($true = vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2EWeakOrder(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_553])])).
% 92.92/13.71 thf(f11208,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType] : (($true = vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2EWeakOrder(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3526])).
% 92.92/13.71 thf(f3526,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : ($true = vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2EWeakOrder(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3525])).
% 92.92/13.71 thf(f3525,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o)),$o,c_2Erelation_2EWeakOrder(sTfun(X0,sTfun(X1,$o))),c_2Erelation_2ERSUBSET(X0,X1))),
% 92.92/13.71 inference(rectify,[],[f618])).
% 92.92/13.71 thf(f618,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X5,$o)),sTfun(sTfun(X0,sTfun(X5,$o)),$o)),$o,c_2Erelation_2EWeakOrder(sTfun(X0,sTfun(X5,$o))),c_2Erelation_2ERSUBSET(X0,X5))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERSUBSET__WeakOrder)).
% 92.92/13.71 thf(f56964,plain,(
% 92.92/13.71 spl854_552),
% 92.92/13.71 inference(avatar_split_clause,[],[f11041,f56962])).
% 92.92/13.71 thf(f56962,plain,(
% 92.92/13.71 spl854_552 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_552])])).
% 92.92/13.71 thf(f11041,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7570])).
% 92.92/13.71 thf(f56960,plain,(
% 92.92/13.71 spl854_551),
% 92.92/13.71 inference(avatar_split_clause,[],[f10528,f56958])).
% 92.92/13.71 thf(f56958,plain,(
% 92.92/13.71 spl854_551 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_551])])).
% 92.92/13.71 thf(f10528,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7028])).
% 92.92/13.71 thf(f7028,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) & (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6402])).
% 92.92/13.71 thf(f6402,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)))),
% 92.92/13.71 inference(definition_folding,[],[f5775,f6401,f6400])).
% 92.92/13.71 thf(f6400,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) <=> ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f6401,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) <=> ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,X0)) | ((c_2Ebool_2EF != $true) & ($true = X1))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f5775,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : (((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)))) <=> ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,X0)) | ((c_2Ebool_2EF != $true) & ($true = X1))))),
% 92.92/13.71 inference(flattening,[],[f5774])).
% 92.92/13.71 thf(f5774,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : (((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)))) <=> (((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,X0))) | ((c_2Ebool_2EF != $true) & ($true = X1))))),
% 92.92/13.71 inference(ennf_transformation,[],[f2998])).
% 92.92/13.71 thf(f2998,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0))) => (c_2Ebool_2EF = $true)) <=> ((($true = X1) => (c_2Ebool_2EF = $true)) => (($true = vAPP($o,$o,vNOT,X0)) => (c_2Ebool_2EF = $true))))),
% 92.92/13.71 inference(fool_elimination,[],[f2997])).
% 92.92/13.71 thf(f2997,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X0 | X1) => c_2Ebool_2EF) <=> ((X1 => c_2Ebool_2EF) => (vAPP($o,$o,vNOT,X0) => c_2Ebool_2EF)))),
% 92.92/13.71 inference(rectify,[],[f288])).
% 92.92/13.71 thf(f288,axiom,(
% 92.92/13.71 ! [X105 : $o,X106 : $o] : ((vAPP($o,$o,vNOT,X105 | X106) => c_2Ebool_2EF) <=> ((X106 => c_2Ebool_2EF) => (vAPP($o,$o,vNOT,X105) => c_2Ebool_2EF)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2)).
% 92.92/13.71 thf(f56956,plain,(
% 92.92/13.71 spl854_550),
% 92.92/13.71 inference(avatar_split_clause,[],[f10527,f56954])).
% 92.92/13.71 thf(f56954,plain,(
% 92.92/13.71 spl854_550 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_550])])).
% 92.92/13.71 thf(f10527,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7028])).
% 92.92/13.71 thf(f56952,plain,(
% 92.92/13.71 spl854_549),
% 92.92/13.71 inference(avatar_split_clause,[],[f10489,f56950])).
% 92.92/13.71 thf(f56950,plain,(
% 92.92/13.71 spl854_549 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_549])])).
% 92.92/13.71 thf(f10489,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7009])).
% 92.92/13.71 thf(f7009,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5120])).
% 92.92/13.71 thf(f5120,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1)) <=> (X0 = X1))),
% 92.92/13.71 inference(rectify,[],[f1224])).
% 92.92/13.71 thf(f1224,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X134),X137)) <=> (X134 = X137))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMIN__MAX__EQ)).
% 92.92/13.71 thf(f56948,plain,(
% 92.92/13.71 spl854_548),
% 92.92/13.71 inference(avatar_split_clause,[],[f10143,f56946])).
% 92.92/13.71 thf(f56946,plain,(
% 92.92/13.71 spl854_548 <=> ! [X0 : $tType,X5 : X0,X1 : X0 > X0 > $o] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X5),X5))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_548])])).
% 92.92/13.71 thf(f10143,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X5),X5))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5521])).
% 92.92/13.71 thf(f5521,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) & ! [X5 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X5),X5)))),
% 92.92/13.71 inference(flattening,[],[f5520])).
% 92.92/13.71 thf(f5520,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X2),X4)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & ! [X5 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X5),X5)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2606])).
% 92.92/13.71 thf(f2606,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X2),X4))) & ! [X5 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X5),X5)))),
% 92.92/13.71 inference(fool_elimination,[],[f2605])).
% 92.92/13.71 thf(f2605,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X2),X4)) & ! [X5 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X5),X5))),
% 92.92/13.71 inference(rectify,[],[f463])).
% 92.92/13.71 thf(f463,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (! [X19 : X0,X50 : X0,X116 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143),X50),X116) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X19),X50)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143),X19),X116)) & ! [X4 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143),X4),X4))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERTC__RULES)).
% 92.92/13.71 thf(f56944,plain,(
% 92.92/13.71 spl854_547),
% 92.92/13.71 inference(avatar_split_clause,[],[f9883,f56942])).
% 92.92/13.71 thf(f56942,plain,(
% 92.92/13.71 spl854_547 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),X1) = X1)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_547])])).
% 92.92/13.71 thf(f9883,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),X1) = X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4986])).
% 92.92/13.71 thf(f4986,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X1),X1) = X1)),
% 92.92/13.71 inference(rectify,[],[f1901])).
% 92.92/13.71 thf(f1901,axiom,(
% 92.92/13.71 ! [X0 : $tType,X111 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EUNION(X0),X111),X111) = X111)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__IDEMPOT)).
% 92.92/13.71 thf(f56940,plain,(
% 92.92/13.71 spl854_546),
% 92.92/13.71 inference(avatar_split_clause,[],[f9882,f56938])).
% 92.92/13.71 thf(f56938,plain,(
% 92.92/13.71 spl854_546 <=> ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),X1) = X1)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_546])])).
% 92.92/13.71 thf(f9882,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),X1) = X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4985])).
% 92.92/13.71 thf(f4985,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X1),X1) = X1)),
% 92.92/13.71 inference(rectify,[],[f1913])).
% 92.92/13.71 thf(f1913,axiom,(
% 92.92/13.71 ! [X0 : $tType,X111 : X0 > $o] : (vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),c_2Epred__set_2EINTER(X0),X111),X111) = X111)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__IDEMPOT)).
% 92.92/13.71 thf(f56936,plain,(
% 92.92/13.71 spl854_545),
% 92.92/13.71 inference(avatar_split_clause,[],[f9881,f56934])).
% 92.92/13.71 thf(f56934,plain,(
% 92.92/13.71 spl854_545 <=> ! [X0 : $tType,X1 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(X0,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINL(X0,tyop_2Eone_2Eone),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_545])])).
% 92.92/13.71 thf(f9881,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(X0,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINL(X0,tyop_2Eone_2Eone),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4984])).
% 92.92/13.71 thf(f4984,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(X0,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINL(X0,tyop_2Eone_2Eone),X1)))),
% 92.92/13.71 inference(rectify,[],[f705])).
% 92.92/13.71 thf(f705,axiom,(
% 92.92/13.71 ! [X0 : $tType,X8 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8) = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(X0,tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Esum_2EINL(X0,tyop_2Eone_2Eone),X8)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2ESOME__DEF)).
% 92.92/13.71 thf(f56645,plain,(
% 92.92/13.71 spl854_544 | ~spl854_308 | ~spl854_532),
% 92.92/13.71 inference(avatar_split_clause,[],[f54524,f54521,f35574,f56643])).
% 92.92/13.71 thf(f56643,plain,(
% 92.92/13.71 spl854_544 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_544])])).
% 92.92/13.71 thf(f54521,plain,(
% 92.92/13.71 spl854_532 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_532])])).
% 92.92/13.71 thf(f54524,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) ) | (~spl854_308 | ~spl854_532)),
% 92.92/13.71 inference(forward_demodulation,[],[f54522,f35576])).
% 92.92/13.71 thf(f54522,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) ) | ~spl854_532),
% 92.92/13.71 inference(avatar_component_clause,[],[f54521])).
% 92.92/13.71 thf(f56558,plain,(
% 92.92/13.71 spl854_543 | ~spl854_168 | ~spl854_525),
% 92.92/13.71 inference(avatar_split_clause,[],[f54425,f54422,f22983,f56556])).
% 92.92/13.71 thf(f56556,plain,(
% 92.92/13.71 spl854_543 <=> ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_543])])).
% 92.92/13.71 thf(f54422,plain,(
% 92.92/13.71 spl854_525 <=> ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_525])])).
% 92.92/13.71 thf(f54425,plain,(
% 92.92/13.71 ( ! [X26 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) ) | (~spl854_168 | ~spl854_525)),
% 92.92/13.71 inference(forward_demodulation,[],[f54423,f22985])).
% 92.92/13.71 thf(f54423,plain,(
% 92.92/13.71 ( ! [X26 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X26),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) ) | ~spl854_525),
% 92.92/13.71 inference(avatar_component_clause,[],[f54422])).
% 92.92/13.71 thf(f54620,plain,(
% 92.92/13.71 spl854_542 | ~spl854_9),
% 92.92/13.71 inference(avatar_split_clause,[],[f30453,f21928,f54618])).
% 92.92/13.71 thf(f54618,plain,(
% 92.92/13.71 spl854_542 <=> ! [X28 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_542])])).
% 92.92/13.71 thf(f30453,plain,(
% 92.92/13.71 ( ! [X28 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28)))) ) | ~spl854_9),
% 92.92/13.71 inference(forward_demodulation,[],[f13615,f21929])).
% 92.92/13.71 thf(f13615,plain,(
% 92.92/13.71 ( ! [X28 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9206,f9122,f9122])).
% 92.92/13.71 thf(f9206,plain,(
% 92.92/13.71 ( ! [X28 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X28))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6597])).
% 92.92/13.71 thf(f54616,plain,(
% 92.92/13.71 spl854_541 | ~spl854_9),
% 92.92/13.71 inference(avatar_split_clause,[],[f30452,f21928,f54614])).
% 92.92/13.71 thf(f54614,plain,(
% 92.92/13.71 spl854_541 <=> ! [X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_541])])).
% 92.92/13.71 thf(f30452,plain,(
% 92.92/13.71 ( ! [X27 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)))) ) | ~spl854_9),
% 92.92/13.71 inference(forward_demodulation,[],[f13614,f21929])).
% 92.92/13.71 thf(f13614,plain,(
% 92.92/13.71 ( ! [X27 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9207,f9122,f9122])).
% 92.92/13.71 thf(f9207,plain,(
% 92.92/13.71 ( ! [X27 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6597])).
% 92.92/13.71 thf(f54612,plain,(
% 92.92/13.71 spl854_540 | ~spl854_103 | ~spl854_196),
% 92.92/13.71 inference(avatar_split_clause,[],[f29758,f23496,f22595,f54610])).
% 92.92/13.71 thf(f54610,plain,(
% 92.92/13.71 spl854_540 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_540])])).
% 92.92/13.71 thf(f22595,plain,(
% 92.92/13.71 spl854_103 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X0)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_103])])).
% 92.92/13.71 thf(f23496,plain,(
% 92.92/13.71 spl854_196 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0)) = X0)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_196])])).
% 92.92/13.71 thf(f29758,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0))) ) | (~spl854_103 | ~spl854_196)),
% 92.92/13.71 inference(forward_demodulation,[],[f9320,f23919])).
% 92.92/13.71 thf(f23919,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0))) ) | (~spl854_103 | ~spl854_196)),
% 92.92/13.71 inference(superposition,[],[f22596,f23497])).
% 92.92/13.71 thf(f23497,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0)) = X0)) ) | ~spl854_196),
% 92.92/13.71 inference(avatar_component_clause,[],[f23496])).
% 92.92/13.71 thf(f22596,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X0)) ) | ~spl854_103),
% 92.92/13.71 inference(avatar_component_clause,[],[f22595])).
% 92.92/13.71 thf(f9320,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4892])).
% 92.92/13.71 thf(f4892,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X0))))),
% 92.92/13.71 inference(rectify,[],[f1650])).
% 92.92/13.71 thf(f1650,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,X136))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Ensnd__def)).
% 92.92/13.71 thf(f54608,plain,(
% 92.92/13.71 spl854_539 | ~spl854_9 | ~spl854_160),
% 92.92/13.71 inference(avatar_split_clause,[],[f29757,f22950,f21928,f54606])).
% 92.92/13.71 thf(f54606,plain,(
% 92.92/13.71 spl854_539 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_539])])).
% 92.92/13.71 thf(f29757,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) ) | (~spl854_9 | ~spl854_160)),
% 92.92/13.71 inference(forward_demodulation,[],[f18198,f29755])).
% 92.92/13.71 thf(f18198,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13680,f13567])).
% 92.92/13.71 thf(f13680,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9321,f13512])).
% 92.92/13.71 thf(f9321,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4893])).
% 92.92/13.71 thf(f4893,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X0))),
% 92.92/13.71 inference(rectify,[],[f933])).
% 92.92/13.71 thf(f933,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV2__def)).
% 92.92/13.71 thf(f54604,plain,(
% 92.92/13.71 spl854_538),
% 92.92/13.71 inference(avatar_split_clause,[],[f20095,f54602])).
% 92.92/13.71 thf(f54602,plain,(
% 92.92/13.71 spl854_538 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,$true),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X2)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_538])])).
% 92.92/13.71 thf(f20095,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,$true),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X2)) )),
% 92.92/13.71 inference(forward_demodulation,[],[f15351,f13591])).
% 92.92/13.71 thf(f15351,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X2)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f12454,f13514,f13512])).
% 92.92/13.71 thf(f12454,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2EiSUB,c_2Ebool_2ET),X2),c_2Earithmetic_2EZERO) = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5308])).
% 92.92/13.71 thf(f54600,plain,(
% 92.92/13.71 spl854_537),
% 92.92/13.71 inference(avatar_split_clause,[],[f19175,f54597])).
% 92.92/13.71 thf(f54597,plain,(
% 92.92/13.71 spl854_537 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_537])])).
% 92.92/13.71 thf(f19175,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 inference(forward_demodulation,[],[f19174,f18124])).
% 92.92/13.71 thf(f19174,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 inference(forward_demodulation,[],[f19173,f13563])).
% 92.92/13.71 thf(f19173,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 inference(forward_demodulation,[],[f15824,f13548])).
% 92.92/13.71 thf(f15824,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 inference(equality_resolution,[],[f15823])).
% 92.92/13.71 thf(f15823,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X1)) )),
% 92.92/13.71 inference(equality_resolution,[],[f14447])).
% 92.92/13.71 thf(f14447,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X1)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10485,f9122,f13512])).
% 92.92/13.71 thf(f10485,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)) | (c_2Enum_2E0 != X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7007])).
% 92.92/13.71 thf(f54595,plain,(
% 92.92/13.71 spl854_536),
% 92.92/13.71 inference(avatar_split_clause,[],[f19172,f54592])).
% 92.92/13.71 thf(f54592,plain,(
% 92.92/13.71 spl854_536 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_536])])).
% 92.92/13.71 thf(f19172,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 inference(forward_demodulation,[],[f19171,f18124])).
% 92.92/13.71 thf(f19171,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 inference(forward_demodulation,[],[f19170,f13563])).
% 92.92/13.71 thf(f19170,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 inference(forward_demodulation,[],[f15822,f13548])).
% 92.92/13.71 thf(f15822,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.71 inference(equality_resolution,[],[f15821])).
% 92.92/13.71 thf(f15821,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X1)) )),
% 92.92/13.71 inference(equality_resolution,[],[f14446])).
% 92.92/13.71 thf(f14446,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X1)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10486,f13512,f9122])).
% 92.92/13.71 thf(f10486,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP11,X1),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != X0) | (c_2Enum_2E0 != X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7007])).
% 92.92/13.71 thf(f54536,plain,(
% 92.92/13.71 spl854_535),
% 92.92/13.71 inference(avatar_split_clause,[],[f18676,f54534])).
% 92.92/13.71 thf(f54534,plain,(
% 92.92/13.71 spl854_535 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_535])])).
% 92.92/13.71 thf(f18676,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f17777,f13567])).
% 92.92/13.71 thf(f17777,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.71 inference(equality_proxy_clausification,[],[f17776])).
% 92.92/13.71 thf(f17776,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f14073])).
% 92.92/13.71 thf(f14073,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9843,f9122,f13512])).
% 92.92/13.71 thf(f9843,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2526])).
% 92.92/13.71 thf(f2526,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0))))),
% 92.92/13.71 inference(fool_elimination,[],[f2525])).
% 92.92/13.71 thf(f2525,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X0)))),
% 92.92/13.71 inference(rectify,[],[f1726])).
% 92.92/13.71 thf(f1726,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X136)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ETWOEXP__NOT__ZERO)).
% 92.92/13.71 thf(f54532,plain,(
% 92.92/13.71 spl854_534),
% 92.92/13.71 inference(avatar_split_clause,[],[f18593,f54530])).
% 92.92/13.71 thf(f54530,plain,(
% 92.92/13.71 spl854_534 <=> ! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X1))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_534])])).
% 92.92/13.71 thf(f18593,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X1))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18592,f18222])).
% 92.92/13.71 thf(f18592,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f15735,f13567])).
% 92.92/13.71 thf(f15735,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1))))) )),
% 92.92/13.71 inference(equality_resolution,[],[f14011])).
% 92.92/13.71 thf(f14011,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1)) != X0)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9766,f13519,f9121,f13512])).
% 92.92/13.71 thf(f9766,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1)) != X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6809])).
% 92.92/13.71 thf(f54528,plain,(
% 92.92/13.71 spl854_533),
% 92.92/13.71 inference(avatar_split_clause,[],[f18257,f54526])).
% 92.92/13.71 thf(f54526,plain,(
% 92.92/13.71 spl854_533 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_533])])).
% 92.92/13.71 thf(f18257,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18256,f18204])).
% 92.92/13.71 thf(f18204,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18203,f18124])).
% 92.92/13.71 thf(f18203,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18202,f13563])).
% 92.92/13.71 thf(f18202,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13682,f13548])).
% 92.92/13.71 thf(f13682,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9323,f13512])).
% 92.92/13.71 thf(f9323,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4895])).
% 92.92/13.71 thf(f4895,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.92/13.71 inference(rectify,[],[f989])).
% 92.92/13.71 thf(f989,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1)).
% 92.92/13.71 thf(f18256,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18255,f18124])).
% 92.92/13.71 thf(f18255,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18254,f13563])).
% 92.92/13.71 thf(f18254,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18253,f13548])).
% 92.92/13.71 thf(f18253,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18252,f18222])).
% 92.92/13.71 thf(f18252,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13698,f13567])).
% 92.92/13.71 thf(f13698,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9342,f9121,f13512,f9121,f13512])).
% 92.92/13.71 thf(f9342,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4912])).
% 92.92/13.71 thf(f4912,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))),
% 92.92/13.71 inference(rectify,[],[f1657])).
% 92.92/13.71 thf(f1657,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Etwotri__formula)).
% 92.92/13.71 thf(f54523,plain,(
% 92.92/13.71 spl854_532),
% 92.92/13.71 inference(avatar_split_clause,[],[f18222,f54521])).
% 92.92/13.71 thf(f54519,plain,(
% 92.92/13.71 spl854_531),
% 92.92/13.71 inference(avatar_split_clause,[],[f18217,f54517])).
% 92.92/13.71 thf(f54517,plain,(
% 92.92/13.71 spl854_531 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_531])])).
% 92.92/13.71 thf(f18217,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18216,f18124])).
% 92.92/13.71 thf(f18216,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18215,f13563])).
% 92.92/13.71 thf(f18215,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13687,f13548])).
% 92.92/13.71 thf(f13687,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9328,f13512])).
% 92.92/13.71 thf(f9328,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4900])).
% 92.92/13.71 thf(f4900,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0)),
% 92.92/13.71 inference(rectify,[],[f990])).
% 92.92/13.71 thf(f990,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X134)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X134)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUC__SUB1)).
% 92.92/13.71 thf(f54515,plain,(
% 92.92/13.71 spl854_530),
% 92.92/13.71 inference(avatar_split_clause,[],[f18210,f54513])).
% 92.92/13.71 thf(f54513,plain,(
% 92.92/13.71 spl854_530 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_530])])).
% 92.92/13.71 thf(f18210,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18209,f18124])).
% 92.92/13.71 thf(f18209,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18208,f13563])).
% 92.92/13.71 thf(f18208,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13684,f13548])).
% 92.92/13.71 thf(f13684,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9325,f13512])).
% 92.92/13.71 thf(f9325,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4897])).
% 92.92/13.71 thf(f4897,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0))),
% 92.92/13.71 inference(rectify,[],[f1721])).
% 92.92/13.71 thf(f1721,axiom,(
% 92.92/13.71 ! [X72 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X72)),X72))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ESUC__SUB)).
% 92.92/13.71 thf(f54511,plain,(
% 92.92/13.71 spl854_529),
% 92.92/13.71 inference(avatar_split_clause,[],[f18207,f54509])).
% 92.92/13.71 thf(f54509,plain,(
% 92.92/13.71 spl854_529 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_529])])).
% 92.92/13.71 thf(f18207,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18206,f18124])).
% 92.92/13.71 thf(f18206,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18205,f13563])).
% 92.92/13.71 thf(f18205,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13683,f13548])).
% 92.92/13.71 thf(f13683,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9324,f13512])).
% 92.92/13.71 thf(f9324,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4896])).
% 92.92/13.71 thf(f4896,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))),
% 92.92/13.71 inference(rectify,[],[f1108])).
% 92.92/13.71 thf(f1108,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X136))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUC__ONE__ADD)).
% 92.92/13.71 thf(f54507,plain,(
% 92.92/13.71 spl854_528),
% 92.92/13.71 inference(avatar_split_clause,[],[f18204,f54505])).
% 92.92/13.71 thf(f54505,plain,(
% 92.92/13.71 spl854_528 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_528])])).
% 92.92/13.71 thf(f54503,plain,(
% 92.92/13.71 spl854_527),
% 92.92/13.71 inference(avatar_split_clause,[],[f18201,f54501])).
% 92.92/13.71 thf(f54501,plain,(
% 92.92/13.71 spl854_527 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_527])])).
% 92.92/13.71 thf(f54499,plain,(
% 92.92/13.71 spl854_526),
% 92.92/13.71 inference(avatar_split_clause,[],[f18179,f54497])).
% 92.92/13.71 thf(f54497,plain,(
% 92.92/13.71 spl854_526 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_526])])).
% 92.92/13.71 thf(f18179,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f18178,f18124])).
% 92.92/13.71 thf(f18178,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f13672,f13563])).
% 92.92/13.71 thf(f13672,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9307,f9122,f9122])).
% 92.92/13.71 thf(f9307,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4881])).
% 92.92/13.71 thf(f4881,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)))),
% 92.92/13.71 inference(rectify,[],[f1137])).
% 92.92/13.71 thf(f1137,axiom,(
% 92.92/13.71 ! [X316 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X316),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__ONE)).
% 92.92/13.71 thf(f54424,plain,(
% 92.92/13.71 spl854_525),
% 92.92/13.71 inference(avatar_split_clause,[],[f18122,f54422])).
% 92.92/13.71 thf(f54420,plain,(
% 92.92/13.71 spl854_524),
% 92.92/13.71 inference(avatar_split_clause,[],[f17460,f54418])).
% 92.92/13.71 thf(f54418,plain,(
% 92.92/13.71 spl854_524 <=> ! [X0 : $tType,X1 : X0 > X0 > $o,X3 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_524])])).
% 92.92/13.71 thf(f17460,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0 > $o] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f10756])).
% 92.92/13.71 thf(f10756,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7355])).
% 92.92/13.71 thf(f7355,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK339(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK339(X0),X1))))) & (! [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK339])],[f7353,f7354])).
% 92.92/13.71 thf(f7354,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2))) => ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK339(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK339(X0),X1)))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7353,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ? [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2)))) & (! [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))))),
% 92.92/13.71 inference(rectify,[],[f7352])).
% 92.92/13.71 thf(f7352,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ? [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2)))) & (! [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3176])).
% 92.92/13.71 thf(f3176,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) <=> ! [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2))))),
% 92.92/13.71 inference(fool_elimination,[],[f3175])).
% 92.92/13.71 thf(f3175,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1) <=> ! [X2 : X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2)))),
% 92.92/13.71 inference(rectify,[],[f410])).
% 92.92/13.71 thf(f410,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X143) <=> ! [X4 : X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X4)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Eirreflexive__def)).
% 92.92/13.71 thf(f54416,plain,(
% 92.92/13.71 spl854_523),
% 92.92/13.71 inference(avatar_split_clause,[],[f17157,f54414])).
% 92.92/13.71 thf(f54414,plain,(
% 92.92/13.71 spl854_523 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((X1 != X2) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_523])])).
% 92.92/13.71 thf(f17157,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((X1 != X2) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2))) )),
% 92.92/13.71 inference(equality_proxy_clausification,[],[f17156])).
% 92.92/13.71 thf(f17156,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12191])).
% 92.92/13.71 thf(f12191,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8304])).
% 92.92/13.71 thf(f8304,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2)) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))) & ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2))))),
% 92.92/13.71 inference(flattening,[],[f8303])).
% 92.92/13.71 thf(f8303,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2)) | (($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)))) & ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f4120])).
% 92.92/13.71 thf(f4120,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2)) <=> (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),X1),X2))) & ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2))))),
% 92.92/13.71 inference(fool_elimination,[],[f4119])).
% 92.92/13.71 thf(f4119,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X2) <=> (vAPP($o,$o,vNOT,(X1 = X2)) & vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X2)))),
% 92.92/13.71 inference(rectify,[],[f1845])).
% 92.92/13.71 thf(f1845,axiom,(
% 92.92/13.71 ! [X0 : $tType,X111 : X0 > $o,X40 : X0 > $o] : (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X111),X40) <=> (vAPP($o,$o,vNOT,(X40 = X111)) & vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X111),X40)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__DEF)).
% 92.92/13.71 thf(f54412,plain,(
% 92.92/13.71 spl854_522),
% 92.92/13.71 inference(avatar_split_clause,[],[f16472,f54410])).
% 92.92/13.71 thf(f54410,plain,(
% 92.92/13.71 spl854_522 <=> ! [X2 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_522])])).
% 92.92/13.71 thf(f16472,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.71 inference(equality_resolution,[],[f16471])).
% 92.92/13.71 thf(f16471,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X2),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X0)) )),
% 92.92/13.71 inference(equality_resolution,[],[f15209])).
% 92.92/13.71 thf(f15209,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X1),X0)) | (X1 != X2) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X0)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f12226,f9122])).
% 92.92/13.71 thf(f12226,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X1),X0)) | (X1 != X2) | (c_2Enum_2E0 != X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8333])).
% 92.92/13.71 thf(f8333,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X1),X0)) | (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) & ((X1 != X2) | (c_2Enum_2E0 != X0)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) | ((X1 = X2) & (c_2Enum_2E0 = X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8332])).
% 92.92/13.71 thf(f8332,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X1),X2),X0)) | (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) & ((X1 != X2) | (c_2Enum_2E0 != X0)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) | ((X1 = X2) & (c_2Enum_2E0 = X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X1),X2),X0))))),
% 92.92/13.71 inference(flattening,[],[f8331])).
% 92.92/13.71 thf(f8331,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X1),X2),X0)) | (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) & ((X1 != X2) | (c_2Enum_2E0 != X0)))) & ((((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) | ((X1 = X2) & (c_2Enum_2E0 = X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X1),X2),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6479])).
% 92.92/13.71 thf(f6479,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sP57,X1),X2),X0)) <=> (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD,X2),X0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) | ((X1 = X2) & (c_2Enum_2E0 = X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f54408,plain,(
% 92.92/13.71 spl854_521),
% 92.92/13.71 inference(avatar_split_clause,[],[f15780,f54406])).
% 92.92/13.71 thf(f54406,plain,(
% 92.92/13.71 spl854_521 <=> ! [X0 : $tType,X1 : X0 > X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_521])])).
% 92.92/13.71 thf(f15780,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.92/13.71 inference(equality_resolution,[],[f10299])).
% 92.92/13.71 thf(f10299,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | (X2 != X3) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6915])).
% 92.92/13.71 thf(f6915,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0] : (((X2 = X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) & ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | (X2 != X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 inference(flattening,[],[f6914])).
% 92.92/13.71 thf(f6914,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0] : (((X2 = X3) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) & ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) | (X2 != X3))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 inference(nnf_transformation,[],[f5675])).
% 92.92/13.71 thf(f5675,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (! [X2 : X0,X3 : X0] : ((X2 = X3) <=> (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2788])).
% 92.92/13.71 thf(f2788,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) => ! [X2 : X0,X3 : X0] : ((X2 = X3) <=> (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 92.92/13.71 inference(fool_elimination,[],[f2787])).
% 92.92/13.71 thf(f2787,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1) => ! [X2 : X0,X3 : X0] : ((X2 = X3) <=> (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 inference(rectify,[],[f615])).
% 92.92/13.71 thf(f615,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X143) => ! [X18 : X0,X39 : X0] : ((X18 = X39) <=> (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X39),X18) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X18),X39))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWeakOrder__EQ)).
% 92.92/13.71 thf(f54404,plain,(
% 92.92/13.71 spl854_520),
% 92.92/13.71 inference(avatar_split_clause,[],[f14060,f54402])).
% 92.92/13.71 thf(f54402,plain,(
% 92.92/13.71 spl854_520 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_520])])).
% 92.92/13.71 thf(f14060,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9821,f9122])).
% 92.92/13.71 thf(f9821,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),c_2Enum_2E0),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2482])).
% 92.92/13.71 thf(f2482,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),c_2Enum_2E0),X0))),
% 92.92/13.71 inference(fool_elimination,[],[f2481])).
% 92.92/13.71 thf(f2481,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),c_2Enum_2E0),X0)),
% 92.92/13.71 inference(rectify,[],[f1562])).
% 92.92/13.71 thf(f1562,axiom,(
% 92.92/13.71 ! [X72 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X72),c_2Enum_2E0),X72)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0R)).
% 92.92/13.71 thf(f54400,plain,(
% 92.92/13.71 spl854_519),
% 92.92/13.71 inference(avatar_split_clause,[],[f14059,f54398])).
% 92.92/13.71 thf(f54398,plain,(
% 92.92/13.71 spl854_519 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_519])])).
% 92.92/13.71 thf(f14059,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9820,f9122])).
% 92.92/13.71 thf(f9820,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,c_2Enum_2E0),X0),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2480])).
% 92.92/13.71 thf(f2480,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,c_2Enum_2E0),X0),X0))),
% 92.92/13.71 inference(fool_elimination,[],[f2479])).
% 92.92/13.71 thf(f2479,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,c_2Enum_2E0),X0),X0)),
% 92.92/13.71 inference(rectify,[],[f1563])).
% 92.92/13.71 thf(f1563,axiom,(
% 92.92/13.71 ! [X72 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,c_2Enum_2E0),X72),X72)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0L)).
% 92.92/13.71 thf(f54396,plain,(
% 92.92/13.71 spl854_518),
% 92.92/13.71 inference(avatar_split_clause,[],[f13096,f54394])).
% 92.92/13.71 thf(f54394,plain,(
% 92.92/13.71 spl854_518 <=> ! [X0 : $tType,X19 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X19)) = X19) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X19)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_518])])).
% 92.92/13.71 thf(f13096,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X19 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X19)) = X19) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X19))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8878])).
% 92.92/13.71 thf(f8878,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : tyop_2Eoption_2Eoption(X0),X4 : X1] : (! [X5 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X5)) = X5) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))) & ! [X6 : X0 > X1] : (c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X6),c_2Eoption_2ENONE(X0))) & ! [X7 : X0 > X1,X8 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X7),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X7,X8))) & ! [X9 : X0,X10 : X1,X11 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X9)),X10),X11) = vAPP(X0,X1,X11,X9)) & ! [X12 : X1,X13 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X12),X13) = X12) & ! [X14 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X14),X3),c_2Eoption_2ESOME(X0)) = X14) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X14))) & ! [X15 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X15),X4),X2) = vAPP(X0,X1,X2,vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X15))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X15))) & ! [X16 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X16),X4),X2) = X4) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X16))) & ! [X17 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X17),X17),c_2Eoption_2ESOME(X0)) = X17) & ! [X18 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X18),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X18) & ! [X19 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X19)) = X19) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X19))) & ! [X20 : tyop_2Eoption_2Eoption(X0)] : ((($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X20))) | (c_2Eoption_2ENONE(X0) != X20)) & ((c_2Eoption_2ENONE(X0) = X20) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X20))))) & ! [X21 : tyop_2Eoption_2Eoption(X0)] : ((($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X21)) | (c_2Eoption_2ENONE(X0) != X21)) & ((c_2Eoption_2ENONE(X0) = X21) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X21)))) & (c_2Ebool_2EF = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) & ! [X22 : X0] : (c_2Ebool_2ET = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X22))) & ! [X23 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),$o),vEQ(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X23)))) & ! [X24 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),$o),vEQ(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X24)))) & ! [X25 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X25)) = X25) & ! [X26 : X0,X27 : X0] : (((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X26) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X27)) | (X26 != X27)) & ((X26 = X27) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X26) != vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X27)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6235])).
% 92.92/13.71 thf(f6235,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : tyop_2Eoption_2Eoption(X0),X4 : X1] : (! [X5 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X5)) = X5) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))) & ! [X6 : X0 > X1] : (c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X6),c_2Eoption_2ENONE(X0))) & ! [X7 : X0 > X1,X8 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X7),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X7,X8))) & ! [X9 : X0,X10 : X1,X11 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X9)),X10),X11) = vAPP(X0,X1,X11,X9)) & ! [X12 : X1,X13 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X12),X13) = X12) & ! [X14 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X14),X3),c_2Eoption_2ESOME(X0)) = X14) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X14))) & ! [X15 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X15),X4),X2) = vAPP(X0,X1,X2,vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X15))) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X15))) & ! [X16 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X16),X4),X2) = X4) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X16))) & ! [X17 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X17),X17),c_2Eoption_2ESOME(X0)) = X17) & ! [X18 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X18),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X18) & ! [X19 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X19)) = X19) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X19))) & ! [X20 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X20))) <=> (c_2Eoption_2ENONE(X0) = X20)) & ! [X21 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X21)) <=> (c_2Eoption_2ENONE(X0) = X21)) & (c_2Ebool_2EF = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) & ! [X22 : X0] : (c_2Ebool_2ET = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X22))) & ! [X23 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),$o),vEQ(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X23)))) & ! [X24 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),$o),vEQ(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X24)))) & ! [X25 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X25)) = X25) & ! [X26 : X0,X27 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X26) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X27)) <=> (X26 = X27)))),
% 92.92/13.71 inference(ennf_transformation,[],[f4622])).
% 92.92/13.71 thf(f4622,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : tyop_2Eoption_2Eoption(X0),X4 : X1] : (! [X5 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X5)) = X5) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))) & ! [X6 : X0 > X1] : (c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X6),c_2Eoption_2ENONE(X0))) & ! [X7 : X0 > X1,X8 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X7),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X7,X8))) & ! [X9 : X0,X10 : X1,X11 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X9)),X10),X11) = vAPP(X0,X1,X11,X9)) & ! [X12 : X1,X13 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X12),X13) = X12) & ! [X14 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X14)) => (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X14),X3),c_2Eoption_2ESOME(X0)) = X14)) & ! [X15 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X15)) => (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X15),X4),X2) = vAPP(X0,X1,X2,vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X15)))) & ! [X16 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X16)) => (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X16),X4),X2) = X4)) & ! [X17 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X17),X17),c_2Eoption_2ESOME(X0)) = X17) & ! [X18 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X18),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X18) & ! [X19 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X19)) => (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X19)) = X19)) & ! [X20 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X20))) <=> (c_2Eoption_2ENONE(X0) = X20)) & ! [X21 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X21)) <=> (c_2Eoption_2ENONE(X0) = X21)) & (c_2Ebool_2EF = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) & ! [X22 : X0] : (c_2Ebool_2ET = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X22))) & ! [X23 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),$o),vEQ(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X23)))) & ! [X24 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),$o),vEQ(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE(X0)),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X24)))) & ! [X25 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X25)) = X25) & ! [X26 : X0,X27 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X26) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X27)) <=> (X26 = X27)))),
% 92.92/13.71 inference(fool_elimination,[],[f4621])).
% 92.92/13.71 thf(f4621,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : tyop_2Eoption_2Eoption(X0),X4 : X1] : (! [X5 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X5)) = X5) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))) & ! [X6 : X0 > X1] : (c_2Eoption_2ENONE(X1) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X6),c_2Eoption_2ENONE(X0))) & ! [X7 : X0 > X1,X8 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1),vAPP(sTfun(X0,X1),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1)),c_2Eoption_2EOPTION__MAP(X0,X1),X7),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8)) = vAPP(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME(X1),vAPP(X0,X1,X7,X8))) & ! [X9 : X0,X10 : X1,X11 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X9)),X10),X11) = vAPP(X0,X1,X11,X9)) & ! [X12 : X1,X13 : X0 > X1] : (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X12),X13) = X12) & ! [X14 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X14) => (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X14),X3),c_2Eoption_2ESOME(X0)) = X14)) & ! [X15 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X15) => (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X15),X4),X2) = vAPP(X0,X1,X2,vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X15)))) & ! [X16 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X16) => (vAPP(sTfun(X0,X1),X1,vAPP(X1,sTfun(sTfun(X0,X1),X1),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X1,sTfun(sTfun(X0,X1),X1)),c_2Eoption_2Eoption__CASE(X0,X1),X16),X4),X2) = X4)) & ! [X17 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X17),X17),c_2Eoption_2ESOME(X0)) = X17) & ! [X18 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X18),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X18) & ! [X19 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X19) => (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X19)) = X19)) & ! [X20 : tyop_2Eoption_2Eoption(X0)] : (vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X20)) <=> (c_2Eoption_2ENONE(X0) = X20)) & ! [X21 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X21) <=> (c_2Eoption_2ENONE(X0) = X21)) & (c_2Ebool_2EF = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) & ! [X22 : X0] : (c_2Ebool_2ET = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X22))) & ! [X23 : X0] : vAPP($o,$o,vNOT,(c_2Eoption_2ENONE(X0) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X23))) & ! [X24 : X0] : vAPP($o,$o,vNOT,(c_2Eoption_2ENONE(X0) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X24))) & ! [X25 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X25)) = X25) & ! [X26 : X0,X27 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X26) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X27)) <=> (X26 = X27)))),
% 92.92/13.71 inference(rectify,[],[f737])).
% 92.92/13.71 thf(f737,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X3 : X0 > X5,X117 : tyop_2Eoption_2Eoption(X0),X217 : X5] : (! [X234 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X234)) = X234) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))) & ! [X233 : X0 > X5] : (c_2Eoption_2ENONE(X5) = vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5),vAPP(sTfun(X0,X5),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5)),c_2Eoption_2EOPTION__MAP(X0,X5),X233),c_2Eoption_2ENONE(X0))) & ! [X231 : X0 > X5,X232 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5),vAPP(sTfun(X0,X5),sTfun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X5)),c_2Eoption_2EOPTION__MAP(X0,X5),X231),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X232)) = vAPP(X5,tyop_2Eoption_2Eoption(X5),c_2Eoption_2ESOME(X5),vAPP(X0,X5,X231,X232))) & ! [X228 : X0,X229 : X5,X230 : X0 > X5] : (vAPP(sTfun(X0,X5),X5,vAPP(X5,sTfun(sTfun(X0,X5),X5),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X5,sTfun(sTfun(X0,X5),X5)),c_2Eoption_2Eoption__CASE(X0,X5),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X228)),X229),X230) = vAPP(X0,X5,X230,X228)) & ! [X226 : X5,X227 : X0 > X5] : (vAPP(sTfun(X0,X5),X5,vAPP(X5,sTfun(sTfun(X0,X5),X5),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X5,sTfun(sTfun(X0,X5),X5)),c_2Eoption_2Eoption__CASE(X0,X5),c_2Eoption_2ENONE(X0)),X226),X227) = X226) & ! [X225 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X225) => (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X225),X117),c_2Eoption_2ESOME(X0)) = X225)) & ! [X224 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X224) => (vAPP(sTfun(X0,X5),X5,vAPP(X5,sTfun(sTfun(X0,X5),X5),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X5,sTfun(sTfun(X0,X5),X5)),c_2Eoption_2Eoption__CASE(X0,X5),X224),X217),X3) = vAPP(X0,X5,X3,vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X224)))) & ! [X223 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X223) => (vAPP(sTfun(X0,X5),X5,vAPP(X5,sTfun(sTfun(X0,X5),X5),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(X5,sTfun(sTfun(X0,X5),X5)),c_2Eoption_2Eoption__CASE(X0,X5),X223),X217),X3) = X217)) & ! [X222 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X222),X222),c_2Eoption_2ESOME(X0)) = X222) & ! [X221 : tyop_2Eoption_2Eoption(X0)] : (vAPP(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)),vAPP(tyop_2Eoption_2Eoption(X0),sTfun(tyop_2Eoption_2Eoption(X0),sTfun(sTfun(X0,tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0))),c_2Eoption_2Eoption__CASE(X0,tyop_2Eoption_2Eoption(X0)),X221),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X221) & ! [X220 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X220) => (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),X220)) = X220)) & ! [X170 : tyop_2Eoption_2Eoption(X0)] : (vAPP($o,$o,vNOT,vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X170)) <=> (c_2Eoption_2ENONE(X0) = X170)) & ! [X219 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__NONE(X0),X219) <=> (c_2Eoption_2ENONE(X0) = X219)) & (c_2Ebool_2EF = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0))) & ! [X218 : X0] : (c_2Ebool_2ET = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X218))) & ! [X93 : X0] : vAPP($o,$o,vNOT,(c_2Eoption_2ENONE(X0) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X93))) & ! [X33 : X0] : vAPP($o,$o,vNOT,(c_2Eoption_2ENONE(X0) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X33))) & ! [X92 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X92)) = X92) & ! [X15 : X0,X28 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X15) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X28)) <=> (X15 = X28)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES)).
% 92.92/13.71 thf(f54392,plain,(
% 92.92/13.71 spl854_517),
% 92.92/13.71 inference(avatar_split_clause,[],[f12038,f54390])).
% 92.92/13.71 thf(f54390,plain,(
% 92.92/13.71 spl854_517 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1) = X2) | ($true != vAPP(X0,$o,X1,X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_517])])).
% 92.92/13.71 thf(f12038,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK569(X0),X2),X1) = X2) | ($true != vAPP(X0,$o,X1,X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8152])).
% 92.92/13.71 thf(f54388,plain,(
% 92.92/13.71 spl854_516),
% 92.92/13.71 inference(avatar_split_clause,[],[f12035,f54386])).
% 92.92/13.71 thf(f54386,plain,(
% 92.92/13.71 spl854_516 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1) = X2) | ($true != vAPP(X0,$o,X1,X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_516])])).
% 92.92/13.71 thf(f12035,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK568(X0),X2),X1) = X2) | ($true != vAPP(X0,$o,X1,X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8148])).
% 92.92/13.71 thf(f54331,plain,(
% 92.92/13.71 spl854_515),
% 92.92/13.71 inference(avatar_split_clause,[],[f12006,f54329])).
% 92.92/13.71 thf(f54329,plain,(
% 92.92/13.71 spl854_515 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1) = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_515])])).
% 92.92/13.71 thf(f12006,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK544(X0),X2),X1) = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8097])).
% 92.92/13.71 thf(f54327,plain,(
% 92.92/13.71 spl854_514),
% 92.92/13.71 inference(avatar_split_clause,[],[f12003,f54325])).
% 92.92/13.71 thf(f54325,plain,(
% 92.92/13.71 spl854_514 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1) = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_514])])).
% 92.92/13.71 thf(f12003,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),sK543(X0),X2),X1) = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8093])).
% 92.92/13.71 thf(f54323,plain,(
% 92.92/13.71 spl854_513),
% 92.92/13.71 inference(avatar_split_clause,[],[f11207,f54321])).
% 92.92/13.71 thf(f54321,plain,(
% 92.92/13.71 spl854_513 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_513])])).
% 92.92/13.71 thf(f11207,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3524])).
% 92.92/13.71 thf(f3524,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3523])).
% 92.92/13.71 thf(f3523,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f460])).
% 92.92/13.71 thf(f460,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ETC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ETC__TRANSITIVE)).
% 92.92/13.71 thf(f54319,plain,(
% 92.92/13.71 spl854_512),
% 92.92/13.71 inference(avatar_split_clause,[],[f11205,f54317])).
% 92.92/13.71 thf(f54317,plain,(
% 92.92/13.71 spl854_512 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_512])])).
% 92.92/13.71 thf(f11205,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3520])).
% 92.92/13.71 thf(f3520,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3519])).
% 92.92/13.71 thf(f3519,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f469])).
% 92.92/13.71 thf(f469,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Etransitive__RTC)).
% 92.92/13.71 thf(f54315,plain,(
% 92.92/13.71 spl854_511),
% 92.92/13.71 inference(avatar_split_clause,[],[f11204,f54313])).
% 92.92/13.71 thf(f54313,plain,(
% 92.92/13.71 spl854_511 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_511])])).
% 92.92/13.71 thf(f11204,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3518])).
% 92.92/13.71 thf(f3518,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3517])).
% 92.92/13.71 thf(f3517,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f540])).
% 92.92/13.71 thf(f540,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Etransitive__EQC)).
% 92.92/13.71 thf(f54311,plain,(
% 92.92/13.71 spl854_510),
% 92.92/13.71 inference(avatar_split_clause,[],[f11202,f54309])).
% 92.92/13.71 thf(f54309,plain,(
% 92.92/13.71 spl854_510 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_510])])).
% 92.92/13.71 thf(f11202,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3514])).
% 92.92/13.71 thf(f3514,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3513])).
% 92.92/13.71 thf(f3513,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f470])).
% 92.92/13.71 thf(f470,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ERTC__REFLEXIVE)).
% 92.92/13.71 thf(f54307,plain,(
% 92.92/13.71 spl854_509),
% 92.92/13.71 inference(avatar_split_clause,[],[f11200,f54305])).
% 92.92/13.71 thf(f54305,plain,(
% 92.92/13.71 spl854_509 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_509])])).
% 92.92/13.71 thf(f11200,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3510])).
% 92.92/13.71 thf(f3510,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3509])).
% 92.92/13.71 thf(f3509,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f473])).
% 92.92/13.71 thf(f473,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ereflexive__RC)).
% 92.92/13.71 thf(f54303,plain,(
% 92.92/13.71 spl854_508),
% 92.92/13.71 inference(avatar_split_clause,[],[f11199,f54301])).
% 92.92/13.71 thf(f54301,plain,(
% 92.92/13.71 spl854_508 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_508])])).
% 92.92/13.71 thf(f11199,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3508])).
% 92.92/13.71 thf(f3508,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3507])).
% 92.92/13.71 thf(f3507,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f542])).
% 92.92/13.71 thf(f542,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ereflexive__EQC)).
% 92.92/13.71 thf(f54299,plain,(
% 92.92/13.71 spl854_507),
% 92.92/13.71 inference(avatar_split_clause,[],[f11198,f54297])).
% 92.92/13.71 thf(f54297,plain,(
% 92.92/13.71 spl854_507 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_507])])).
% 92.92/13.71 thf(f11198,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3506])).
% 92.92/13.71 thf(f3506,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3505])).
% 92.92/13.71 thf(f3505,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f541])).
% 92.92/13.71 thf(f541,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Esymmetric__EQC)).
% 92.92/13.71 thf(f54295,plain,(
% 92.92/13.71 spl854_506),
% 92.92/13.71 inference(avatar_split_clause,[],[f11197,f54293])).
% 92.92/13.71 thf(f54293,plain,(
% 92.92/13.71 spl854_506 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_506])])).
% 92.92/13.71 thf(f11197,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3504])).
% 92.92/13.71 thf(f3504,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3503])).
% 92.92/13.71 thf(f3503,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f459])).
% 92.92/13.71 thf(f459,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ESC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2ESC__SYMMETRIC)).
% 92.92/13.71 thf(f48749,plain,(
% 92.92/13.71 ~spl854_498 | ~spl854_505),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f48748])).
% 92.92/13.71 thf(f48748,plain,(
% 92.92/13.71 $false | (~spl854_498 | ~spl854_505)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f48747])).
% 92.92/13.71 thf(f48747,plain,(
% 92.92/13.71 ($true = $false) | (~spl854_498 | ~spl854_505)),
% 92.92/13.71 inference(forward_demodulation,[],[f48745,f48712])).
% 92.92/13.71 thf(f48712,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($false = X0)) ) | ~spl854_498),
% 92.92/13.71 inference(avatar_component_clause,[],[f48711])).
% 92.92/13.71 thf(f48745,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))) ) | ~spl854_505),
% 92.92/13.71 inference(avatar_component_clause,[],[f48744])).
% 92.92/13.71 thf(f48744,plain,(
% 92.92/13.71 spl854_505 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_505])])).
% 92.92/13.71 thf(f48746,plain,(
% 92.92/13.71 spl854_505),
% 92.92/13.71 inference(avatar_split_clause,[],[f11196,f48744])).
% 92.92/13.71 thf(f11196,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f3502])).
% 92.92/13.71 thf(f3502,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f3501])).
% 92.92/13.71 thf(f3501,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f522])).
% 92.92/13.71 thf(f522,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2EEQC(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__EQUIVALENCE)).
% 92.92/13.71 thf(f48739,plain,(
% 92.92/13.71 spl854_504),
% 92.92/13.71 inference(avatar_split_clause,[],[f10775,f48737])).
% 92.92/13.71 thf(f48737,plain,(
% 92.92/13.71 spl854_504 <=> ! [X0 : $tType,X1 : X0 > X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_504])])).
% 92.92/13.71 thf(f10775,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7377])).
% 92.92/13.71 thf(f7377,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK350(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK350(X0),X1)))) & (! [X3 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK350])],[f7375,f7376])).
% 92.92/13.71 thf(f7376,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK350(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK350(X0),X1))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7375,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ? [X2 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2))) & (! [X3 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X3)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))))),
% 92.92/13.71 inference(rectify,[],[f7374])).
% 92.92/13.71 thf(f7374,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ? [X2 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2))) & (! [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3186])).
% 92.92/13.71 thf(f3186,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) <=> ! [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2)))),
% 92.92/13.71 inference(fool_elimination,[],[f3185])).
% 92.92/13.71 thf(f3185,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1) <=> ! [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X2))),
% 92.92/13.71 inference(rectify,[],[f409])).
% 92.92/13.71 thf(f409,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X143) <=> ! [X4 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X4))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ereflexive__def)).
% 92.92/13.71 thf(f48734,plain,(
% 92.92/13.71 spl854_503),
% 92.92/13.71 inference(avatar_split_clause,[],[f10690,f48732])).
% 92.92/13.71 thf(f48732,plain,(
% 92.92/13.71 spl854_503 <=> ! [X0 : $tType,X1 : X0 > X0,X3 : X0] : ((vAPP(X0,X0,X1,X3) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_503])])).
% 92.92/13.71 thf(f10690,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0] : ((vAPP(X0,X0,X1,X3) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7299])).
% 92.92/13.71 thf(f7299,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) | (vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK319(X0),X1)) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK319(X0),X1))))) & (! [X3 : X0] : (vAPP(X0,X0,X1,X3) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK319])],[f7297,f7298])).
% 92.92/13.71 thf(f7298,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (? [X2 : X0] : (vAPP(X0,X0,X1,X2) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2))) => (vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK319(X0),X1)) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,vAPP(sTfun(X0,X0),X0,sK319(X0),X1)))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7297,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) | ? [X2 : X0] : (vAPP(X0,X0,X1,X2) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)))) & (! [X3 : X0] : (vAPP(X0,X0,X1,X3) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1))))),
% 92.92/13.71 inference(rectify,[],[f7296])).
% 92.92/13.71 thf(f7296,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : ((($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) | ? [X2 : X0] : (vAPP(X0,X0,X1,X2) != vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2)))) & (! [X2 : X0] : (vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3142])).
% 92.92/13.71 thf(f3142,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1)) <=> ! [X2 : X0] : (vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2))))),
% 92.92/13.71 inference(fool_elimination,[],[f3141])).
% 92.92/13.71 thf(f3141,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (vAPP(sTfun(X0,X0),$o,c_2Erelation_2EIDEM(X0),X1) <=> ! [X2 : X0] : (vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,vAPP(X0,X0,X1,X2))))),
% 92.92/13.71 inference(rectify,[],[f599])).
% 92.92/13.71 thf(f599,axiom,(
% 92.92/13.71 ! [X139 : $tType,X3 : X139 > X139] : (vAPP(sTfun(X139,X139),$o,c_2Erelation_2EIDEM(X139),X3) <=> ! [X4 : X139] : (vAPP(X139,X139,X3,X4) = vAPP(X139,X139,X3,vAPP(X139,X139,X3,X4))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM)).
% 92.92/13.71 thf(f48729,plain,(
% 92.92/13.71 spl854_502),
% 92.92/13.71 inference(avatar_split_clause,[],[f10574,f48727])).
% 92.92/13.71 thf(f48727,plain,(
% 92.92/13.71 spl854_502 <=> ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,sK263(X0),X1)) = X1) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_502])])).
% 92.92/13.71 thf(f10574,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,sK263(X0),X1)) = X1) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7073])).
% 92.92/13.71 thf(f7073,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1)) | ! [X2 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) != X1)) & ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,sK263(X0),X1)) = X1) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK263])],[f7071,f7072])).
% 92.92/13.71 thf(f7072,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : (? [X3 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3) = X1) => (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),vAPP(tyop_2Eoption_2Eoption(X0),X0,sK263(X0),X1)) = X1))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f7071,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1)) | ! [X2 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) != X1)) & (? [X3 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X3) = X1) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1))))),
% 92.92/13.71 inference(rectify,[],[f7070])).
% 92.92/13.71 thf(f7070,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1)) | ! [X2 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) != X1)) & (? [X2 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) = X1) | ($true != vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3026])).
% 92.92/13.71 thf(f3026,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : (($true = vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1)) <=> ? [X2 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) = X1))),
% 92.92/13.71 inference(fool_elimination,[],[f3025])).
% 92.92/13.71 thf(f3025,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X1) <=> ? [X2 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2) = X1))),
% 92.92/13.71 inference(rectify,[],[f732])).
% 92.92/13.71 thf(f732,axiom,(
% 92.92/13.71 ! [X0 : $tType,X215 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(X0),$o,c_2Eoption_2EIS__SOME(X0),X215) <=> ? [X4 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X4) = X215))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EIS__SOME__EXISTS)).
% 92.92/13.71 thf(f48725,plain,(
% 92.92/13.71 spl854_501),
% 92.92/13.71 inference(avatar_split_clause,[],[f10074,f48723])).
% 92.92/13.71 thf(f48723,plain,(
% 92.92/13.71 spl854_501 <=> ! [X0 : $tType,X1 : X0] : (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_501])])).
% 92.92/13.71 thf(f10074,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2578])).
% 92.92/13.71 thf(f2578,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1))) & (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,c_2Emin_2E_3D(X0)),X1))))),
% 92.92/13.71 inference(fool_elimination,[],[f2577])).
% 92.92/13.71 thf(f2577,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0] : ((vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),(^[X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)))) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)) & (vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),(^[X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X3),X1)))) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)))),
% 92.92/13.71 inference(rectify,[],[f772])).
% 92.92/13.71 thf(f772,axiom,(
% 92.92/13.71 ! [X0 : $tType,X70 : X0] : ((vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),(^[X19 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X70),X19)))) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X70)) & (vAPP(sTfun(X0,$o),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Esome(X0),(^[X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X4),X70)))) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X70)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Esome__EQ)).
% 92.92/13.71 thf(f48721,plain,(
% 92.92/13.71 spl854_500),
% 92.92/13.71 inference(avatar_split_clause,[],[f9392,f48719])).
% 92.92/13.71 thf(f48719,plain,(
% 92.92/13.71 spl854_500 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_500])])).
% 92.92/13.71 thf(f9392,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4925])).
% 92.92/13.71 thf(f48717,plain,(
% 92.92/13.71 spl854_498 | spl854_499 | ~spl854_198),
% 92.92/13.71 inference(avatar_split_clause,[],[f23993,f23504,f48714,f48711])).
% 92.92/13.71 thf(f48714,plain,(
% 92.92/13.71 spl854_499 <=> ($true = vAPP(sTfun($o,$o),$o,c_2EnormalForms_2EUNIV__POINT($o),vNOT))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_499])])).
% 92.92/13.71 thf(f23504,plain,(
% 92.92/13.71 spl854_198 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_198])])).
% 92.92/13.71 thf(f23993,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,c_2EnormalForms_2EUNIV__POINT($o),vNOT)) | ($false = X0)) ) | ~spl854_198),
% 92.92/13.71 inference(not_proxy_clausification,[],[f23992])).
% 92.92/13.71 thf(f23992,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,c_2EnormalForms_2EUNIV__POINT($o),vNOT)) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_198),
% 92.92/13.71 inference(not_proxy_clausification,[],[f23932])).
% 92.92/13.71 thf(f23932,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,c_2EnormalForms_2EUNIV__POINT($o),vNOT))) | ($true = vAPP($o,$o,vNOT,X0))) ) | ~spl854_198),
% 92.92/13.71 inference(primitive_instantiation,[],[f23505])).
% 92.92/13.71 thf(f23505,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) | ($true = vAPP(X0,$o,X1,X2))) ) | ~spl854_198),
% 92.92/13.71 inference(avatar_component_clause,[],[f23504])).
% 92.92/13.71 thf(f48127,plain,(
% 92.92/13.71 spl854_497 | ~spl854_22 | ~spl854_180),
% 92.92/13.71 inference(avatar_split_clause,[],[f23306,f23181,f22006,f48124])).
% 92.92/13.71 thf(f48124,plain,(
% 92.92/13.71 spl854_497 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,c_2Earithmetic_2EEVEN)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_497])])).
% 92.92/13.71 thf(f22006,plain,(
% 92.92/13.71 spl854_22 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_22])])).
% 92.92/13.71 thf(f23181,plain,(
% 92.92/13.71 spl854_180 <=> ! [X0 : tyop_2Enum_2Enum > $o,X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_180])])).
% 92.92/13.71 thf(f23306,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,c_2Earithmetic_2EEVEN))) | (~spl854_22 | ~spl854_180)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f23285])).
% 92.92/13.71 thf(f23285,plain,(
% 92.92/13.71 ($true != $true) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,c_2Earithmetic_2EEVEN))) | (~spl854_22 | ~spl854_180)),
% 92.92/13.71 inference(superposition,[],[f23182,f22007])).
% 92.92/13.71 thf(f22007,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) ) | ~spl854_22),
% 92.92/13.71 inference(avatar_component_clause,[],[f22006])).
% 92.92/13.71 thf(f23182,plain,(
% 92.92/13.71 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0)))) ) | ~spl854_180),
% 92.92/13.71 inference(avatar_component_clause,[],[f23181])).
% 92.92/13.71 thf(f47700,plain,(
% 92.92/13.71 spl854_496 | ~spl854_23 | ~spl854_180),
% 92.92/13.71 inference(avatar_split_clause,[],[f23304,f23181,f22010,f47697])).
% 92.92/13.71 thf(f47697,plain,(
% 92.92/13.71 spl854_496 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,c_2Edivides_2Eprime)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_496])])).
% 92.92/13.71 thf(f22010,plain,(
% 92.92/13.71 spl854_23 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_23])])).
% 92.92/13.71 thf(f23304,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,c_2Edivides_2Eprime))) | (~spl854_23 | ~spl854_180)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f23288])).
% 92.92/13.71 thf(f23288,plain,(
% 92.92/13.71 ($true != $true) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,c_2Edivides_2Eprime))) | (~spl854_23 | ~spl854_180)),
% 92.92/13.71 inference(superposition,[],[f23182,f22011])).
% 92.92/13.71 thf(f22011,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))) ) | ~spl854_23),
% 92.92/13.71 inference(avatar_component_clause,[],[f22010])).
% 92.92/13.71 thf(f47031,plain,(
% 92.92/13.71 spl854_495 | ~spl854_22 | ~spl854_179),
% 92.92/13.71 inference(avatar_split_clause,[],[f23271,f23177,f22006,f47028])).
% 92.92/13.71 thf(f47028,plain,(
% 92.92/13.71 spl854_495 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,c_2Earithmetic_2EEVEN)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_495])])).
% 92.92/13.71 thf(f23177,plain,(
% 92.92/13.71 spl854_179 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_179])])).
% 92.92/13.71 thf(f23271,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,c_2Earithmetic_2EEVEN))) | (~spl854_22 | ~spl854_179)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f23250])).
% 92.92/13.71 thf(f23250,plain,(
% 92.92/13.71 ($true != $true) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,c_2Earithmetic_2EEVEN))) | (~spl854_22 | ~spl854_179)),
% 92.92/13.71 inference(superposition,[],[f23178,f22007])).
% 92.92/13.71 thf(f23178,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)))) ) | ~spl854_179),
% 92.92/13.71 inference(avatar_component_clause,[],[f23177])).
% 92.92/13.71 thf(f46669,plain,(
% 92.92/13.71 spl854_494 | ~spl854_23 | ~spl854_179),
% 92.92/13.71 inference(avatar_split_clause,[],[f23269,f23177,f22010,f46666])).
% 92.92/13.71 thf(f46666,plain,(
% 92.92/13.71 spl854_494 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,c_2Edivides_2Eprime)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_494])])).
% 92.92/13.71 thf(f23269,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,c_2Edivides_2Eprime))) | (~spl854_23 | ~spl854_179)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f23253])).
% 92.92/13.71 thf(f23253,plain,(
% 92.92/13.71 ($true != $true) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,c_2Edivides_2Eprime))) | (~spl854_23 | ~spl854_179)),
% 92.92/13.71 inference(superposition,[],[f23178,f22011])).
% 92.92/13.71 thf(f46482,plain,(
% 92.92/13.71 spl854_493 | ~spl854_5 | ~spl854_51),
% 92.92/13.71 inference(avatar_split_clause,[],[f22193,f22141,f21881,f46480])).
% 92.92/13.71 thf(f46480,plain,(
% 92.92/13.71 spl854_493 <=> ! [X0 : $o] : ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X0),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_493])])).
% 92.92/13.71 thf(f22141,plain,(
% 92.92/13.71 spl854_51 <=> ! [X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_51])])).
% 92.92/13.71 thf(f22193,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X0),$true))) ) | (~spl854_5 | ~spl854_51)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f22192])).
% 92.92/13.71 thf(f22192,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X0),$true))) ) | (~spl854_5 | ~spl854_51)),
% 92.92/13.71 inference(superposition,[],[f22142,f21882])).
% 92.92/13.71 thf(f22142,plain,(
% 92.92/13.71 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),$true))) ) | ~spl854_51),
% 92.92/13.71 inference(avatar_component_clause,[],[f22141])).
% 92.92/13.71 thf(f46250,plain,(
% 92.92/13.71 spl854_492 | ~spl854_5 | ~spl854_50),
% 92.92/13.71 inference(avatar_split_clause,[],[f22187,f22137,f21881,f46248])).
% 92.92/13.71 thf(f46248,plain,(
% 92.92/13.71 spl854_492 <=> ! [X0 : $o] : ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X0),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_492])])).
% 92.92/13.71 thf(f22137,plain,(
% 92.92/13.71 spl854_50 <=> ! [X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_50])])).
% 92.92/13.71 thf(f22187,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X0),$true))) ) | (~spl854_5 | ~spl854_50)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f22186])).
% 92.92/13.71 thf(f22186,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X0),$true))) ) | (~spl854_5 | ~spl854_50)),
% 92.92/13.71 inference(superposition,[],[f22138,f21882])).
% 92.92/13.71 thf(f22138,plain,(
% 92.92/13.71 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),$true))) ) | ~spl854_50),
% 92.92/13.71 inference(avatar_component_clause,[],[f22137])).
% 92.92/13.71 thf(f46106,plain,(
% 92.92/13.71 spl854_491 | ~spl854_5 | ~spl854_49),
% 92.92/13.71 inference(avatar_split_clause,[],[f22181,f22133,f21881,f46104])).
% 92.92/13.71 thf(f46104,plain,(
% 92.92/13.71 spl854_491 <=> ! [X0 : $o] : ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X0),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_491])])).
% 92.92/13.71 thf(f22133,plain,(
% 92.92/13.71 spl854_49 <=> ! [X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_49])])).
% 92.92/13.71 thf(f22181,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X0),$true))) ) | (~spl854_5 | ~spl854_49)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f22180])).
% 92.92/13.71 thf(f22180,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X0),$true))) ) | (~spl854_5 | ~spl854_49)),
% 92.92/13.71 inference(superposition,[],[f22134,f21882])).
% 92.92/13.71 thf(f22134,plain,(
% 92.92/13.71 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),$true))) ) | ~spl854_49),
% 92.92/13.71 inference(avatar_component_clause,[],[f22133])).
% 92.92/13.71 thf(f45962,plain,(
% 92.92/13.71 spl854_490 | ~spl854_5 | ~spl854_48),
% 92.92/13.71 inference(avatar_split_clause,[],[f22175,f22129,f21881,f45960])).
% 92.92/13.71 thf(f45960,plain,(
% 92.92/13.71 spl854_490 <=> ! [X0 : $o] : ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,$true),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_490])])).
% 92.92/13.71 thf(f22129,plain,(
% 92.92/13.71 spl854_48 <=> ! [X0 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,$true),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_48])])).
% 92.92/13.71 thf(f22175,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,$true),X0))) ) | (~spl854_5 | ~spl854_48)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f22174])).
% 92.92/13.71 thf(f22174,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,$true),X0))) ) | (~spl854_5 | ~spl854_48)),
% 92.92/13.71 inference(superposition,[],[f22130,f21882])).
% 92.92/13.71 thf(f22130,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,$true),X0))) ) | ~spl854_48),
% 92.92/13.71 inference(avatar_component_clause,[],[f22129])).
% 92.92/13.71 thf(f45819,plain,(
% 92.92/13.71 spl854_489 | ~spl854_5 | ~spl854_47),
% 92.92/13.71 inference(avatar_split_clause,[],[f22165,f22125,f21881,f45817])).
% 92.92/13.71 thf(f45817,plain,(
% 92.92/13.71 spl854_489 <=> ! [X0 : $o] : ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X0),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_489])])).
% 92.92/13.71 thf(f22125,plain,(
% 92.92/13.71 spl854_47 <=> ! [X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_47])])).
% 92.92/13.71 thf(f22165,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X0),$true))) ) | (~spl854_5 | ~spl854_47)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f22164])).
% 92.92/13.71 thf(f22164,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true != $true) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X0),$true))) ) | (~spl854_5 | ~spl854_47)),
% 92.92/13.71 inference(superposition,[],[f22126,f21882])).
% 92.92/13.71 thf(f22126,plain,(
% 92.92/13.71 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),$true))) ) | ~spl854_47),
% 92.92/13.71 inference(avatar_component_clause,[],[f22125])).
% 92.92/13.71 thf(f45467,plain,(
% 92.92/13.71 spl854_488 | ~spl854_486 | ~spl854_16 | ~spl854_178),
% 92.92/13.71 inference(avatar_split_clause,[],[f23236,f23173,f21977,f44586,f45465])).
% 92.92/13.71 thf(f45465,plain,(
% 92.92/13.71 spl854_488 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Eind__type_2EFNIL($o),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_488])])).
% 92.92/13.71 thf(f44586,plain,(
% 92.92/13.71 spl854_486 <=> ($true = c_2Ebool_2EARB($o))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_486])])).
% 92.92/13.71 thf(f21977,plain,(
% 92.92/13.71 spl854_16 <=> ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : (c_2Ebool_2EARB(X0) = vAPP(tyop_2Enum_2Enum,X0,c_2Eind__type_2EFNIL(X0),X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_16])])).
% 92.92/13.71 thf(f23173,plain,(
% 92.92/13.71 spl854_178 <=> ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_178])])).
% 92.92/13.71 thf(f23236,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true != c_2Ebool_2EARB($o)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Eind__type_2EFNIL($o),X0))) ) | (~spl854_16 | ~spl854_178)),
% 92.92/13.71 inference(superposition,[],[f23174,f21978])).
% 92.92/13.71 thf(f21978,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EARB(X0) = vAPP(tyop_2Enum_2Enum,X0,c_2Eind__type_2EFNIL(X0),X1))) ) | ~spl854_16),
% 92.92/13.71 inference(avatar_component_clause,[],[f21977])).
% 92.92/13.71 thf(f23174,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0))) | ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) ) | ~spl854_178),
% 92.92/13.71 inference(avatar_component_clause,[],[f23173])).
% 92.92/13.71 thf(f44593,plain,(
% 92.92/13.71 spl854_487),
% 92.92/13.71 inference(avatar_split_clause,[],[f17224,f44591])).
% 92.92/13.71 thf(f44591,plain,(
% 92.92/13.71 spl854_487 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_487])])).
% 92.92/13.71 thf(f17224,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0))) )),
% 92.92/13.71 inference(duplicate_literal_removal,[],[f11804])).
% 92.92/13.71 thf(f11804,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7962])).
% 92.92/13.71 thf(f44589,plain,(
% 92.92/13.71 spl854_485 | spl854_486 | ~spl854_5 | ~spl854_16),
% 92.92/13.71 inference(avatar_split_clause,[],[f21984,f21977,f21881,f44586,f44583])).
% 92.92/13.71 thf(f44583,plain,(
% 92.92/13.71 spl854_485 <=> ! [X0 : tyop_2Enum_2Enum] : ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Eind__type_2EFNIL($o),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_485])])).
% 92.92/13.71 thf(f21984,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = c_2Ebool_2EARB($o)) | ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Eind__type_2EFNIL($o),X0))) ) | (~spl854_5 | ~spl854_16)),
% 92.92/13.71 inference(superposition,[],[f21978,f21882])).
% 92.92/13.71 thf(f44581,plain,(
% 92.92/13.71 spl854_484),
% 92.92/13.71 inference(avatar_split_clause,[],[f17223,f44579])).
% 92.92/13.71 thf(f44579,plain,(
% 92.92/13.71 spl854_484 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_484])])).
% 92.92/13.71 thf(f17223,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0))) )),
% 92.92/13.71 inference(duplicate_literal_removal,[],[f11815])).
% 92.92/13.71 thf(f11815,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7973])).
% 92.92/13.71 thf(f44577,plain,(
% 92.92/13.71 spl854_483),
% 92.92/13.71 inference(avatar_split_clause,[],[f17219,f44575])).
% 92.92/13.71 thf(f44575,plain,(
% 92.92/13.71 spl854_483 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_483])])).
% 92.92/13.71 thf(f17219,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(duplicate_literal_removal,[],[f11890])).
% 92.92/13.71 thf(f11890,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0)) | ($true = X1) | ($true = X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8019])).
% 92.92/13.71 thf(f8019,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0)) | (($true != X0) & ($true = X1)) | (($true != X2) & ($true = X1))) & (((($true = X0) | ($true != X1)) & (($true = X2) | ($true != X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0))))),
% 92.92/13.71 inference(rectify,[],[f8018])).
% 92.92/13.71 thf(f8018,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X1),X0),X2)) | (($true != X2) & ($true = X0)) | (($true != X1) & ($true = X0))) & (((($true = X2) | ($true != X0)) & (($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X1),X0),X2))))),
% 92.92/13.71 inference(flattening,[],[f8017])).
% 92.92/13.71 thf(f8017,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X1),X0),X2)) | ((($true != X2) & ($true = X0)) | (($true != X1) & ($true = X0)))) & (((($true = X2) | ($true != X0)) & (($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X1),X0),X2))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6454])).
% 92.92/13.71 thf(f6454,plain,(
% 92.92/13.71 ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X1),X0),X2)) <=> ((($true = X2) | ($true != X0)) & (($true = X1) | ($true != X0))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44573,plain,(
% 92.92/13.71 spl854_482),
% 92.92/13.71 inference(avatar_split_clause,[],[f17214,f44571])).
% 92.92/13.71 thf(f44571,plain,(
% 92.92/13.71 spl854_482 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_482])])).
% 92.92/13.71 thf(f17214,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11914])).
% 92.92/13.71 thf(f11914,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8029])).
% 92.92/13.71 thf(f44569,plain,(
% 92.92/13.71 spl854_481),
% 92.92/13.71 inference(avatar_split_clause,[],[f17213,f44567])).
% 92.92/13.71 thf(f44567,plain,(
% 92.92/13.71 spl854_481 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_481])])).
% 92.92/13.71 thf(f17213,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11913])).
% 92.92/13.71 thf(f11913,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8029])).
% 92.92/13.71 thf(f44565,plain,(
% 92.92/13.71 spl854_480),
% 92.92/13.71 inference(avatar_split_clause,[],[f17210,f44563])).
% 92.92/13.71 thf(f44563,plain,(
% 92.92/13.71 spl854_480 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_480])])).
% 92.92/13.71 thf(f17210,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11918])).
% 92.92/13.71 thf(f11918,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8032])).
% 92.92/13.71 thf(f44561,plain,(
% 92.92/13.71 spl854_479),
% 92.92/13.71 inference(avatar_split_clause,[],[f17209,f44559])).
% 92.92/13.71 thf(f44559,plain,(
% 92.92/13.71 spl854_479 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_479])])).
% 92.92/13.71 thf(f17209,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11917])).
% 92.92/13.71 thf(f11917,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8032])).
% 92.92/13.71 thf(f44557,plain,(
% 92.92/13.71 spl854_478),
% 92.92/13.71 inference(avatar_split_clause,[],[f17196,f44555])).
% 92.92/13.71 thf(f44555,plain,(
% 92.92/13.71 spl854_478 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_478])])).
% 92.92/13.71 thf(f17196,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11943])).
% 92.92/13.71 thf(f11943,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8042])).
% 92.92/13.71 thf(f44553,plain,(
% 92.92/13.71 spl854_477),
% 92.92/13.71 inference(avatar_split_clause,[],[f17195,f44551])).
% 92.92/13.71 thf(f44551,plain,(
% 92.92/13.71 spl854_477 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_477])])).
% 92.92/13.71 thf(f17195,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11942])).
% 92.92/13.71 thf(f11942,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8042])).
% 92.92/13.71 thf(f44549,plain,(
% 92.92/13.71 spl854_476),
% 92.92/13.71 inference(avatar_split_clause,[],[f17185,f44547])).
% 92.92/13.71 thf(f44547,plain,(
% 92.92/13.71 spl854_476 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_476])])).
% 92.92/13.71 thf(f17185,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11962])).
% 92.92/13.71 thf(f11962,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8051])).
% 92.92/13.71 thf(f44545,plain,(
% 92.92/13.71 spl854_475),
% 92.92/13.71 inference(avatar_split_clause,[],[f17179,f44543])).
% 92.92/13.71 thf(f44543,plain,(
% 92.92/13.71 spl854_475 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_475])])).
% 92.92/13.71 thf(f17179,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11981])).
% 92.92/13.71 thf(f11981,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8060])).
% 92.92/13.71 thf(f44534,plain,(
% 92.92/13.71 spl854_474),
% 92.92/13.71 inference(avatar_split_clause,[],[f17178,f44532])).
% 92.92/13.71 thf(f44532,plain,(
% 92.92/13.71 spl854_474 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_474])])).
% 92.92/13.71 thf(f17178,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true = X2)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f11979])).
% 92.92/13.71 thf(f11979,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8060])).
% 92.92/13.71 thf(f44530,plain,(
% 92.92/13.71 spl854_473),
% 92.92/13.71 inference(avatar_split_clause,[],[f17145,f44528])).
% 92.92/13.71 thf(f44528,plain,(
% 92.92/13.71 spl854_473 <=> ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),$true)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_473])])).
% 92.92/13.71 thf(f17145,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),$true)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f16475])).
% 92.92/13.71 thf(f16475,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),$true)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(equality_resolution,[],[f12236])).
% 92.92/13.71 thf(f12236,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0)) | ($true != X0) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8341])).
% 92.92/13.71 thf(f44526,plain,(
% 92.92/13.71 spl854_472),
% 92.92/13.71 inference(avatar_split_clause,[],[f17142,f44524])).
% 92.92/13.71 thf(f44524,plain,(
% 92.92/13.71 spl854_472 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,$true),X1),X0)) | ($false = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_472])])).
% 92.92/13.71 thf(f17142,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,$true),X1),X0)) | ($false = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f16482])).
% 92.92/13.71 thf(f16482,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,$true),X1),X0)) | (vAPP($o,$o,vNOT,X1) = $true)) )),
% 92.92/13.71 inference(equality_resolution,[],[f12243])).
% 92.92/13.71 thf(f12243,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true != X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8345])).
% 92.92/13.71 thf(f44522,plain,(
% 92.92/13.71 spl854_471),
% 92.92/13.71 inference(avatar_split_clause,[],[f17139,f44520])).
% 92.92/13.71 thf(f44520,plain,(
% 92.92/13.71 spl854_471 <=> ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),$true)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_471])])).
% 92.92/13.71 thf(f17139,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),$true)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f16484])).
% 92.92/13.71 thf(f16484,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),$true)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(equality_resolution,[],[f12253])).
% 92.92/13.71 thf(f12253,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0)) | ($true != X0) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8349])).
% 92.92/13.71 thf(f44518,plain,(
% 92.92/13.71 spl854_470),
% 92.92/13.71 inference(avatar_split_clause,[],[f17078,f44516])).
% 92.92/13.71 thf(f44516,plain,(
% 92.92/13.71 spl854_470 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_470])])).
% 92.92/13.71 thf(f17078,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12549])).
% 92.92/13.71 thf(f12549,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8468])).
% 92.92/13.71 thf(f8468,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8467])).
% 92.92/13.71 thf(f8467,plain,(
% 92.92/13.71 ! [X1 : $o,X0 : $o,X3 : $o] : ((($true != X1) & ($true = X0) & ($true = vAPP($o,$o,vNOT,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X3),X0),X1)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6511])).
% 92.92/13.71 thf(f6511,plain,(
% 92.92/13.71 ! [X1 : $o,X0 : $o,X3 : $o] : ((($true != X1) & ($true = X0) & ($true = vAPP($o,$o,vNOT,X3))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X3),X0),X1)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44514,plain,(
% 92.92/13.71 spl854_469),
% 92.92/13.71 inference(avatar_split_clause,[],[f17077,f44512])).
% 92.92/13.71 thf(f44512,plain,(
% 92.92/13.71 spl854_469 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_469])])).
% 92.92/13.71 thf(f17077,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12557])).
% 92.92/13.71 thf(f12557,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8472])).
% 92.92/13.71 thf(f8472,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8471])).
% 92.92/13.71 thf(f8471,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X3 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X3),X1),X0)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6514])).
% 92.92/13.71 thf(f6514,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X3 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X3))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X3),X1),X0)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44510,plain,(
% 92.92/13.71 spl854_468),
% 92.92/13.71 inference(avatar_split_clause,[],[f17072,f44508])).
% 92.92/13.71 thf(f44508,plain,(
% 92.92/13.71 spl854_468 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_468])])).
% 92.92/13.71 thf(f17072,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12605])).
% 92.92/13.71 thf(f12605,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8489])).
% 92.92/13.71 thf(f8489,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8488])).
% 92.92/13.71 thf(f8488,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X1 : $o] : ((($true != X2) & ($true = X3) & (vAPP($o,$o,vNOT,X1) = $true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X1),X3),X2)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6529])).
% 92.92/13.71 thf(f6529,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X1 : $o] : ((($true != X2) & ($true = X3) & (vAPP($o,$o,vNOT,X1) = $true)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X1),X3),X2)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44506,plain,(
% 92.92/13.71 spl854_467),
% 92.92/13.71 inference(avatar_split_clause,[],[f17071,f44504])).
% 92.92/13.71 thf(f44504,plain,(
% 92.92/13.71 spl854_467 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_467])])).
% 92.92/13.71 thf(f17071,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12608])).
% 92.92/13.71 thf(f12608,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8490])).
% 92.92/13.71 thf(f8490,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6528])).
% 92.92/13.71 thf(f6528,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44502,plain,(
% 92.92/13.71 spl854_466),
% 92.92/13.71 inference(avatar_split_clause,[],[f17070,f44500])).
% 92.92/13.71 thf(f44500,plain,(
% 92.92/13.71 spl854_466 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_466])])).
% 92.92/13.71 thf(f17070,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12613])).
% 92.92/13.71 thf(f12613,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8492])).
% 92.92/13.71 thf(f8492,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8491])).
% 92.92/13.71 thf(f8491,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X1 : $o] : ((($true != X3) & ($true = X2) & (vAPP($o,$o,vNOT,X1) = $true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X1),X2),X3)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6532])).
% 92.92/13.71 thf(f6532,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X1 : $o] : ((($true != X3) & ($true = X2) & (vAPP($o,$o,vNOT,X1) = $true)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X1),X2),X3)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44498,plain,(
% 92.92/13.71 spl854_465),
% 92.92/13.71 inference(avatar_split_clause,[],[f17069,f44496])).
% 92.92/13.71 thf(f44496,plain,(
% 92.92/13.71 spl854_465 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_465])])).
% 92.92/13.71 thf(f17069,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($false = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12616])).
% 92.92/13.71 thf(f12616,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8494])).
% 92.92/13.71 thf(f8494,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8493])).
% 92.92/13.71 thf(f8493,plain,(
% 92.92/13.71 ! [X1 : $o,X0 : $o,X2 : $o] : ((($true != X1) & ($true = X0) & ($true = vAPP($o,$o,vNOT,X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X0),X1)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6531])).
% 92.92/13.71 thf(f6531,plain,(
% 92.92/13.71 ! [X1 : $o,X0 : $o,X2 : $o] : ((($true != X1) & ($true = X0) & ($true = vAPP($o,$o,vNOT,X2))) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X0),X1)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44494,plain,(
% 92.92/13.71 spl854_464 | ~spl854_26 | ~spl854_443),
% 92.92/13.71 inference(avatar_split_clause,[],[f44445,f44401,f22023,f44492])).
% 92.92/13.71 thf(f44492,plain,(
% 92.92/13.71 spl854_464 <=> ! [X0 : $o] : (c_2Enum_2EZERO__REP = vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_464])])).
% 92.92/13.71 thf(f22023,plain,(
% 92.92/13.71 spl854_26 <=> ! [X0 : $o] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_26])])).
% 92.92/13.71 thf(f44401,plain,(
% 92.92/13.71 spl854_443 <=> (c_2Enum_2EZERO__REP = vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_443])])).
% 92.92/13.71 thf(f44445,plain,(
% 92.92/13.71 ( ! [X0 : $o] : ((c_2Enum_2EZERO__REP = vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0)))) ) | (~spl854_26 | ~spl854_443)),
% 92.92/13.71 inference(superposition,[],[f44403,f22024])).
% 92.92/13.71 thf(f22024,plain,(
% 92.92/13.71 ( ! [X0 : $o] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0))) ) | ~spl854_26),
% 92.92/13.71 inference(avatar_component_clause,[],[f22023])).
% 92.92/13.71 thf(f44403,plain,(
% 92.92/13.71 (c_2Enum_2EZERO__REP = vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_443),
% 92.92/13.71 inference(avatar_component_clause,[],[f44401])).
% 92.92/13.71 thf(f44490,plain,(
% 92.92/13.71 spl854_463),
% 92.92/13.71 inference(avatar_split_clause,[],[f17042,f44488])).
% 92.92/13.71 thf(f44488,plain,(
% 92.92/13.71 spl854_463 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_463])])).
% 92.92/13.71 thf(f17042,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12758])).
% 92.92/13.71 thf(f12758,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8601])).
% 92.92/13.71 thf(f44486,plain,(
% 92.92/13.71 spl854_462),
% 92.92/13.71 inference(avatar_split_clause,[],[f17041,f44484])).
% 92.92/13.71 thf(f44484,plain,(
% 92.92/13.71 spl854_462 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true = X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_462])])).
% 92.92/13.71 thf(f17041,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true = X2)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12756])).
% 92.92/13.71 thf(f12756,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8601])).
% 92.92/13.71 thf(f44482,plain,(
% 92.92/13.71 spl854_461),
% 92.92/13.71 inference(avatar_split_clause,[],[f17038,f44480])).
% 92.92/13.71 thf(f44480,plain,(
% 92.92/13.71 spl854_461 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_461])])).
% 92.92/13.71 thf(f17038,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12762])).
% 92.92/13.71 thf(f12762,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8604])).
% 92.92/13.71 thf(f44478,plain,(
% 92.92/13.71 spl854_460),
% 92.92/13.71 inference(avatar_split_clause,[],[f17037,f44476])).
% 92.92/13.71 thf(f44476,plain,(
% 92.92/13.71 spl854_460 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_460])])).
% 92.92/13.71 thf(f17037,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12761])).
% 92.92/13.71 thf(f12761,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8604])).
% 92.92/13.71 thf(f44474,plain,(
% 92.92/13.71 spl854_459),
% 92.92/13.71 inference(avatar_split_clause,[],[f17034,f44472])).
% 92.92/13.71 thf(f44472,plain,(
% 92.92/13.71 spl854_459 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_459])])).
% 92.92/13.71 thf(f17034,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12766])).
% 92.92/13.71 thf(f12766,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8607])).
% 92.92/13.71 thf(f44470,plain,(
% 92.92/13.71 spl854_458),
% 92.92/13.71 inference(avatar_split_clause,[],[f17033,f44468])).
% 92.92/13.71 thf(f44468,plain,(
% 92.92/13.71 spl854_458 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_458])])).
% 92.92/13.71 thf(f17033,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12765])).
% 92.92/13.71 thf(f12765,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8607])).
% 92.92/13.71 thf(f44466,plain,(
% 92.92/13.71 spl854_457),
% 92.92/13.71 inference(avatar_split_clause,[],[f17030,f44464])).
% 92.92/13.71 thf(f44464,plain,(
% 92.92/13.71 spl854_457 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)) | ($true = X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_457])])).
% 92.92/13.71 thf(f17030,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)) | ($true = X0)) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f12770])).
% 92.92/13.71 thf(f12770,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8610])).
% 92.92/13.71 thf(f44462,plain,(
% 92.92/13.71 spl854_456),
% 92.92/13.71 inference(avatar_split_clause,[],[f16582,f44460])).
% 92.92/13.71 thf(f44460,plain,(
% 92.92/13.71 spl854_456 <=> ! [X3 : $o] : (($true = X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,$true),$true),X3)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_456])])).
% 92.92/13.71 thf(f16582,plain,(
% 92.92/13.71 ( ! [X3 : $o] : (($true = X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,$true),$true),X3))) )),
% 92.92/13.71 inference(equality_resolution,[],[f16581])).
% 92.92/13.71 thf(f16581,plain,(
% 92.92/13.71 ( ! [X3 : $o,X0 : $o] : (($true = X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,$true),$true),X3)) | ($true != X0)) )),
% 92.92/13.71 inference(equality_resolution,[],[f16580])).
% 92.92/13.71 thf(f16580,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X0 : $o] : (($true = X3) | ($true != X2) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,$true),X2),X3)) | ($true != X0)) )),
% 92.92/13.71 inference(equality_resolution,[],[f12578])).
% 92.92/13.71 thf(f12578,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X3) | ($true != X1) | ($true != X2) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X1),X2),X3)) | ($true != X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6519])).
% 92.92/13.71 thf(f6519,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X3) | ($true != X1) | (($true != X2) & ($true = X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X1),X2),X3)) | (($true != X0) & ($true = X1)))),
% 92.92/13.71 inference(definition_folding,[],[f6099,f6518])).
% 92.92/13.71 thf(f6518,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X1 : $o] : ((($true != X3) & ($true = X2) & ($true = X1)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X1),X2),X3)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f6099,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X3) | ($true != X1) | (($true != X2) & ($true = X0)) | (($true != X3) & ($true = X2) & ($true = X1)) | (($true != X0) & ($true = X1)))),
% 92.92/13.71 inference(flattening,[],[f6098])).
% 92.92/13.71 thf(f6098,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X3) | ($true != X1)) | (($true != X2) & ($true = X0))) | (((($true != X3) & ($true = X2)) & ($true = X1)) | (($true != X0) & ($true = X1))))),
% 92.92/13.71 inference(ennf_transformation,[],[f4298])).
% 92.92/13.71 thf(f4298,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X1) => (($true = X2) => ($true = X3))) & (($true = X1) => ($true = X0))) => ((($true = X0) => ($true = X2)) => (($true = X1) => ($true = X3))))),
% 92.92/13.71 inference(fool_elimination,[],[f4297])).
% 92.92/13.71 thf(f4297,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X1 => (X2 => X3)) & (X1 => X0)) => ((X0 => X2) => (X1 => X3)))),
% 92.92/13.71 inference(rectify,[],[f231])).
% 92.92/13.71 thf(f231,axiom,(
% 92.92/13.71 ! [X8 : $o,X59 : $o,X12 : $o,X60 : $o] : (((X59 => (X12 => X60)) & (X59 => X8)) => ((X8 => X12) => (X59 => X60)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken)).
% 92.92/13.71 thf(f44458,plain,(
% 92.92/13.71 spl854_455),
% 92.92/13.71 inference(avatar_split_clause,[],[f16573,f44456])).
% 92.92/13.71 thf(f44456,plain,(
% 92.92/13.71 spl854_455 <=> ! [X2 : $o] : (($true = X2) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,$true),$true),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_455])])).
% 92.92/13.71 thf(f16573,plain,(
% 92.92/13.71 ( ! [X2 : $o] : (($true = X2) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,$true),$true),X2))) )),
% 92.92/13.71 inference(equality_resolution,[],[f16572])).
% 92.92/13.71 thf(f16572,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = X2) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X1),$true),X2)) | ($true != X1)) )),
% 92.92/13.71 inference(equality_resolution,[],[f16571])).
% 92.92/13.71 thf(f16571,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X2) | ($true != X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X1),X3),X2)) | ($true != X1)) )),
% 92.92/13.71 inference(equality_resolution,[],[f12571])).
% 92.92/13.71 thf(f12571,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X1),X3),X2)) | ($true != X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6517])).
% 92.92/13.71 thf(f6517,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X2) | ($true != X0) | (($true != X3) & ($true = X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X1),X3),X2)) | (($true != X1) & ($true = X0)))),
% 92.92/13.71 inference(definition_folding,[],[f6097,f6516])).
% 92.92/13.71 thf(f6516,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X1 : $o] : ((($true != X2) & ($true = X3) & ($true = X1)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X1),X3),X2)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f6097,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X2) | ($true != X0) | (($true != X3) & ($true = X1)) | (($true != X2) & ($true = X3) & ($true = X1)) | (($true != X1) & ($true = X0)))),
% 92.92/13.71 inference(flattening,[],[f6096])).
% 92.92/13.71 thf(f6096,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X2) | ($true != X0)) | (($true != X3) & ($true = X1))) | (((($true != X2) & ($true = X3)) & ($true = X1)) | (($true != X1) & ($true = X0))))),
% 92.92/13.71 inference(ennf_transformation,[],[f4296])).
% 92.92/13.71 thf(f4296,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X1) => (($true = X3) => ($true = X2))) & (($true = X0) => ($true = X1))) => ((($true = X1) => ($true = X3)) => (($true = X0) => ($true = X2))))),
% 92.92/13.71 inference(fool_elimination,[],[f4295])).
% 92.92/13.71 thf(f4295,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X1 => (X3 => X2)) & (X0 => X1)) => ((X1 => X3) => (X0 => X2)))),
% 92.92/13.71 inference(rectify,[],[f230])).
% 92.92/13.71 thf(f230,axiom,(
% 92.92/13.71 ! [X8 : $o,X59 : $o,X12 : $o,X60 : $o] : (((X59 => (X60 => X12)) & (X8 => X59)) => ((X59 => X60) => (X8 => X12)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen)).
% 92.92/13.71 thf(f44454,plain,(
% 92.92/13.71 spl854_454),
% 92.92/13.71 inference(avatar_split_clause,[],[f16483,f44452])).
% 92.92/13.71 thf(f44452,plain,(
% 92.92/13.71 spl854_454 <=> ! [X2 : $o,X0 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),$true),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_454])])).
% 92.92/13.71 thf(f16483,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12240])).
% 92.92/13.71 thf(f12240,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8345])).
% 92.92/13.71 thf(f44444,plain,(
% 92.92/13.71 spl854_453),
% 92.92/13.71 inference(avatar_split_clause,[],[f16481,f44442])).
% 92.92/13.71 thf(f44442,plain,(
% 92.92/13.71 spl854_453 <=> ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),$true)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_453])])).
% 92.92/13.71 thf(f16481,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),$true)) | ($true = X1)) )),
% 92.92/13.71 inference(equality_resolution,[],[f12244])).
% 92.92/13.71 thf(f12244,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0)) | ($true != X0) | ($true = X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8345])).
% 92.92/13.71 thf(f44440,plain,(
% 92.92/13.71 spl854_452),
% 92.92/13.71 inference(avatar_split_clause,[],[f16386,f44438])).
% 92.92/13.71 thf(f44438,plain,(
% 92.92/13.71 spl854_452 <=> ! [X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,$true),$true),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_452])])).
% 92.92/13.71 thf(f16386,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,$true),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f16385])).
% 92.92/13.71 thf(f16385,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = X0) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11972])).
% 92.92/13.71 thf(f11972,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8057])).
% 92.92/13.71 thf(f44436,plain,(
% 92.92/13.71 spl854_451),
% 92.92/13.71 inference(avatar_split_clause,[],[f16384,f44434])).
% 92.92/13.71 thf(f44434,plain,(
% 92.92/13.71 spl854_451 <=> ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),$true)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_451])])).
% 92.92/13.71 thf(f16384,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),$true))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11974])).
% 92.92/13.71 thf(f11974,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8057])).
% 92.92/13.71 thf(f44432,plain,(
% 92.92/13.71 spl854_450),
% 92.92/13.71 inference(avatar_split_clause,[],[f16382,f44430])).
% 92.92/13.71 thf(f44430,plain,(
% 92.92/13.71 spl854_450 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,$true),X1),X0)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_450])])).
% 92.92/13.71 thf(f16382,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,$true),X1),X0)) | ($true = X1)) )),
% 92.92/13.71 inference(equality_resolution,[],[f11976])).
% 92.92/13.71 thf(f11976,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)) | ($true = X1) | ($true != X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8057])).
% 92.92/13.71 thf(f44428,plain,(
% 92.92/13.71 spl854_449),
% 92.92/13.71 inference(avatar_split_clause,[],[f16371,f44426])).
% 92.92/13.71 thf(f44426,plain,(
% 92.92/13.71 spl854_449 <=> ! [X2 : $o,X0 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),$true),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_449])])).
% 92.92/13.71 thf(f16371,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11954])).
% 92.92/13.71 thf(f11954,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8048])).
% 92.92/13.71 thf(f44424,plain,(
% 92.92/13.71 spl854_448),
% 92.92/13.71 inference(avatar_split_clause,[],[f16370,f44422])).
% 92.92/13.71 thf(f44422,plain,(
% 92.92/13.71 spl854_448 <=> ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),$true)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_448])])).
% 92.92/13.71 thf(f16370,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),$true))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11955])).
% 92.92/13.71 thf(f11955,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8048])).
% 92.92/13.71 thf(f44420,plain,(
% 92.92/13.71 spl854_447),
% 92.92/13.71 inference(avatar_split_clause,[],[f16361,f44418])).
% 92.92/13.71 thf(f44418,plain,(
% 92.92/13.71 spl854_447 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,$true),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_447])])).
% 92.92/13.71 thf(f16361,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,$true),X1),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11934])).
% 92.92/13.71 thf(f11934,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8040])).
% 92.92/13.71 thf(f44416,plain,(
% 92.92/13.71 spl854_446),
% 92.92/13.71 inference(avatar_split_clause,[],[f16360,f44414])).
% 92.92/13.71 thf(f44414,plain,(
% 92.92/13.71 spl854_446 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,$true),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_446])])).
% 92.92/13.71 thf(f16360,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,$true),X1),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11935])).
% 92.92/13.71 thf(f11935,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8040])).
% 92.92/13.71 thf(f44412,plain,(
% 92.92/13.71 spl854_445),
% 92.92/13.71 inference(avatar_split_clause,[],[f16359,f44410])).
% 92.92/13.71 thf(f44410,plain,(
% 92.92/13.71 spl854_445 <=> ! [X2 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),$true),$true)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_445])])).
% 92.92/13.71 thf(f16359,plain,(
% 92.92/13.71 ( ! [X2 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),$true),$true))) )),
% 92.92/13.71 inference(equality_resolution,[],[f16358])).
% 92.92/13.71 thf(f16358,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),$true))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11936])).
% 92.92/13.71 thf(f11936,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8040])).
% 92.92/13.71 thf(f44408,plain,(
% 92.92/13.71 spl854_444),
% 92.92/13.71 inference(avatar_split_clause,[],[f16347,f44406])).
% 92.92/13.71 thf(f44406,plain,(
% 92.92/13.71 spl854_444 <=> ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X1),X1),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_444])])).
% 92.92/13.71 thf(f16347,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X1),X1),X2))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11926])).
% 92.92/13.71 thf(f11926,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | (X0 != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8035])).
% 92.92/13.71 thf(f8035,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((((($true = X2) | (X0 != X1)) & ((X0 = X1) | ($true != X2))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2))) & (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2)) | (((X0 != X1) | ($true != X2)) & ((X0 = X1) | ($true = X2)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6460])).
% 92.92/13.71 thf(f6460,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = X2) <=> (X0 = X1)) <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2)))),
% 92.92/13.71 inference(definition_folding,[],[f3966,f6459,f6458,f6457,f6456])).
% 92.92/13.71 thf(f3966,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = X2) <=> (X0 = X1)) <=> ((($true = vAPP($o,$o,vNOT,X2)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true = X0)) & (($true = vAPP($o,$o,vNOT,X2)) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X1)) & ((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0)) | ($true = X2)) & (($true = X0) | ($true = X1) | ($true = X2))))),
% 92.92/13.71 inference(fool_elimination,[],[f3965])).
% 92.92/13.71 thf(f3965,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((X2 <=> (X0 = X1)) <=> ((vAPP($o,$o,vNOT,X2) | vAPP($o,$o,vNOT,X1) | X0) & (vAPP($o,$o,vNOT,X2) | vAPP($o,$o,vNOT,X0) | X1) & (vAPP($o,$o,vNOT,X1) | vAPP($o,$o,vNOT,X0) | X2) & (X0 | X1 | X2)))),
% 92.92/13.71 inference(rectify,[],[f294])).
% 92.92/13.71 thf(f294,axiom,(
% 92.92/13.71 ! [X107 : $o,X103 : $o,X108 : $o] : ((X108 <=> (X103 = X107)) <=> ((vAPP($o,$o,vNOT,X108) | vAPP($o,$o,vNOT,X103) | X107) & (vAPP($o,$o,vNOT,X108) | vAPP($o,$o,vNOT,X107) | X103) & (vAPP($o,$o,vNOT,X103) | vAPP($o,$o,vNOT,X107) | X108) & (X107 | X103 | X108)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq)).
% 92.92/13.71 thf(f44404,plain,(
% 92.92/13.71 spl854_443 | ~spl854_131 | ~spl854_232),
% 92.92/13.71 inference(avatar_split_clause,[],[f23691,f23643,f22780,f44401])).
% 92.92/13.71 thf(f22780,plain,(
% 92.92/13.71 spl854_131 <=> ! [X0 : tyop_2Emin_2Eind] : ((vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) = X0) | ($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_131])])).
% 92.92/13.71 thf(f23643,plain,(
% 92.92/13.71 spl854_232 <=> ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,c_2Enum_2EZERO__REP))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_232])])).
% 92.92/13.71 thf(f23691,plain,(
% 92.92/13.71 (c_2Enum_2EZERO__REP = vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (~spl854_131 | ~spl854_232)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f23688])).
% 92.92/13.71 thf(f23688,plain,(
% 92.92/13.71 ($true != $true) | (c_2Enum_2EZERO__REP = vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (~spl854_131 | ~spl854_232)),
% 92.92/13.71 inference(superposition,[],[f22781,f23645])).
% 92.92/13.71 thf(f23645,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,c_2Enum_2EZERO__REP)) | ~spl854_232),
% 92.92/13.71 inference(avatar_component_clause,[],[f23643])).
% 92.92/13.71 thf(f22781,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) = X0)) ) | ~spl854_131),
% 92.92/13.71 inference(avatar_component_clause,[],[f22780])).
% 92.92/13.71 thf(f44399,plain,(
% 92.92/13.71 spl854_442),
% 92.92/13.71 inference(avatar_split_clause,[],[f16322,f44397])).
% 92.92/13.71 thf(f44397,plain,(
% 92.92/13.71 spl854_442 <=> ! [X2 : $o,X0 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),$true),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_442])])).
% 92.92/13.71 thf(f16322,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11888])).
% 92.92/13.71 thf(f11888,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8019])).
% 92.92/13.71 thf(f44395,plain,(
% 92.92/13.71 spl854_441),
% 92.92/13.71 inference(avatar_split_clause,[],[f16321,f44393])).
% 92.92/13.71 thf(f44393,plain,(
% 92.92/13.71 spl854_441 <=> ! [X2 : $o,X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),$true),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_441])])).
% 92.92/13.71 thf(f16321,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11889])).
% 92.92/13.71 thf(f11889,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8019])).
% 92.92/13.71 thf(f44391,plain,(
% 92.92/13.71 spl854_440),
% 92.92/13.71 inference(avatar_split_clause,[],[f16313,f44389])).
% 92.92/13.71 thf(f44389,plain,(
% 92.92/13.71 spl854_440 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,$true),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_440])])).
% 92.92/13.71 thf(f16313,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,$true),X1),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11878])).
% 92.92/13.71 thf(f11878,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8014])).
% 92.92/13.71 thf(f44387,plain,(
% 92.92/13.71 spl854_439),
% 92.92/13.71 inference(avatar_split_clause,[],[f16312,f44385])).
% 92.92/13.71 thf(f44385,plain,(
% 92.92/13.71 spl854_439 <=> ! [X2 : $o,X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),$true),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_439])])).
% 92.92/13.71 thf(f16312,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),$true),X0))) )),
% 92.92/13.71 inference(equality_resolution,[],[f11879])).
% 92.92/13.71 thf(f11879,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8014])).
% 92.92/13.71 thf(f44383,plain,(
% 92.92/13.71 spl854_438),
% 92.92/13.71 inference(avatar_split_clause,[],[f14784,f44381])).
% 92.92/13.71 thf(f44381,plain,(
% 92.92/13.71 spl854_438 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_438])])).
% 92.92/13.71 thf(f14784,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f11081,f9121])).
% 92.92/13.71 thf(f11081,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7605])).
% 92.92/13.71 thf(f44379,plain,(
% 92.92/13.71 spl854_437),
% 92.92/13.71 inference(avatar_split_clause,[],[f14783,f44377])).
% 92.92/13.71 thf(f44377,plain,(
% 92.92/13.71 spl854_437 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_437])])).
% 92.92/13.71 thf(f14783,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f11082,f9121])).
% 92.92/13.71 thf(f11082,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7605])).
% 92.92/13.71 thf(f44375,plain,(
% 92.92/13.71 spl854_436),
% 92.92/13.71 inference(avatar_split_clause,[],[f14429,f44373])).
% 92.92/13.71 thf(f44373,plain,(
% 92.92/13.71 spl854_436 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_436])])).
% 92.92/13.71 thf(f14429,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10460,f9122,f9122])).
% 92.92/13.71 thf(f10460,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6990])).
% 92.92/13.71 thf(f6990,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) | (c_2Enum_2E0 != X1) | (c_2Enum_2E0 != X0)) & (((c_2Enum_2E0 = X1) & (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))))),
% 92.92/13.71 inference(flattening,[],[f6989])).
% 92.92/13.71 thf(f6989,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) | ((c_2Enum_2E0 != X1) | (c_2Enum_2E0 != X0))) & (((c_2Enum_2E0 = X1) & (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5113])).
% 92.92/13.71 thf(f5113,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)) <=> ((c_2Enum_2E0 = X1) & (c_2Enum_2E0 = X0)))),
% 92.92/13.71 inference(rectify,[],[f1004])).
% 92.92/13.71 thf(f1004,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137)) <=> ((c_2Enum_2E0 = X137) & (c_2Enum_2E0 = X134)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__EQ__0)).
% 92.92/13.71 thf(f44371,plain,(
% 92.92/13.71 spl854_435),
% 92.92/13.71 inference(avatar_split_clause,[],[f14428,f44369])).
% 92.92/13.71 thf(f44369,plain,(
% 92.92/13.71 spl854_435 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_435])])).
% 92.92/13.71 thf(f14428,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10461,f9122,f9122])).
% 92.92/13.71 thf(f10461,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6990])).
% 92.92/13.71 thf(f44367,plain,(
% 92.92/13.71 spl854_434),
% 92.92/13.71 inference(avatar_split_clause,[],[f14423,f44365])).
% 92.92/13.71 thf(f44365,plain,(
% 92.92/13.71 spl854_434 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_434])])).
% 92.92/13.71 thf(f14423,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10454,f9122,f9122])).
% 92.92/13.71 thf(f10454,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6986])).
% 92.92/13.71 thf(f6986,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) | (c_2Enum_2E0 != X0)) & ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) & (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1))))),
% 92.92/13.71 inference(flattening,[],[f6985])).
% 92.92/13.71 thf(f6985,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) | (c_2Enum_2E0 != X0))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) & (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f2980])).
% 92.92/13.71 thf(f2980,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)) <=> (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1)) & (c_2Enum_2E0 = X0)))),
% 92.92/13.71 inference(fool_elimination,[],[f2979])).
% 92.92/13.71 thf(f2979,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),X1)) <=> (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X1) & (c_2Enum_2E0 = X0)))),
% 92.92/13.71 inference(rectify,[],[f1199])).
% 92.92/13.71 thf(f1199,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X136),X27)) <=> (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X27) & (c_2Enum_2E0 = X136)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEXP__EQ__0)).
% 92.92/13.71 thf(f44363,plain,(
% 92.92/13.71 spl854_433),
% 92.92/13.71 inference(avatar_split_clause,[],[f14418,f44361])).
% 92.92/13.71 thf(f44361,plain,(
% 92.92/13.71 spl854_433 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_433])])).
% 92.92/13.71 thf(f14418,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10449,f9122,f9122])).
% 92.92/13.71 thf(f10449,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6983])).
% 92.92/13.71 thf(f6983,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)) | (c_2Enum_2E0 != X1) | (c_2Enum_2E0 != X0)) & (((c_2Enum_2E0 = X1) & (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))))),
% 92.92/13.71 inference(flattening,[],[f6982])).
% 92.92/13.71 thf(f6982,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)) | ((c_2Enum_2E0 != X1) | (c_2Enum_2E0 != X0))) & (((c_2Enum_2E0 = X1) & (c_2Enum_2E0 = X0)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5111])).
% 92.92/13.71 thf(f5111,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)) <=> ((c_2Enum_2E0 = X1) & (c_2Enum_2E0 = X0)))),
% 92.92/13.71 inference(rectify,[],[f1580])).
% 92.92/13.71 thf(f1580,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X136),X27)) <=> ((c_2Enum_2E0 = X27) & (c_2Enum_2E0 = X136)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__EQ__0)).
% 92.92/13.71 thf(f44329,plain,(
% 92.92/13.71 spl854_432),
% 92.92/13.71 inference(avatar_split_clause,[],[f14417,f44327])).
% 92.92/13.71 thf(f44327,plain,(
% 92.92/13.71 spl854_432 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_432])])).
% 92.92/13.71 thf(f14417,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10450,f9122,f9122])).
% 92.92/13.71 thf(f10450,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6983])).
% 92.92/13.71 thf(f44325,plain,(
% 92.92/13.71 spl854_431),
% 92.92/13.71 inference(avatar_split_clause,[],[f14410,f44323])).
% 92.92/13.71 thf(f44323,plain,(
% 92.92/13.71 spl854_431 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_431])])).
% 92.92/13.71 thf(f14410,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10441,f9122,f9122])).
% 92.92/13.71 thf(f10441,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6978])).
% 92.92/13.71 thf(f6978,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0)) | (c_2Enum_2E0 != X0) | (c_2Enum_2E0 != X1)) & (((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X1)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))))),
% 92.92/13.71 inference(flattening,[],[f6977])).
% 92.92/13.71 thf(f6977,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0)) | ((c_2Enum_2E0 != X0) | (c_2Enum_2E0 != X1))) & (((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X1)) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5108])).
% 92.92/13.71 thf(f5108,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0)) <=> ((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X1)))),
% 92.92/13.71 inference(rectify,[],[f1234])).
% 92.92/13.71 thf(f1234,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X27),X136)) <=> ((c_2Enum_2E0 = X136) & (c_2Enum_2E0 = X27)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMAX__EQ__0)).
% 92.92/13.71 thf(f44321,plain,(
% 92.92/13.71 spl854_430),
% 92.92/13.71 inference(avatar_split_clause,[],[f14409,f44319])).
% 92.92/13.71 thf(f44319,plain,(
% 92.92/13.71 spl854_430 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_430])])).
% 92.92/13.71 thf(f14409,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f10442,f9122,f9122])).
% 92.92/13.71 thf(f10442,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6978])).
% 92.92/13.71 thf(f44317,plain,(
% 92.92/13.71 spl854_429),
% 92.92/13.71 inference(avatar_split_clause,[],[f14015,f44315])).
% 92.92/13.71 thf(f44315,plain,(
% 92.92/13.71 spl854_429 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_429])])).
% 92.92/13.71 thf(f14015,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9770,f9122,f9122])).
% 92.92/13.71 thf(f9770,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,c_2Enum_2E0),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6810])).
% 92.92/13.71 thf(f6810,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,c_2Enum_2E0),X0)) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,c_2Enum_2E0),X0))))),
% 92.92/13.71 inference(nnf_transformation,[],[f2406])).
% 92.92/13.71 thf(f2406,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,c_2Enum_2E0),X0)) <=> (c_2Enum_2E0 = X0))),
% 92.92/13.71 inference(fool_elimination,[],[f2405])).
% 92.92/13.71 thf(f2405,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,c_2Enum_2E0),X0) <=> (c_2Enum_2E0 = X0))),
% 92.92/13.71 inference(rectify,[],[f1464])).
% 92.92/13.71 thf(f1464,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,c_2Enum_2E0),X134) <=> (c_2Enum_2E0 = X134))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EZERO__DIVIDES)).
% 92.92/13.71 thf(f44313,plain,(
% 92.92/13.71 spl854_428),
% 92.92/13.71 inference(avatar_split_clause,[],[f13967,f44311])).
% 92.92/13.71 thf(f44311,plain,(
% 92.92/13.71 spl854_428 <=> ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_428])])).
% 92.92/13.71 thf(f13967,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9710,f9122])).
% 92.92/13.71 thf(f9710,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6777])).
% 92.92/13.71 thf(f44309,plain,(
% 92.92/13.71 spl854_427),
% 92.92/13.71 inference(avatar_split_clause,[],[f13961,f44307])).
% 92.92/13.71 thf(f44307,plain,(
% 92.92/13.71 spl854_427 <=> ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_427])])).
% 92.92/13.71 thf(f13961,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0)))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9699,f9122])).
% 92.92/13.71 thf(f9699,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6760])).
% 92.92/13.71 thf(f44305,plain,(
% 92.92/13.71 spl854_426),
% 92.92/13.71 inference(avatar_split_clause,[],[f13959,f44303])).
% 92.92/13.71 thf(f44303,plain,(
% 92.92/13.71 spl854_426 <=> ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_426])])).
% 92.92/13.71 thf(f13959,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0)))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9695,f9122])).
% 92.92/13.71 thf(f9695,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,c_2Enum_2E0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK171,X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6754])).
% 92.92/13.71 thf(f44301,plain,(
% 92.92/13.71 spl854_425),
% 92.92/13.71 inference(avatar_split_clause,[],[f13828,f44299])).
% 92.92/13.71 thf(f44299,plain,(
% 92.92/13.71 spl854_425 <=> ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_425])])).
% 92.92/13.71 thf(f13828,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9536,f13519])).
% 92.92/13.71 thf(f9536,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2148])).
% 92.92/13.71 thf(f2148,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)))),
% 92.92/13.71 inference(fool_elimination,[],[f2147])).
% 92.92/13.71 thf(f2147,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X0) | vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0))),
% 92.92/13.71 inference(rectify,[],[f1085])).
% 92.92/13.71 thf(f1085,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,X136) | vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X136))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__OR__ODD)).
% 92.92/13.71 thf(f44297,plain,(
% 92.92/13.71 spl854_424),
% 92.92/13.71 inference(avatar_split_clause,[],[f13596,f44295])).
% 92.92/13.71 thf(f44295,plain,(
% 92.92/13.71 spl854_424 <=> ! [X4 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X4) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X4)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_424])])).
% 92.92/13.71 thf(f13596,plain,(
% 92.92/13.71 ( ! [X4 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X4) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X4))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9230,f9122,f9122])).
% 92.92/13.71 thf(f9230,plain,(
% 92.92/13.71 ( ! [X4 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X4) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),X4))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6597])).
% 92.92/13.71 thf(f44293,plain,(
% 92.92/13.71 spl854_423),
% 92.92/13.71 inference(avatar_split_clause,[],[f13119,f44291])).
% 92.92/13.71 thf(f44291,plain,(
% 92.92/13.71 spl854_423 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_423])])).
% 92.92/13.71 thf(f13119,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8886])).
% 92.92/13.71 thf(f8886,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8885])).
% 92.92/13.71 thf(f8885,plain,(
% 92.92/13.71 ! [X1 : $o,X2 : $o,X0 : $o] : ((($true != X1) & ($true = X2) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X0),X2),X1)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6570])).
% 92.92/13.71 thf(f6570,plain,(
% 92.92/13.71 ! [X1 : $o,X2 : $o,X0 : $o] : ((($true != X1) & ($true = X2) & ($true = X0)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X0),X2),X1)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44289,plain,(
% 92.92/13.71 spl854_422 | ~spl854_56 | ~spl854_311),
% 92.92/13.71 inference(avatar_split_clause,[],[f42383,f37352,f22210,f44287])).
% 92.92/13.71 thf(f44287,plain,(
% 92.92/13.71 spl854_422 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_422])])).
% 92.92/13.71 thf(f22210,plain,(
% 92.92/13.71 spl854_56 <=> ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_56])])).
% 92.92/13.71 thf(f37352,plain,(
% 92.92/13.71 spl854_311 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_311])])).
% 92.92/13.71 thf(f42383,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))) ) | (~spl854_56 | ~spl854_311)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f42366])).
% 92.92/13.71 thf(f42366,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true != $true) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))) ) | (~spl854_56 | ~spl854_311)),
% 92.92/13.71 inference(superposition,[],[f22211,f37353])).
% 92.92/13.71 thf(f37353,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))) ) | ~spl854_311),
% 92.92/13.71 inference(avatar_component_clause,[],[f37352])).
% 92.92/13.71 thf(f22211,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) ) | ~spl854_56),
% 92.92/13.71 inference(avatar_component_clause,[],[f22210])).
% 92.92/13.71 thf(f44285,plain,(
% 92.92/13.71 spl854_421),
% 92.92/13.71 inference(avatar_split_clause,[],[f13118,f44283])).
% 92.92/13.71 thf(f44283,plain,(
% 92.92/13.71 spl854_421 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_421])])).
% 92.92/13.71 thf(f13118,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8886])).
% 92.92/13.71 thf(f44281,plain,(
% 92.92/13.71 spl854_420),
% 92.92/13.71 inference(avatar_split_clause,[],[f12617,f44279])).
% 92.92/13.71 thf(f44279,plain,(
% 92.92/13.71 spl854_420 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_420])])).
% 92.92/13.71 thf(f12617,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8494])).
% 92.92/13.71 thf(f44277,plain,(
% 92.92/13.71 spl854_419),
% 92.92/13.71 inference(avatar_split_clause,[],[f12614,f44275])).
% 92.92/13.71 thf(f44275,plain,(
% 92.92/13.71 spl854_419 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_419])])).
% 92.92/13.71 thf(f12614,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8492])).
% 92.92/13.71 thf(f44273,plain,(
% 92.92/13.71 spl854_418),
% 92.92/13.71 inference(avatar_split_clause,[],[f12609,f44271])).
% 92.92/13.71 thf(f44271,plain,(
% 92.92/13.71 spl854_418 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_418])])).
% 92.92/13.71 thf(f12609,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8490])).
% 92.92/13.71 thf(f44269,plain,(
% 92.92/13.71 spl854_417),
% 92.92/13.71 inference(avatar_split_clause,[],[f12606,f44267])).
% 92.92/13.71 thf(f44267,plain,(
% 92.92/13.71 spl854_417 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_417])])).
% 92.92/13.71 thf(f12606,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8489])).
% 92.92/13.71 thf(f44265,plain,(
% 92.92/13.71 spl854_416),
% 92.92/13.71 inference(avatar_split_clause,[],[f12573,f44263])).
% 92.92/13.71 thf(f44263,plain,(
% 92.92/13.71 spl854_416 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_416])])).
% 92.92/13.71 thf(f12573,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8478])).
% 92.92/13.71 thf(f8478,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8477])).
% 92.92/13.71 thf(f8477,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X1 : $o] : ((($true != X3) & ($true = X2) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X1),X2),X3)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6518])).
% 92.92/13.71 thf(f44261,plain,(
% 92.92/13.71 spl854_415),
% 92.92/13.71 inference(avatar_split_clause,[],[f12572,f44259])).
% 92.92/13.71 thf(f44259,plain,(
% 92.92/13.71 spl854_415 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_415])])).
% 92.92/13.71 thf(f12572,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8478])).
% 92.92/13.71 thf(f44257,plain,(
% 92.92/13.71 spl854_414),
% 92.92/13.71 inference(avatar_split_clause,[],[f12566,f44255])).
% 92.92/13.71 thf(f44255,plain,(
% 92.92/13.71 spl854_414 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_414])])).
% 92.92/13.71 thf(f12566,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8476])).
% 92.92/13.71 thf(f8476,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8475])).
% 92.92/13.71 thf(f8475,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X1 : $o] : ((($true != X2) & ($true = X3) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X1),X3),X2)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6516])).
% 92.92/13.71 thf(f44253,plain,(
% 92.92/13.71 spl854_413),
% 92.92/13.71 inference(avatar_split_clause,[],[f12565,f44251])).
% 92.92/13.71 thf(f44251,plain,(
% 92.92/13.71 spl854_413 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_413])])).
% 92.92/13.71 thf(f12565,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8476])).
% 92.92/13.71 thf(f44249,plain,(
% 92.92/13.71 spl854_412),
% 92.92/13.71 inference(avatar_split_clause,[],[f12561,f44247])).
% 92.92/13.71 thf(f44247,plain,(
% 92.92/13.71 spl854_412 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_412])])).
% 92.92/13.71 thf(f12561,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8474])).
% 92.92/13.71 thf(f8474,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8473])).
% 92.92/13.71 thf(f8473,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X0 : $o] : ((($true != X3) & ($true = X2) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X0),X2),X3)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6513])).
% 92.92/13.71 thf(f6513,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X0 : $o] : ((($true != X3) & ($true = X2) & ($true = X0)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X0),X2),X3)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44179,plain,(
% 92.92/13.71 spl854_411),
% 92.92/13.71 inference(avatar_split_clause,[],[f12560,f44177])).
% 92.92/13.71 thf(f44177,plain,(
% 92.92/13.71 spl854_411 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_411])])).
% 92.92/13.71 thf(f12560,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8474])).
% 92.92/13.71 thf(f44175,plain,(
% 92.92/13.71 spl854_410),
% 92.92/13.71 inference(avatar_split_clause,[],[f12558,f44173])).
% 92.92/13.71 thf(f44173,plain,(
% 92.92/13.71 spl854_410 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_410])])).
% 92.92/13.71 thf(f12558,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8472])).
% 92.92/13.71 thf(f44171,plain,(
% 92.92/13.71 spl854_409),
% 92.92/13.71 inference(avatar_split_clause,[],[f12553,f44169])).
% 92.92/13.71 thf(f44169,plain,(
% 92.92/13.71 spl854_409 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_409])])).
% 92.92/13.71 thf(f12553,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8470])).
% 92.92/13.71 thf(f8470,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8469])).
% 92.92/13.71 thf(f8469,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X0 : $o] : ((($true != X2) & ($true = X3) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X0),X3),X2)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6510])).
% 92.92/13.71 thf(f6510,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X0 : $o] : ((($true != X2) & ($true = X3) & ($true = X0)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X0),X3),X2)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44167,plain,(
% 92.92/13.71 spl854_408),
% 92.92/13.71 inference(avatar_split_clause,[],[f12552,f44165])).
% 92.92/13.71 thf(f44165,plain,(
% 92.92/13.71 spl854_408 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_408])])).
% 92.92/13.71 thf(f12552,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8470])).
% 92.92/13.71 thf(f44163,plain,(
% 92.92/13.71 spl854_407),
% 92.92/13.71 inference(avatar_split_clause,[],[f12550,f44161])).
% 92.92/13.71 thf(f44161,plain,(
% 92.92/13.71 spl854_407 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_407])])).
% 92.92/13.71 thf(f12550,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8468])).
% 92.92/13.71 thf(f44159,plain,(
% 92.92/13.71 spl854_406),
% 92.92/13.71 inference(avatar_split_clause,[],[f12545,f44157])).
% 92.92/13.71 thf(f44157,plain,(
% 92.92/13.71 spl854_406 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_406])])).
% 92.92/13.71 thf(f12545,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8466])).
% 92.92/13.71 thf(f8466,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6507])).
% 92.92/13.71 thf(f6507,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44155,plain,(
% 92.92/13.71 spl854_405),
% 92.92/13.71 inference(avatar_split_clause,[],[f12544,f44153])).
% 92.92/13.71 thf(f44153,plain,(
% 92.92/13.71 spl854_405 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_405])])).
% 92.92/13.71 thf(f12544,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8466])).
% 92.92/13.71 thf(f44151,plain,(
% 92.92/13.71 spl854_404),
% 92.92/13.71 inference(avatar_split_clause,[],[f12542,f44149])).
% 92.92/13.71 thf(f44149,plain,(
% 92.92/13.71 spl854_404 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_404])])).
% 92.92/13.71 thf(f12542,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8465])).
% 92.92/13.71 thf(f8465,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8464])).
% 92.92/13.71 thf(f8464,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X1 : $o] : ((($true != X2) & ($true = X3) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X1),X3),X2)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6508])).
% 92.92/13.71 thf(f6508,plain,(
% 92.92/13.71 ! [X2 : $o,X3 : $o,X1 : $o] : ((($true != X2) & ($true = X3) & ($true = X1)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X1),X3),X2)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44147,plain,(
% 92.92/13.71 spl854_403),
% 92.92/13.71 inference(avatar_split_clause,[],[f12541,f44145])).
% 92.92/13.71 thf(f44145,plain,(
% 92.92/13.71 spl854_403 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_403])])).
% 92.92/13.71 thf(f12541,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8465])).
% 92.92/13.71 thf(f44143,plain,(
% 92.92/13.71 spl854_402),
% 92.92/13.71 inference(avatar_split_clause,[],[f12537,f44141])).
% 92.92/13.71 thf(f44141,plain,(
% 92.92/13.71 spl854_402 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_402])])).
% 92.92/13.71 thf(f12537,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8463])).
% 92.92/13.71 thf(f8463,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8462])).
% 92.92/13.71 thf(f8462,plain,(
% 92.92/13.71 ! [X1 : $o,X0 : $o,X2 : $o] : ((($true != X1) & ($true = X0) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X0),X1)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6504])).
% 92.92/13.71 thf(f6504,plain,(
% 92.92/13.71 ! [X1 : $o,X0 : $o,X2 : $o] : ((($true != X1) & ($true = X0) & ($true = X2)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X0),X1)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44098,plain,(
% 92.92/13.71 spl854_401),
% 92.92/13.71 inference(avatar_split_clause,[],[f12536,f44096])).
% 92.92/13.71 thf(f44096,plain,(
% 92.92/13.71 spl854_401 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_401])])).
% 92.92/13.71 thf(f12536,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8463])).
% 92.92/13.71 thf(f44094,plain,(
% 92.92/13.71 spl854_400),
% 92.92/13.71 inference(avatar_split_clause,[],[f12534,f44092])).
% 92.92/13.71 thf(f44092,plain,(
% 92.92/13.71 spl854_400 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_400])])).
% 92.92/13.71 thf(f12534,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8461])).
% 92.92/13.71 thf(f8461,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true != X0) & ($true = X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f8460])).
% 92.92/13.71 thf(f8460,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X1 : $o] : ((($true != X3) & ($true = X2) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X1),X2),X3)))),
% 92.92/13.71 inference(nnf_transformation,[],[f6505])).
% 92.92/13.71 thf(f6505,plain,(
% 92.92/13.71 ! [X3 : $o,X2 : $o,X1 : $o] : ((($true != X3) & ($true = X2) & ($true = X1)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X1),X2),X3)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f44090,plain,(
% 92.92/13.71 spl854_399),
% 92.92/13.71 inference(avatar_split_clause,[],[f12533,f44088])).
% 92.92/13.71 thf(f44088,plain,(
% 92.92/13.71 spl854_399 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_399])])).
% 92.92/13.71 thf(f12533,plain,(
% 92.92/13.71 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X2) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8461])).
% 92.92/13.71 thf(f43886,plain,(
% 92.92/13.71 spl854_398 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f12064,f29086,f43884])).
% 92.92/13.71 thf(f43884,plain,(
% 92.92/13.71 spl854_398 <=> ! [X0 : $tType,X6 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK580(X0),X1))) | ($true = vAPP(X0,$o,X1,X6)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_398])])).
% 92.92/13.71 thf(f12064,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X6 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK580(X0),X1))) | ($true = vAPP(X0,$o,X1,X6))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8187])).
% 92.92/13.71 thf(f43629,plain,(
% 92.92/13.71 spl854_397 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f12019,f29086,f43627])).
% 92.92/13.71 thf(f43627,plain,(
% 92.92/13.71 spl854_397 <=> ! [X0 : $tType,X1 : X0 > $o,X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK547(X0),X1))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_397])])).
% 92.92/13.71 thf(f12019,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : $o,X3 : X0,X1 : X0 > $o] : (($true = X2) | ($true != vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK547(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8111])).
% 92.92/13.71 thf(f43425,plain,(
% 92.92/13.71 spl854_396 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f12001,f29086,f43423])).
% 92.92/13.71 thf(f43423,plain,(
% 92.92/13.71 spl854_396 <=> ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK541(X0),X2))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_396])])).
% 92.92/13.71 thf(f12001,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : $o] : (($true = X1) | ($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK541(X0),X2)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8089])).
% 92.92/13.71 thf(f43217,plain,(
% 92.92/13.71 spl854_305 | spl854_395),
% 92.92/13.71 inference(avatar_split_clause,[],[f11998,f43215,f29086])).
% 92.92/13.71 thf(f43215,plain,(
% 92.92/13.71 spl854_395 <=> ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK539(X0),X2))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_395])])).
% 92.92/13.71 thf(f11998,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : $o] : (($true = vAPP(X0,$o,X2,X3)) | ($true = X1) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK539(X0),X2)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8083])).
% 92.92/13.71 thf(f42960,plain,(
% 92.92/13.71 spl854_305 | spl854_394),
% 92.92/13.71 inference(avatar_split_clause,[],[f11865,f42958,f29086])).
% 92.92/13.71 thf(f42958,plain,(
% 92.92/13.71 spl854_394 <=> ! [X0 : $tType,X2 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK531(X0),X2))) | ($true != vAPP(X0,$o,X2,X4)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_394])])).
% 92.92/13.71 thf(f11865,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK531(X0),X2))) | ($true = X1) | ($true != vAPP(X0,$o,X2,X4))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8007])).
% 92.92/13.71 thf(f42703,plain,(
% 92.92/13.71 spl854_393 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f11850,f29086,f42701])).
% 92.92/13.71 thf(f42701,plain,(
% 92.92/13.71 spl854_393 <=> ! [X0 : $tType,X4 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK529(X0),X1))) | ($true != vAPP(X0,$o,X1,X4)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_393])])).
% 92.92/13.71 thf(f11850,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X4 : X0] : (($true = X2) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK529(X0),X1))) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7996])).
% 92.92/13.71 thf(f42446,plain,(
% 92.92/13.71 spl854_392 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f11428,f29086,f42444])).
% 92.92/13.71 thf(f42444,plain,(
% 92.92/13.71 spl854_392 <=> ! [X0 : $tType,X13 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X13)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK395(X0),X1))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_392])])).
% 92.92/13.71 thf(f11428,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X13 : X0] : (($true = X2) | ($true != vAPP(X0,$o,X1,X13)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK395(X0),X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7704])).
% 92.92/13.71 thf(f42442,plain,(
% 92.92/13.71 spl854_391),
% 92.92/13.71 inference(avatar_split_clause,[],[f11170,f42440])).
% 92.92/13.71 thf(f42440,plain,(
% 92.92/13.71 spl854_391 <=> ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK385(X0),X1))) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_391])])).
% 92.92/13.71 thf(f11170,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK385(X0),X1))) | ($true != vAPP(sTfun(X0,$o),$o,sP24(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7675])).
% 92.92/13.71 thf(f42438,plain,(
% 92.92/13.71 spl854_390),
% 92.92/13.71 inference(avatar_split_clause,[],[f11078,f42436])).
% 92.92/13.71 thf(f42436,plain,(
% 92.92/13.71 spl854_390 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_390])])).
% 92.92/13.71 thf(f11078,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7603])).
% 92.92/13.71 thf(f7603,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0)))))),
% 92.92/13.71 inference(flattening,[],[f7602])).
% 92.92/13.71 thf(f7602,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0))) | (($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0)))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3394])).
% 92.92/13.71 thf(f3394,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0))) <=> (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0))))),
% 92.92/13.71 inference(fool_elimination,[],[f3393])).
% 92.92/13.71 thf(f3393,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X1),X0)) <=> (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X1) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X0)))),
% 92.92/13.71 inference(rectify,[],[f1096])).
% 92.92/13.71 thf(f1096,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X27),X136)) <=> (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X27) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,c_2Enum_2E0),X136)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXP__IFF)).
% 92.92/13.71 thf(f42434,plain,(
% 92.92/13.71 spl854_389),
% 92.92/13.71 inference(avatar_split_clause,[],[f10794,f42432])).
% 92.92/13.71 thf(f42432,plain,(
% 92.92/13.71 spl854_389 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_389])])).
% 92.92/13.71 thf(f10794,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7397])).
% 92.92/13.71 thf(f7397,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6418])).
% 92.92/13.71 thf(f6418,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f5793,f6417])).
% 92.92/13.71 thf(f6417,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1)) <=> ! [X2 : X0 > $o] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X2,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) & ($true = vAPP(X0,$o,X2,X4))) | ! [X3 : X0] : ($true != vAPP(X0,$o,X2,X3))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f5793,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ! [X2 : X0 > $o] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X2,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) & ($true = vAPP(X0,$o,X2,X4))) | ! [X3 : X0] : ($true != vAPP(X0,$o,X2,X3))))),
% 92.92/13.71 inference(ennf_transformation,[],[f3192])).
% 92.92/13.71 thf(f3192,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ! [X2 : X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,X2,X3)) => ? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4)) => ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X2,X5)))) & ($true = vAPP(X0,$o,X2,X4)))))),
% 92.92/13.71 inference(fool_elimination,[],[f3191])).
% 92.92/13.71 thf(f3191,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) <=> ! [X2 : X0 > $o] : (? [X3 : X0] : vAPP(X0,$o,X2,X3) => ? [X4 : X0] : (! [X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4) => vAPP($o,$o,vNOT,vAPP(X0,$o,X2,X5))) & vAPP(X0,$o,X2,X4))))),
% 92.92/13.71 inference(rectify,[],[f421])).
% 92.92/13.71 thf(f421,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) <=> ! [X45 : X0 > $o] : (? [X146 : X0] : vAPP(X0,$o,X45,X146) => ? [X147 : X0] : (! [X71 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X71),X147) => vAPP($o,$o,vNOT,vAPP(X0,$o,X45,X71))) & vAPP(X0,$o,X45,X147))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__DEF)).
% 92.92/13.71 thf(f42426,plain,(
% 92.92/13.71 spl854_388),
% 92.92/13.71 inference(avatar_split_clause,[],[f10793,f42424])).
% 92.92/13.71 thf(f42424,plain,(
% 92.92/13.71 spl854_388 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_388])])).
% 92.92/13.71 thf(f10793,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP21(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7397])).
% 92.92/13.71 thf(f42422,plain,(
% 92.92/13.71 spl854_387),
% 92.92/13.71 inference(avatar_split_clause,[],[f10787,f42420])).
% 92.92/13.71 thf(f42420,plain,(
% 92.92/13.71 spl854_387 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_387])])).
% 92.92/13.71 thf(f10787,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7389])).
% 92.92/13.71 thf(f7389,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6416])).
% 92.92/13.71 thf(f6416,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f5792,f6415])).
% 92.92/13.71 thf(f6415,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1)) <=> ! [X2 : X0 > $o] : (! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3))))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f5792,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ! [X2 : X0 > $o] : (! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ! [X4 : X0] : (($true = vAPP(X0,$o,X2,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3))))))),
% 92.92/13.71 inference(ennf_transformation,[],[f3190])).
% 92.92/13.71 thf(f3190,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) <=> ! [X2 : X0 > $o] : (! [X3 : X0] : (! [X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3)) => ($true = vAPP(X0,$o,X2,X4))) => ($true = vAPP(X0,$o,X2,X3))) => ! [X5 : X0] : ($true = vAPP(X0,$o,X2,X5))))),
% 92.92/13.71 inference(fool_elimination,[],[f3189])).
% 92.92/13.71 thf(f3189,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) <=> ! [X2 : X0 > $o] : (! [X3 : X0] : (! [X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3) => vAPP(X0,$o,X2,X4)) => vAPP(X0,$o,X2,X3)) => ! [X5 : X0] : vAPP(X0,$o,X2,X5)))),
% 92.92/13.71 inference(rectify,[],[f554])).
% 92.92/13.71 thf(f554,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) <=> ! [X43 : X0 > $o] : (! [X19 : X0] : (! [X50 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X50),X19) => vAPP(X0,$o,X43,X50)) => vAPP(X0,$o,X43,X19)) => ! [X23 : X0] : vAPP(X0,$o,X43,X23)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__EQ__INDUCTION__THM)).
% 92.92/13.71 thf(f42418,plain,(
% 92.92/13.71 spl854_386),
% 92.92/13.71 inference(avatar_split_clause,[],[f10786,f42416])).
% 92.92/13.71 thf(f42416,plain,(
% 92.92/13.71 spl854_386 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_386])])).
% 92.92/13.71 thf(f10786,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP20(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7389])).
% 92.92/13.71 thf(f42414,plain,(
% 92.92/13.71 spl854_385),
% 92.92/13.71 inference(avatar_split_clause,[],[f10768,f42412])).
% 92.92/13.71 thf(f42412,plain,(
% 92.92/13.71 spl854_385 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_385])])).
% 92.92/13.71 thf(f10768,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7365])).
% 92.92/13.71 thf(f7365,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6414])).
% 92.92/13.71 thf(f6414,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) <=> ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f5787,f6413])).
% 92.92/13.71 thf(f6413,plain,(
% 92.92/13.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f5787,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f5786])).
% 92.92/13.71 thf(f5786,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 92.92/13.71 inference(ennf_transformation,[],[f3180])).
% 92.92/13.71 thf(f3180,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => ? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X5)))))),
% 92.92/13.71 inference(fool_elimination,[],[f3179])).
% 92.92/13.71 thf(f3179,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1) <=> ! [X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) => ? [X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X5))))),
% 92.92/13.71 inference(rectify,[],[f453])).
% 92.92/13.71 thf(f453,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X143) <=> ! [X4 : X0,X12 : X0,X84 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X84) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12)) => ? [X159 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X84),X159) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X12),X159))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ediamond__def)).
% 92.92/13.71 thf(f42410,plain,(
% 92.92/13.71 spl854_384),
% 92.92/13.71 inference(avatar_split_clause,[],[f10767,f42408])).
% 92.92/13.71 thf(f42408,plain,(
% 92.92/13.71 spl854_384 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_384])])).
% 92.92/13.71 thf(f10767,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP19(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7365])).
% 92.92/13.71 thf(f42406,plain,(
% 92.92/13.71 spl854_383),
% 92.92/13.71 inference(avatar_split_clause,[],[f10754,f42404])).
% 92.92/13.71 thf(f42404,plain,(
% 92.92/13.71 spl854_383 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_383])])).
% 92.92/13.71 thf(f10754,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7351])).
% 92.92/13.71 thf(f7351,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))))),
% 92.92/13.71 inference(flattening,[],[f7350])).
% 92.92/13.71 thf(f7350,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3174])).
% 92.92/13.71 thf(f3174,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))))),
% 92.92/13.71 inference(fool_elimination,[],[f3173])).
% 92.92/13.71 thf(f3173,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.92/13.71 inference(rectify,[],[f441])).
% 92.92/13.71 thf(f441,axiom,(
% 92.92/13.71 ! [X140 : $tType,X156 : X140 > X140 > $o] : (vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2EWeakOrder(X140),X156) <=> (vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Etransitive(X140),X156) & vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Eantisymmetric(X140),X156) & vAPP(sTfun(X140,sTfun(X140,$o)),$o,c_2Erelation_2Ereflexive(X140),X156)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWeakOrder)).
% 92.92/13.71 thf(f42402,plain,(
% 92.92/13.71 spl854_382),
% 92.92/13.71 inference(avatar_split_clause,[],[f10753,f42400])).
% 92.92/13.71 thf(f42400,plain,(
% 92.92/13.71 spl854_382 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_382])])).
% 92.92/13.71 thf(f10753,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7351])).
% 92.92/13.71 thf(f42398,plain,(
% 92.92/13.71 spl854_381),
% 92.92/13.71 inference(avatar_split_clause,[],[f10752,f42396])).
% 92.92/13.71 thf(f42396,plain,(
% 92.92/13.71 spl854_381 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_381])])).
% 92.92/13.71 thf(f10752,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7351])).
% 92.92/13.71 thf(f42394,plain,(
% 92.92/13.71 spl854_380),
% 92.92/13.71 inference(avatar_split_clause,[],[f10747,f42392])).
% 92.92/13.71 thf(f42392,plain,(
% 92.92/13.71 spl854_380 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_380])])).
% 92.92/13.71 thf(f10747,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7345])).
% 92.92/13.71 thf(f42390,plain,(
% 92.92/13.71 spl854_379),
% 92.92/13.71 inference(avatar_split_clause,[],[f10746,f42388])).
% 92.92/13.71 thf(f42388,plain,(
% 92.92/13.71 spl854_379 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_379])])).
% 92.92/13.71 thf(f10746,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7345])).
% 92.92/13.71 thf(f42362,plain,(
% 92.92/13.71 spl854_378),
% 92.92/13.71 inference(avatar_split_clause,[],[f10744,f42360])).
% 92.92/13.71 thf(f42360,plain,(
% 92.92/13.71 spl854_378 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_378])])).
% 92.92/13.71 thf(f10744,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7343])).
% 92.92/13.71 thf(f42358,plain,(
% 92.92/13.71 spl854_377),
% 92.92/13.71 inference(avatar_split_clause,[],[f10743,f42356])).
% 92.92/13.71 thf(f42356,plain,(
% 92.92/13.71 spl854_377 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_377])])).
% 92.92/13.71 thf(f10743,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7343])).
% 92.92/13.71 thf(f42354,plain,(
% 92.92/13.71 spl854_376),
% 92.92/13.71 inference(avatar_split_clause,[],[f10737,f42352])).
% 92.92/13.71 thf(f42352,plain,(
% 92.92/13.71 spl854_376 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_376])])).
% 92.92/13.71 thf(f10737,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7337])).
% 92.92/13.71 thf(f7337,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1))))),
% 92.92/13.71 inference(flattening,[],[f7336])).
% 92.92/13.71 thf(f7336,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)) | (($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))) & ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f3164])).
% 92.92/13.71 thf(f3164,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)) <=> (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) & ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1))))),
% 92.92/13.71 inference(fool_elimination,[],[f3163])).
% 92.92/13.71 thf(f3163,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)))),
% 92.92/13.71 inference(rectify,[],[f413])).
% 92.92/13.71 thf(f413,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X143) <=> (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X143) & vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X143)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Eequivalence__def)).
% 92.92/13.71 thf(f42350,plain,(
% 92.92/13.71 spl854_375),
% 92.92/13.71 inference(avatar_split_clause,[],[f10736,f42348])).
% 92.92/13.71 thf(f42348,plain,(
% 92.92/13.71 spl854_375 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_375])])).
% 92.92/13.71 thf(f10736,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Esymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7337])).
% 92.92/13.71 thf(f42346,plain,(
% 92.92/13.71 spl854_374),
% 92.92/13.71 inference(avatar_split_clause,[],[f10735,f42344])).
% 92.92/13.71 thf(f42344,plain,(
% 92.92/13.71 spl854_374 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_374])])).
% 92.92/13.71 thf(f10735,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eequivalence(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7337])).
% 92.92/13.71 thf(f42342,plain,(
% 92.92/13.71 spl854_373),
% 92.92/13.71 inference(avatar_split_clause,[],[f10734,f42340])).
% 92.92/13.71 thf(f42340,plain,(
% 92.92/13.71 spl854_373 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_373])])).
% 92.92/13.71 thf(f10734,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7335])).
% 92.92/13.71 thf(f7335,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6412])).
% 92.92/13.71 thf(f6412,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) <=> ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f5785,f6411])).
% 92.92/13.71 thf(f6411,plain,(
% 92.92/13.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f5785,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f5784])).
% 92.92/13.71 thf(f5784,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 92.92/13.71 inference(ennf_transformation,[],[f3162])).
% 92.92/13.71 thf(f3162,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => ? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X5)))))),
% 92.92/13.71 inference(fool_elimination,[],[f3161])).
% 92.92/13.71 thf(f3161,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1) <=> ! [X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) => ? [X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X4),X5) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X1),X3),X5))))),
% 92.92/13.71 inference(rectify,[],[f454])).
% 92.92/13.71 thf(f454,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X143) <=> ! [X4 : X0,X12 : X0,X84 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X84) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12)) => ? [X159 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143),X84),X159) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERC(X0),X143),X12),X159))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Ercdiamond__def)).
% 92.92/13.71 thf(f42338,plain,(
% 92.92/13.71 spl854_372),
% 92.92/13.71 inference(avatar_split_clause,[],[f10733,f42336])).
% 92.92/13.71 thf(f42336,plain,(
% 92.92/13.71 spl854_372 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_372])])).
% 92.92/13.71 thf(f10733,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP18(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7335])).
% 92.92/13.71 thf(f42334,plain,(
% 92.92/13.71 spl854_371),
% 92.92/13.71 inference(avatar_split_clause,[],[f10726,f42332])).
% 92.92/13.71 thf(f42332,plain,(
% 92.92/13.71 spl854_371 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_371])])).
% 92.92/13.71 thf(f10726,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7329])).
% 92.92/13.71 thf(f7329,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f6410])).
% 92.92/13.71 thf(f6410,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) <=> ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f5783,f6409])).
% 92.92/13.71 thf(f6409,plain,(
% 92.92/13.71 ! [X1 : X0 > X0 > $o,X0 : $tType] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f5783,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 92.92/13.71 inference(flattening,[],[f5782])).
% 92.92/13.71 thf(f5782,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : (? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 92.92/13.71 inference(ennf_transformation,[],[f3158])).
% 92.92/13.71 thf(f3158,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)) <=> ! [X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) => ? [X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X5)))))),
% 92.92/13.71 inference(fool_elimination,[],[f3157])).
% 92.92/13.71 thf(f3157,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1) <=> ! [X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) => ? [X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X4),X5) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X1),X3),X5))))),
% 92.92/13.71 inference(rectify,[],[f456])).
% 92.92/13.71 thf(f456,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X143) <=> ! [X4 : X0,X12 : X0,X84 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X84) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X143,X4),X12)) => ? [X159 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143),X84),X159) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2ERTC(X0),X143),X12),X159))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWCR__def)).
% 92.92/13.71 thf(f42330,plain,(
% 92.92/13.71 spl854_370),
% 92.92/13.71 inference(avatar_split_clause,[],[f10725,f42328])).
% 92.92/13.71 thf(f42328,plain,(
% 92.92/13.71 spl854_370 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_370])])).
% 92.92/13.71 thf(f10725,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,sP17(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWCR(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7329])).
% 92.92/13.71 thf(f42326,plain,(
% 92.92/13.71 spl854_369),
% 92.92/13.71 inference(avatar_split_clause,[],[f10718,f42324])).
% 92.92/13.71 thf(f42324,plain,(
% 92.92/13.71 spl854_369 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_369])])).
% 92.92/13.71 thf(f10718,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7323])).
% 92.92/13.71 thf(f42322,plain,(
% 92.92/13.71 spl854_368 | ~spl854_80),
% 92.92/13.71 inference(avatar_split_clause,[],[f32120,f22339,f42320])).
% 92.92/13.71 thf(f42320,plain,(
% 92.92/13.71 spl854_368 <=> ! [X1 : $o] : (($true = vAPP($o,$o,iCOMB,X1)) | ($false = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_368])])).
% 92.92/13.71 thf(f22339,plain,(
% 92.92/13.71 spl854_80 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X2 : X1] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),c_2Ecombin_2EK(X0,X1),X3),X2) = X3)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_80])])).
% 92.92/13.71 thf(f32120,plain,(
% 92.92/13.71 ( ! [X1 : $o] : (($true = vAPP($o,$o,iCOMB,X1)) | ($false = X1)) ) | ~spl854_80),
% 92.92/13.71 inference(forward_demodulation,[],[f17762,f22340])).
% 92.92/13.71 thf(f22340,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : ((vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),c_2Ecombin_2EK(X0,X1),X3),X2) = X3)) ) | ~spl854_80),
% 92.92/13.71 inference(avatar_component_clause,[],[f22339])).
% 92.92/13.71 thf(f17762,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(sTfun($o,$o),sTfun($o,sTfun($o,$o)),c_2Ecombin_2EK(sTfun($o,$o),$o),iCOMB),X0),X1)) | ($false = X1)) )),
% 92.92/13.71 inference(binary_proxy_clausification,[],[f14079])).
% 92.92/13.71 thf(f14079,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(sTfun($o,$o),sTfun($o,sTfun($o,$o)),c_2Ecombin_2EK(sTfun($o,$o),$o),iCOMB),X0),X1) = X1)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9857,f13535])).
% 92.92/13.71 thf(f13535,plain,(
% 92.92/13.71 (c_2EConseqConv_2EASM__MARKER = vAPP(sTfun($o,$o),sTfun($o,sTfun($o,$o)),c_2Ecombin_2EK(sTfun($o,$o),$o),iCOMB))),
% 92.92/13.71 inference(definition_unfolding,[],[f9130,f9976])).
% 92.92/13.71 thf(f9130,plain,(
% 92.92/13.71 (c_2EConseqConv_2EASM__MARKER = vAPP(sTfun($o,$o),sTfun($o,sTfun($o,$o)),kCOMB,iCOMB))),
% 92.92/13.71 inference(cnf_transformation,[],[f2006])).
% 92.92/13.71 thf(f2006,plain,(
% 92.92/13.71 (c_2EConseqConv_2EASM__MARKER = vAPP(sTfun($o,$o),sTfun($o,sTfun($o,$o)),kCOMB,iCOMB))),
% 92.92/13.71 inference(fool_elimination,[],[f2005])).
% 92.92/13.71 thf(f2005,plain,(
% 92.92/13.71 (c_2EConseqConv_2EASM__MARKER = (^[X0 : $o, X1 : $o] : (X1)))),
% 92.92/13.71 inference(rectify,[],[f206])).
% 92.92/13.71 thf(f206,axiom,(
% 92.92/13.71 (c_2EConseqConv_2EASM__MARKER = (^[X70 : $o, X4 : $o] : (X4)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EASM__MARKER__DEF)).
% 92.92/13.71 thf(f9857,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : ((vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2EConseqConv_2EASM__MARKER,X0),X1) = X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4960])).
% 92.92/13.71 thf(f4960,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2EConseqConv_2EASM__MARKER,X0),X1) = X1)),
% 92.92/13.71 inference(rectify,[],[f246])).
% 92.92/13.71 thf(f246,axiom,(
% 92.92/13.71 ! [X70 : $o,X4 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2EConseqConv_2EASM__MARKER,X70),X4) = X4)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EASM__MARKER__THM)).
% 92.92/13.71 thf(f42318,plain,(
% 92.92/13.71 spl854_367),
% 92.92/13.71 inference(avatar_split_clause,[],[f10713,f42316])).
% 92.92/13.71 thf(f42316,plain,(
% 92.92/13.71 spl854_367 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_367])])).
% 92.92/13.71 thf(f10713,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakLinearOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7321])).
% 92.92/13.71 thf(f42314,plain,(
% 92.92/13.71 spl854_366),
% 92.92/13.71 inference(avatar_split_clause,[],[f10711,f42312])).
% 92.92/13.71 thf(f42312,plain,(
% 92.92/13.71 spl854_366 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_366])])).
% 92.92/13.71 thf(f10711,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etransitive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7316])).
% 92.92/13.71 thf(f42310,plain,(
% 92.92/13.71 spl854_365),
% 92.92/13.71 inference(avatar_split_clause,[],[f10710,f42308])).
% 92.92/13.71 thf(f42308,plain,(
% 92.92/13.71 spl854_365 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_365])])).
% 92.92/13.71 thf(f10710,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ereflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EPreOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7316])).
% 92.92/13.71 thf(f42306,plain,(
% 92.92/13.71 spl854_364),
% 92.92/13.71 inference(avatar_split_clause,[],[f10708,f42304])).
% 92.92/13.71 thf(f42304,plain,(
% 92.92/13.71 spl854_364 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_364])])).
% 92.92/13.71 thf(f10708,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7314])).
% 92.92/13.71 thf(f42302,plain,(
% 92.92/13.71 spl854_363),
% 92.92/13.71 inference(avatar_split_clause,[],[f10707,f42300])).
% 92.92/13.71 thf(f42300,plain,(
% 92.92/13.71 spl854_363 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_363])])).
% 92.92/13.71 thf(f10707,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ELinearOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7314])).
% 92.92/13.71 thf(f42298,plain,(
% 92.92/13.71 spl854_362),
% 92.92/13.71 inference(avatar_split_clause,[],[f10705,f42296])).
% 92.92/13.71 thf(f42296,plain,(
% 92.92/13.71 spl854_362 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_362])])).
% 92.92/13.71 thf(f10705,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Etrichotomous(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7312])).
% 92.92/13.71 thf(f42294,plain,(
% 92.92/13.71 spl854_361),
% 92.92/13.71 inference(avatar_split_clause,[],[f10704,f42292])).
% 92.92/13.71 thf(f42292,plain,(
% 92.92/13.71 spl854_361 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_361])])).
% 92.92/13.71 thf(f10704,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongLinearOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7312])).
% 92.92/13.71 thf(f42290,plain,(
% 92.92/13.71 spl854_360),
% 92.92/13.71 inference(avatar_split_clause,[],[f10471,f42288])).
% 92.92/13.71 thf(f42288,plain,(
% 92.92/13.71 spl854_360 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) != vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_360])])).
% 92.92/13.71 thf(f10471,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) != vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7000])).
% 92.92/13.71 thf(f7000,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) | (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK254,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK254,X1),X0)),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0))) & ((! [X3 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0))) | (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) != vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1))))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK254])],[f6998,f6999])).
% 92.92/13.71 thf(f6999,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) => (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK254,X1),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sK254,X1),X0)),X0))))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f6998,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0))) & ((! [X3 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0))) | (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) != vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1))))),
% 92.92/13.71 inference(rectify,[],[f6997])).
% 92.92/13.71 thf(f6997,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0))) & ((! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0))) | (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) != vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1))))),
% 92.92/13.71 inference(flattening,[],[f6996])).
% 92.92/13.71 thf(f6996,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : (((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) | (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X1,X0)))) & ((! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0))) | (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) != vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5770])).
% 92.92/13.71 thf(f5770,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) <=> (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0))))),
% 92.92/13.71 inference(ennf_transformation,[],[f2982])).
% 92.92/13.71 thf(f2982,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) <=> (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0)) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X1,X0))))),
% 92.92/13.71 inference(fool_elimination,[],[f2981])).
% 92.92/13.71 thf(f2981,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum > $o] : ((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X1)) <=> (! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X0) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X1,X2))) & vAPP(tyop_2Enum_2Enum,$o,X1,X0)))),
% 92.92/13.71 inference(rectify,[],[f1434])).
% 92.92/13.71 thf(f1434,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X43 : tyop_2Enum_2Enum > $o] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,X43) = vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X136)) <=> (! [X104 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X104),X136) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X43,X104))) & vAPP(tyop_2Enum_2Enum,$o,X43,X136)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2EOLEAST__EQ__SOME)).
% 92.92/13.71 thf(f42286,plain,(
% 92.92/13.71 spl854_359),
% 92.92/13.71 inference(avatar_split_clause,[],[f10314,f42284])).
% 92.92/13.71 thf(f42284,plain,(
% 92.92/13.71 spl854_359 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_359])])).
% 92.92/13.71 thf(f10314,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5688])).
% 92.92/13.71 thf(f5688,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2814])).
% 92.92/13.71 thf(f2814,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f2813])).
% 92.92/13.71 thf(f2813,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f562])).
% 92.92/13.71 thf(f562,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eantisymmetric(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__antisymmetric)).
% 92.92/13.71 thf(f42282,plain,(
% 92.92/13.71 spl854_358),
% 92.92/13.71 inference(avatar_split_clause,[],[f10313,f42280])).
% 92.92/13.71 thf(f42280,plain,(
% 92.92/13.71 spl854_358 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_358])])).
% 92.92/13.71 thf(f10313,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5687])).
% 92.92/13.71 thf(f5687,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2812])).
% 92.92/13.71 thf(f2812,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f2811])).
% 92.92/13.71 thf(f2811,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f556])).
% 92.92/13.71 thf(f556,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Eirreflexive(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__irreflexive)).
% 92.92/13.71 thf(f42278,plain,(
% 92.92/13.71 spl854_357 | ~spl854_80),
% 92.92/13.71 inference(avatar_split_clause,[],[f31602,f22339,f42276])).
% 92.92/13.71 thf(f42276,plain,(
% 92.92/13.71 spl854_357 <=> ! [X1 : $o] : (($false = vAPP($o,$o,iCOMB,X1)) | ($true = X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_357])])).
% 92.92/13.71 thf(f31602,plain,(
% 92.92/13.71 ( ! [X1 : $o] : (($false = vAPP($o,$o,iCOMB,X1)) | ($true = X1)) ) | ~spl854_80),
% 92.92/13.71 inference(forward_demodulation,[],[f17763,f22340])).
% 92.92/13.71 thf(f17763,plain,(
% 92.92/13.71 ( ! [X0 : $o,X1 : $o] : (($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(sTfun($o,$o),sTfun($o,sTfun($o,$o)),c_2Ecombin_2EK(sTfun($o,$o),$o),iCOMB),X0),X1)) | ($true = X1)) )),
% 92.92/13.71 inference(binary_proxy_clausification,[],[f14079])).
% 92.92/13.71 thf(f42274,plain,(
% 92.92/13.71 spl854_356),
% 92.92/13.71 inference(avatar_split_clause,[],[f10301,f42272])).
% 92.92/13.71 thf(f42272,plain,(
% 92.92/13.71 spl854_356 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_356])])).
% 92.92/13.71 thf(f10301,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5676])).
% 92.92/13.71 thf(f5676,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2790])).
% 92.92/13.71 thf(f2790,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f2789])).
% 92.92/13.71 thf(f2789,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f614])).
% 92.92/13.71 thf(f614,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWeakOrder(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWeakOrd__Ord)).
% 92.92/13.71 thf(f42270,plain,(
% 92.92/13.71 spl854_355),
% 92.92/13.71 inference(avatar_split_clause,[],[f10296,f42268])).
% 92.92/13.71 thf(f42268,plain,(
% 92.92/13.71 spl854_355 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_355])])).
% 92.92/13.71 thf(f10296,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5673])).
% 92.92/13.71 thf(f5673,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2784])).
% 92.92/13.71 thf(f2784,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1)))),
% 92.92/13.71 inference(fool_elimination,[],[f2783])).
% 92.92/13.71 thf(f2783,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X1))),
% 92.92/13.71 inference(rectify,[],[f613])).
% 92.92/13.71 thf(f613,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EStrongOrder(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EOrder(X0),X143))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EStrongOrd__Ord)).
% 92.92/13.71 thf(f42266,plain,(
% 92.92/13.71 spl854_354),
% 92.92/13.71 inference(avatar_split_clause,[],[f10292,f42264])).
% 92.92/13.71 thf(f42264,plain,(
% 92.92/13.71 spl854_354 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0] : ((X2 = X3) | (vAPP(X0,X0,X1,X2) != vAPP(X0,X0,X1,X3)) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_354])])).
% 92.92/13.71 thf(f10292,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0] : ((X2 = X3) | (vAPP(X0,X0,X1,X2) != vAPP(X0,X0,X1,X3)) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6913])).
% 92.92/13.71 thf(f6913,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (! [X2 : X0,X3 : X0] : (((vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,X3)) | (X2 != X3)) & ((X2 = X3) | (vAPP(X0,X0,X1,X2) != vAPP(X0,X0,X1,X3)))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)))),
% 92.92/13.71 inference(nnf_transformation,[],[f5670])).
% 92.92/13.71 thf(f5670,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (! [X2 : X0,X3 : X0] : ((vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,X3)) <=> (X2 = X3)) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2778])).
% 92.92/13.71 thf(f2778,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) => ! [X2 : X0,X3 : X0] : ((vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,X3)) <=> (X2 = X3)))),
% 92.92/13.71 inference(fool_elimination,[],[f2777])).
% 92.92/13.71 thf(f2777,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0] : (vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1) => ! [X2 : X0,X3 : X0] : ((vAPP(X0,X0,X1,X2) = vAPP(X0,X0,X1,X3)) <=> (X2 = X3)))),
% 92.92/13.71 inference(rectify,[],[f596])).
% 92.92/13.71 thf(f596,axiom,(
% 92.92/13.71 ! [X139 : $tType,X3 : X139 > X139] : (vAPP(sTfun(X139,X139),$o,c_2Erelation_2EINVOL(X139),X3) => ! [X73 : X139,X79 : X139] : ((vAPP(X139,X139,X3,X73) = vAPP(X139,X139,X3,X79)) <=> (X73 = X79)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EINVOL__ONE__ONE)).
% 92.92/13.71 thf(f42262,plain,(
% 92.92/13.71 spl854_353),
% 92.92/13.71 inference(avatar_split_clause,[],[f10155,f42260])).
% 92.92/13.71 thf(f42260,plain,(
% 92.92/13.71 spl854_353 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X1] : ((X2 = X3) | (vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3) != vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_353])])).
% 92.92/13.71 thf(f10155,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1] : ((X2 = X3) | (vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3) != vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6849])).
% 92.92/13.71 thf(f6849,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1,X3 : X1] : (((vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3) = vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)) | (X2 != X3)) & ((X2 = X3) | (vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3) != vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)))) & ! [X4 : X0,X5 : X0] : (((vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X4) = vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)) | (X4 != X5)) & ((X4 = X5) | (vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X4) != vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))))),
% 92.92/13.71 inference(nnf_transformation,[],[f5096])).
% 92.92/13.71 thf(f5096,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1,X3 : X1] : ((vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3) = vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)) <=> (X2 = X3)) & ! [X4 : X0,X5 : X0] : ((vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X4) = vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)) <=> (X4 = X5)))),
% 92.92/13.71 inference(rectify,[],[f673])).
% 92.92/13.71 thf(f673,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType] : (! [X12 : X5,X15 : X5] : ((vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X15) = vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X12)) <=> (X12 = X15)) & ! [X70 : X0,X4 : X0] : ((vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X4) = vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X70)) <=> (X4 = X70)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EINR__INL__11)).
% 92.92/13.71 thf(f42258,plain,(
% 92.92/13.71 spl854_352),
% 92.92/13.71 inference(avatar_split_clause,[],[f10153,f42256])).
% 92.92/13.71 thf(f42256,plain,(
% 92.92/13.71 spl854_352 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X5 : X0] : ((X4 = X5) | (vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X4) != vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_352])])).
% 92.92/13.71 thf(f10153,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X4 : X0,X5 : X0] : ((X4 = X5) | (vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X4) != vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X5))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6849])).
% 92.92/13.71 thf(f42254,plain,(
% 92.92/13.71 spl854_351),
% 92.92/13.71 inference(avatar_split_clause,[],[f10078,f42252])).
% 92.92/13.71 thf(f42252,plain,(
% 92.92/13.71 spl854_351 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_351])])).
% 92.92/13.71 thf(f10078,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5518])).
% 92.92/13.71 thf(f5518,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1))))),
% 92.92/13.71 inference(ennf_transformation,[],[f2582])).
% 92.92/13.71 thf(f2582,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1))) & (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)) => ($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1))))),
% 92.92/13.71 inference(fool_elimination,[],[f2581])).
% 92.92/13.71 thf(f2581,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) & (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)))),
% 92.92/13.71 inference(rectify,[],[f650])).
% 92.92/13.71 thf(f650,axiom,(
% 92.92/13.71 ! [X0 : $tType,X143 : X0 > X0 > $o] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ediamond(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X143)) & (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X143) => vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X143)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Eestablish__CR)).
% 92.92/13.71 thf(f42250,plain,(
% 92.92/13.71 spl854_350),
% 92.92/13.71 inference(avatar_split_clause,[],[f10077,f42248])).
% 92.92/13.71 thf(f42248,plain,(
% 92.92/13.71 spl854_350 <=> ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_350])])).
% 92.92/13.71 thf(f10077,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X1 : X0 > X0 > $o] : (($true = vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2ECR(X0),X1)) | ($true != vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2Ercdiamond(X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5518])).
% 92.92/13.71 thf(f42246,plain,(
% 92.92/13.71 spl854_349),
% 92.92/13.71 inference(avatar_split_clause,[],[f9828,f42244])).
% 92.92/13.71 thf(f42244,plain,(
% 92.92/13.71 spl854_349 <=> ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EINVOL(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2Einv(X0,X0)) = $true)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_349])])).
% 92.92/13.71 thf(f9828,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EINVOL(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2Einv(X0,X0)) = $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2496])).
% 92.92/13.71 thf(f2496,plain,(
% 92.92/13.71 ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EINVOL(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2Einv(X0,X0)) = $true)),
% 92.92/13.71 inference(fool_elimination,[],[f2495])).
% 92.92/13.71 thf(f2495,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EINVOL(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2Einv(X0,X0))),
% 92.92/13.71 inference(rectify,[],[f600])).
% 92.92/13.71 thf(f600,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EINVOL(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2Einv(X0,X0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Einv__INVOL)).
% 92.92/13.71 thf(f42242,plain,(
% 92.92/13.71 spl854_348),
% 92.92/13.71 inference(avatar_split_clause,[],[f9711,f42240])).
% 92.92/13.71 thf(f42240,plain,(
% 92.92/13.71 spl854_348 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_348])])).
% 92.92/13.71 thf(f9711,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK178,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6777])).
% 92.92/13.71 thf(f42238,plain,(
% 92.92/13.71 spl854_347),
% 92.92/13.71 inference(avatar_split_clause,[],[f9700,f42236])).
% 92.92/13.71 thf(f42236,plain,(
% 92.92/13.71 spl854_347 <=> ! [X0 : tyop_2Enum_2Enum > $o,X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_347])])).
% 92.92/13.71 thf(f9700,plain,(
% 92.92/13.71 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK173,X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6760])).
% 92.92/13.71 thf(f42234,plain,(
% 92.92/13.71 spl854_346 | ~spl854_102 | ~spl854_196),
% 92.92/13.71 inference(avatar_split_clause,[],[f23920,f23496,f22591,f42232])).
% 92.92/13.71 thf(f42232,plain,(
% 92.92/13.71 spl854_346 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_346])])).
% 92.92/13.71 thf(f22591,plain,(
% 92.92/13.71 spl854_102 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X1)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_102])])).
% 92.92/13.71 thf(f23920,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0))) ) | (~spl854_102 | ~spl854_196)),
% 92.92/13.71 inference(superposition,[],[f22592,f23497])).
% 92.92/13.71 thf(f22592,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X1)) ) | ~spl854_102),
% 92.92/13.71 inference(avatar_component_clause,[],[f22591])).
% 92.92/13.71 thf(f42230,plain,(
% 92.92/13.71 spl854_345),
% 92.92/13.71 inference(avatar_split_clause,[],[f9489,f42228])).
% 92.92/13.71 thf(f42228,plain,(
% 92.92/13.71 spl854_345 <=> ! [X0 : $tType,X2 : tyop_2Eind__type_2Erecspace(X0)] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2)) = X2)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_345])])).
% 92.92/13.71 thf(f9489,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : tyop_2Eind__type_2Erecspace(X0)] : ((vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2)) = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6621])).
% 92.92/13.71 thf(f6621,plain,(
% 92.92/13.71 ! [X0 : $tType] : (! [X1 : tyop_2Enum_2Enum > X0 > $o] : ((($true = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),$o,c_2Eind__type_2EZRECSPACE(X0),X1)) | (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),X1)) != X1)) & ((vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),X1)) = X1) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),$o,c_2Eind__type_2EZRECSPACE(X0),X1)))) & ! [X2 : tyop_2Eind__type_2Erecspace(X0)] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2)) = X2))),
% 92.92/13.71 inference(nnf_transformation,[],[f2128])).
% 92.92/13.71 thf(f2128,plain,(
% 92.92/13.71 ! [X0 : $tType] : (! [X1 : tyop_2Enum_2Enum > X0 > $o] : (($true = vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),$o,c_2Eind__type_2EZRECSPACE(X0),X1)) <=> (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),X1)) = X1)) & ! [X2 : tyop_2Eind__type_2Erecspace(X0)] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2)) = X2))),
% 92.92/13.71 inference(fool_elimination,[],[f2127])).
% 92.92/13.71 thf(f2127,plain,(
% 92.92/13.71 ! [X0 : $tType] : (! [X1 : tyop_2Enum_2Enum > X0 > $o] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),$o,c_2Eind__type_2EZRECSPACE(X0),X1) <=> (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),X1)) = X1)) & ! [X2 : tyop_2Eind__type_2Erecspace(X0)] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X2)) = X2))),
% 92.92/13.71 inference(rectify,[],[f1521])).
% 92.92/13.71 thf(f1521,axiom,(
% 92.92/13.71 ! [X0 : $tType] : (! [X112 : tyop_2Enum_2Enum > X0 > $o] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),$o,c_2Eind__type_2EZRECSPACE(X0),X112) <=> (vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),X112)) = X112)) & ! [X72 : tyop_2Eind__type_2Erecspace(X0)] : (vAPP(sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),tyop_2Eind__type_2Erecspace(X0),c_2Eind__type_2Emk__rec(X0),vAPP(tyop_2Eind__type_2Erecspace(X0),sTfun(tyop_2Enum_2Enum,sTfun(X0,$o)),c_2Eind__type_2Edest__rec(X0),X72)) = X72))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2Erecspace__repfns)).
% 92.92/13.71 thf(f42226,plain,(
% 92.92/13.71 spl854_344),
% 92.92/13.71 inference(avatar_split_clause,[],[f9410,f42224])).
% 92.92/13.71 thf(f42224,plain,(
% 92.92/13.71 spl854_344 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_344])])).
% 92.92/13.71 thf(f9410,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME(tyop_2Enum_2Enum),X0) = vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2112])).
% 92.92/13.71 thf(f42074,plain,(
% 92.92/13.71 spl854_343 | ~spl854_103 | ~spl854_196),
% 92.92/13.71 inference(avatar_split_clause,[],[f23919,f23496,f22595,f42072])).
% 92.92/13.71 thf(f42072,plain,(
% 92.92/13.71 spl854_343 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_343])])).
% 92.92/13.71 thf(f41707,plain,(
% 92.92/13.71 spl854_342 | ~spl854_149),
% 92.92/13.71 inference(avatar_split_clause,[],[f30159,f22902,f41705])).
% 92.92/13.71 thf(f41705,plain,(
% 92.92/13.71 spl854_342 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_342])])).
% 92.92/13.71 thf(f22902,plain,(
% 92.92/13.71 spl854_149 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_149])])).
% 92.92/13.71 thf(f30159,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)))) ) | ~spl854_149),
% 92.92/13.71 inference(forward_demodulation,[],[f9151,f22903])).
% 92.92/13.71 thf(f22903,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) ) | ~spl854_149),
% 92.92/13.71 inference(avatar_component_clause,[],[f22902])).
% 92.92/13.71 thf(f9151,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4836])).
% 92.92/13.71 thf(f41703,plain,(
% 92.92/13.71 spl854_341),
% 92.92/13.71 inference(avatar_split_clause,[],[f16196,f41701])).
% 92.92/13.71 thf(f41701,plain,(
% 92.92/13.71 spl854_341 <=> ! [X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2)),X1) = X2)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_341])])).
% 92.92/13.71 thf(f16196,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2)),X1) = X2)) )),
% 92.92/13.71 inference(equality_resolution,[],[f11758])).
% 92.92/13.71 thf(f11758,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X2) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) != X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7936])).
% 92.92/13.71 thf(f7936,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X2) | ((($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X2),c_2Enum_2E0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) != X0))) & ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X2),c_2Enum_2E0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) = X0) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X2)))),
% 92.92/13.71 inference(flattening,[],[f7935])).
% 92.92/13.71 thf(f7935,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X2) | ((($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X2),c_2Enum_2E0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) != X0))) & (((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X2),c_2Enum_2E0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) = X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) != X2)))),
% 92.92/13.71 inference(nnf_transformation,[],[f3934])).
% 92.92/13.71 thf(f3934,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X2) <=> ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X2),c_2Enum_2E0)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) = X0)))),
% 92.92/13.71 inference(fool_elimination,[],[f3933])).
% 92.92/13.71 thf(f3933,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1) = X2) <=> ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X2),c_2Enum_2E0) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X2) = X0)))),
% 92.92/13.71 inference(rectify,[],[f1134])).
% 92.92/13.71 thf(f1134,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum,X108 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X134),X137) = X108) <=> ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X108),c_2Enum_2E0) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X134),X137)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X137),X108) = X134)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__RIGHT__EQ)).
% 92.92/13.71 thf(f41699,plain,(
% 92.92/13.71 spl854_340),
% 92.92/13.71 inference(avatar_split_clause,[],[f16042,f41697])).
% 92.92/13.71 thf(f41697,plain,(
% 92.92/13.71 spl854_340 <=> ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_340])])).
% 92.92/13.71 thf(f16042,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),X0)))) )),
% 92.92/13.71 inference(equality_resolution,[],[f14757])).
% 92.92/13.71 thf(f14757,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X2),X0) != X1)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f11044,f9121])).
% 92.92/13.71 thf(f11044,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X1)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X2),X0) != X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f7574])).
% 92.92/13.71 thf(f41695,plain,(
% 92.92/13.71 spl854_339),
% 92.92/13.71 inference(avatar_split_clause,[],[f14973,f41693])).
% 92.92/13.71 thf(f41693,plain,(
% 92.92/13.71 spl854_339 <=> ! [X2 : tyop_2Enum_2Enum > tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_339])])).
% 92.92/13.71 thf(f14973,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum > tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X2),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f11344,f9122,f9122])).
% 92.92/13.71 thf(f11344,plain,(
% 92.92/13.71 ( ! [X2 : tyop_2Enum_2Enum > tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X2),c_2Enum_2E0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5213])).
% 92.92/13.71 thf(f5213,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum > tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X2,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X2),X0))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X2),c_2Enum_2E0)))),
% 92.92/13.71 inference(rectify,[],[f1689])).
% 92.92/13.71 thf(f1689,axiom,(
% 92.92/13.71 ! [X6 : tyop_2Enum_2Enum,X462 : tyop_2Enum_2Enum,X114 : tyop_2Enum_2Enum > tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X114),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X462),X6)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X114,X462)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X114),X6))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap,X114),c_2Enum_2E0)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enmap__thm)).
% 92.92/13.71 thf(f41691,plain,(
% 92.92/13.71 spl854_338),
% 92.92/13.71 inference(avatar_split_clause,[],[f14086,f41689])).
% 92.92/13.71 thf(f41689,plain,(
% 92.92/13.71 spl854_338 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_338])])).
% 92.92/13.71 thf(f14086,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X1),X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9874,f9121,f9121])).
% 92.92/13.71 thf(f9874,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4977])).
% 92.92/13.71 thf(f4977,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X1))),
% 92.92/13.71 inference(rectify,[],[f997])).
% 92.92/13.71 thf(f997,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X137),X134))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__SYM)).
% 92.92/13.71 thf(f41686,plain,(
% 92.92/13.71 spl854_337),
% 92.92/13.71 inference(avatar_split_clause,[],[f13569,f41683])).
% 92.92/13.71 thf(f41683,plain,(
% 92.92/13.71 spl854_337 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_337])])).
% 92.92/13.71 thf(f41681,plain,(
% 92.92/13.71 spl854_336),
% 92.92/13.71 inference(avatar_split_clause,[],[f12391,f41679])).
% 92.92/13.71 thf(f41679,plain,(
% 92.92/13.71 spl854_336 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1] : (vAPP(sTfun(X1,X0),X0,vAPP(X1,sTfun(sTfun(X1,X0),X0),c_2Ecombin_2E_3A_3E(X0,X1),X2),X3) = vAPP(X1,X0,X3,X2))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_336])])).
% 92.92/13.71 thf(f12391,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X1 > X0] : ((vAPP(sTfun(X1,X0),X0,vAPP(X1,sTfun(sTfun(X1,X0),X0),c_2Ecombin_2E_3A_3E(X0,X1),X2),X3) = vAPP(X1,X0,X3,X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5263])).
% 92.92/13.71 thf(f5263,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X1 > X0] : (vAPP(sTfun(X1,X0),X0,vAPP(X1,sTfun(sTfun(X1,X0),X0),c_2Ecombin_2E_3A_3E(X0,X1),X2),X3) = vAPP(X1,X0,X3,X2))),
% 92.92/13.71 inference(rectify,[],[f320])).
% 92.92/13.71 thf(f320,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X8 : X5,X25 : X5 > X0] : (vAPP(sTfun(X5,X0),X0,vAPP(X5,sTfun(sTfun(X5,X0),X0),c_2Ecombin_2E_3A_3E(X0,X5),X8),X25) = vAPP(X5,X0,X25,X8))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EAPP__DEF)).
% 92.92/13.71 thf(f41677,plain,(
% 92.92/13.71 spl854_335),
% 92.92/13.71 inference(avatar_split_clause,[],[f10170,f41675])).
% 92.92/13.71 thf(f41675,plain,(
% 92.92/13.71 spl854_335 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_335])])).
% 92.92/13.71 thf(f10170,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5530])).
% 92.92/13.71 thf(f5530,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X0)))),
% 92.92/13.71 inference(flattening,[],[f5529])).
% 92.92/13.71 thf(f5529,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) | (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X0)))),
% 92.92/13.71 inference(ennf_transformation,[],[f2618])).
% 92.92/13.71 thf(f2618,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0))) => ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X0)))),
% 92.92/13.71 inference(fool_elimination,[],[f2617])).
% 92.92/13.71 thf(f2617,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X1) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),X0)) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1))) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X1) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X0))),
% 92.92/13.71 inference(rectify,[],[f1571])).
% 92.92/13.71 thf(f1571,axiom,(
% 92.92/13.71 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (! [X323 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X323),X49) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X323),X72)) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X323),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49))) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49)),X49) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49)),X72))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__IS__GREATEST__COMMON__DIVISOR)).
% 92.92/13.71 thf(f41673,plain,(
% 92.92/13.71 spl854_334),
% 92.92/13.71 inference(avatar_split_clause,[],[f10169,f41671])).
% 92.92/13.71 thf(f41671,plain,(
% 92.92/13.71 spl854_334 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_334])])).
% 92.92/13.71 thf(f10169,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1)),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5530])).
% 92.92/13.71 thf(f41669,plain,(
% 92.92/13.71 spl854_333),
% 92.92/13.71 inference(avatar_split_clause,[],[f10167,f41667])).
% 92.92/13.71 thf(f41667,plain,(
% 92.92/13.71 spl854_333 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_333])])).
% 92.92/13.71 thf(f10167,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5528])).
% 92.92/13.71 thf(f5528,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0))))),
% 92.92/13.71 inference(flattening,[],[f5527])).
% 92.92/13.71 thf(f5527,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)),X2)) | (($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X2)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0))))),
% 92.92/13.71 inference(ennf_transformation,[],[f2616])).
% 92.92/13.71 thf(f2616,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X2))) => ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0))))),
% 92.92/13.71 inference(fool_elimination,[],[f2615])).
% 92.92/13.71 thf(f2615,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X2) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X2)) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)),X2)) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)))),
% 92.92/13.71 inference(rectify,[],[f1589])).
% 92.92/13.71 thf(f1589,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (! [X108 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X136),X108) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X27),X108)) => vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X27),X136)),X108)) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X27),X136)) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X27),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X27),X136)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__IS__LEAST__COMMON__MULTIPLE)).
% 92.92/13.71 thf(f41665,plain,(
% 92.92/13.71 spl854_332),
% 92.92/13.71 inference(avatar_split_clause,[],[f10166,f41663])).
% 92.92/13.71 thf(f41663,plain,(
% 92.92/13.71 spl854_332 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_332])])).
% 92.92/13.71 thf(f10166,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5528])).
% 92.92/13.71 thf(f41661,plain,(
% 92.92/13.71 spl854_331),
% 92.92/13.71 inference(avatar_split_clause,[],[f9878,f41659])).
% 92.92/13.71 thf(f41659,plain,(
% 92.92/13.71 spl854_331 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)),X1) = X0)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_331])])).
% 92.92/13.71 thf(f9878,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)),X1) = X0)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4981])).
% 92.92/13.71 thf(f4981,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1)),X1) = X0)),
% 92.92/13.71 inference(rectify,[],[f1056])).
% 92.92/13.71 thf(f1056,axiom,(
% 92.92/13.71 ! [X72 : tyop_2Enum_2Enum,X279 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X72),X279)),X279) = X72)),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__SUB)).
% 92.92/13.71 thf(f41657,plain,(
% 92.92/13.71 spl854_330),
% 92.92/13.71 inference(avatar_split_clause,[],[f9876,f41655])).
% 92.92/13.71 thf(f41655,plain,(
% 92.92/13.71 spl854_330 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_330])])).
% 92.92/13.71 thf(f9876,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4979])).
% 92.92/13.71 thf(f4979,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X0))),
% 92.92/13.71 inference(rectify,[],[f948])).
% 92.92/13.71 thf(f948,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X137),X134))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__SYM)).
% 92.92/13.71 thf(f41653,plain,(
% 92.92/13.71 spl854_329),
% 92.92/13.71 inference(avatar_split_clause,[],[f9873,f41651])).
% 92.92/13.71 thf(f41651,plain,(
% 92.92/13.71 spl854_329 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X1),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_329])])).
% 92.92/13.71 thf(f9873,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4976])).
% 92.92/13.71 thf(f4976,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X1),X0))),
% 92.92/13.71 inference(rectify,[],[f1573])).
% 92.92/13.71 thf(f1573,axiom,(
% 92.92/13.71 ! [X72 : tyop_2Enum_2Enum,X49 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X49) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X49),X72))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__SYM)).
% 92.92/13.71 thf(f41623,plain,(
% 92.92/13.71 spl854_328),
% 92.92/13.71 inference(avatar_split_clause,[],[f9871,f41621])).
% 92.92/13.71 thf(f41621,plain,(
% 92.92/13.71 spl854_328 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X1),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_328])])).
% 92.92/13.71 thf(f9871,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4974])).
% 92.92/13.71 thf(f4974,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X1),X0))),
% 92.92/13.71 inference(rectify,[],[f1251])).
% 92.92/13.71 thf(f1251,axiom,(
% 92.92/13.71 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X136),X27) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X27),X136))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__COMM)).
% 92.92/13.71 thf(f41619,plain,(
% 92.92/13.71 spl854_327),
% 92.92/13.71 inference(avatar_split_clause,[],[f9870,f41617])).
% 92.92/13.71 thf(f41617,plain,(
% 92.92/13.71 spl854_327 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_327])])).
% 92.92/13.71 thf(f9870,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4973])).
% 92.92/13.71 thf(f4973,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X1),X0))),
% 92.92/13.71 inference(rectify,[],[f1221])).
% 92.92/13.71 thf(f1221,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X137),X134))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMIN__COMM)).
% 92.92/13.71 thf(f41615,plain,(
% 92.92/13.71 spl854_326),
% 92.92/13.71 inference(avatar_split_clause,[],[f9869,f41613])).
% 92.92/13.71 thf(f41613,plain,(
% 92.92/13.71 spl854_326 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_326])])).
% 92.92/13.71 thf(f9869,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4972])).
% 92.92/13.71 thf(f4972,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X1),X0))),
% 92.92/13.71 inference(rectify,[],[f1220])).
% 92.92/13.71 thf(f1220,axiom,(
% 92.92/13.71 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X134),X137) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X137),X134))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMAX__COMM)).
% 92.92/13.71 thf(f41611,plain,(
% 92.92/13.71 spl854_325),
% 92.92/13.71 inference(avatar_split_clause,[],[f9868,f41609])).
% 92.92/13.71 thf(f41609,plain,(
% 92.92/13.71 spl854_325 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),X1))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_325])])).
% 92.92/13.71 thf(f9868,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4971])).
% 92.92/13.71 thf(f4971,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X1),X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),X1))),
% 92.92/13.71 inference(rectify,[],[f1592])).
% 92.92/13.71 thf(f1592,axiom,(
% 92.92/13.71 ! [X35 : tyop_2Enum_2Enum,X73 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X73),X35) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X35),X73))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM)).
% 92.92/13.71 thf(f41607,plain,(
% 92.92/13.71 spl854_324),
% 92.92/13.71 inference(avatar_split_clause,[],[f9847,f41605])).
% 92.92/13.71 thf(f9847,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : (($true = vAPP(sTfun(X0,X0),$o,vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),$o),c_2Eind__type_2EISO(X0,X0),iCOMB),iCOMB))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2534])).
% 92.92/13.71 thf(f2534,plain,(
% 92.92/13.71 ! [X0 : $tType] : ($true = vAPP(sTfun(X0,X0),$o,vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),$o),c_2Eind__type_2EISO(X0,X0),iCOMB),iCOMB))),
% 92.92/13.71 inference(fool_elimination,[],[f2533])).
% 92.92/13.71 thf(f2533,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(X0,X0),$o,vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),$o),c_2Eind__type_2EISO(X0,X0),(^[X1 : X0] : (X1))),(^[X2 : X0] : (X2)))),
% 92.92/13.71 inference(rectify,[],[f1547])).
% 92.92/13.71 thf(f1547,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(X0,X0),$o,vAPP(sTfun(X0,X0),sTfun(sTfun(X0,X0),$o),c_2Eind__type_2EISO(X0,X0),(^[X8 : X0] : (X8))),(^[X4 : X0] : (X4)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EISO__REFL)).
% 92.92/13.71 thf(f41603,plain,(
% 92.92/13.71 spl854_323),
% 92.92/13.71 inference(avatar_split_clause,[],[f9827,f41601])).
% 92.92/13.71 thf(f41601,plain,(
% 92.92/13.71 spl854_323 <=> ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ETC(X0)) = $true)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_323])])).
% 92.92/13.71 thf(f9827,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ETC(X0)) = $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2494])).
% 92.92/13.71 thf(f2494,plain,(
% 92.92/13.71 ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ETC(X0)) = $true)),
% 92.92/13.71 inference(fool_elimination,[],[f2493])).
% 92.92/13.71 thf(f2493,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ETC(X0))),
% 92.92/13.71 inference(rectify,[],[f629])).
% 92.92/13.71 thf(f629,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ETC(X0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM__TC)).
% 92.92/13.71 thf(f41599,plain,(
% 92.92/13.71 spl854_322),
% 92.92/13.71 inference(avatar_split_clause,[],[f9826,f41597])).
% 92.92/13.71 thf(f41597,plain,(
% 92.92/13.71 spl854_322 <=> ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERTC(X0)) = $true)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_322])])).
% 92.92/13.71 thf(f9826,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERTC(X0)) = $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2492])).
% 92.92/13.71 thf(f2492,plain,(
% 92.92/13.71 ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERTC(X0)) = $true)),
% 92.92/13.71 inference(fool_elimination,[],[f2491])).
% 92.92/13.71 thf(f2491,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERTC(X0))),
% 92.92/13.71 inference(rectify,[],[f630])).
% 92.92/13.71 thf(f630,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERTC(X0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM__RTC)).
% 92.92/13.71 thf(f41595,plain,(
% 92.92/13.71 spl854_321),
% 92.92/13.71 inference(avatar_split_clause,[],[f9825,f41593])).
% 92.92/13.71 thf(f41593,plain,(
% 92.92/13.71 spl854_321 <=> ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERC(X0)) = $true)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_321])])).
% 92.92/13.71 thf(f9825,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERC(X0)) = $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2490])).
% 92.92/13.71 thf(f2490,plain,(
% 92.92/13.71 ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERC(X0)) = $true)),
% 92.92/13.71 inference(fool_elimination,[],[f2489])).
% 92.92/13.71 thf(f2489,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERC(X0))),
% 92.92/13.71 inference(rectify,[],[f627])).
% 92.92/13.71 thf(f627,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ERC(X0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM__RC)).
% 92.92/13.71 thf(f41591,plain,(
% 92.92/13.71 spl854_320),
% 92.92/13.71 inference(avatar_split_clause,[],[f9824,f41589])).
% 92.92/13.71 thf(f41589,plain,(
% 92.92/13.71 spl854_320 <=> ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESC(X0)) = $true)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_320])])).
% 92.92/13.71 thf(f9824,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESC(X0)) = $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2488])).
% 92.92/13.71 thf(f2488,plain,(
% 92.92/13.71 ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESC(X0)) = $true)),
% 92.92/13.71 inference(fool_elimination,[],[f2487])).
% 92.92/13.71 thf(f2487,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESC(X0))),
% 92.92/13.71 inference(rectify,[],[f628])).
% 92.92/13.71 thf(f628,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESC(X0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM__SC)).
% 92.92/13.71 thf(f41587,plain,(
% 92.92/13.71 spl854_319),
% 92.92/13.71 inference(avatar_split_clause,[],[f9823,f41585])).
% 92.92/13.71 thf(f41585,plain,(
% 92.92/13.71 spl854_319 <=> ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESTRORD(X0)) = $true)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_319])])).
% 92.92/13.71 thf(f9823,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESTRORD(X0)) = $true)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2486])).
% 92.92/13.71 thf(f2486,plain,(
% 92.92/13.71 ! [X0 : $tType] : (vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESTRORD(X0)) = $true)),
% 92.92/13.71 inference(fool_elimination,[],[f2485])).
% 92.92/13.71 thf(f2485,plain,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESTRORD(X0))),
% 92.92/13.71 inference(rectify,[],[f626])).
% 92.92/13.71 thf(f626,axiom,(
% 92.92/13.71 ! [X0 : $tType] : vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),$o,c_2Erelation_2EIDEM(sTfun(X0,sTfun(X0,$o))),c_2Erelation_2ESTRORD(X0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EIDEM__STRORD)).
% 92.92/13.71 thf(f41556,plain,(
% 92.92/13.71 spl854_318),
% 92.92/13.71 inference(avatar_split_clause,[],[f9319,f41554])).
% 92.92/13.71 thf(f41554,plain,(
% 92.92/13.71 spl854_318 <=> ! [X0 : $tType] : (c_2Emin_2E_3D(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),c_2Emin_2E_3D(X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_318])])).
% 92.92/13.71 thf(f9319,plain,(
% 92.92/13.71 ( ! [X0 : $tType] : ((c_2Emin_2E_3D(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),c_2Emin_2E_3D(X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f638])).
% 92.92/13.71 thf(f638,axiom,(
% 92.92/13.71 ! [X0 : $tType] : (c_2Emin_2E_3D(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),c_2Erelation_2Einv(X0,X0),c_2Emin_2E_3D(X0)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2Einv__Id)).
% 92.92/13.71 thf(f41339,plain,(
% 92.92/13.71 spl854_317),
% 92.92/13.71 inference(avatar_split_clause,[],[f20008,f41337])).
% 92.92/13.71 thf(f41337,plain,(
% 92.92/13.71 spl854_317 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),$true) = X1)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_317])])).
% 92.92/13.71 thf(f20008,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),$true) = X1)) )),
% 92.92/13.71 inference(forward_demodulation,[],[f15297,f13591])).
% 92.92/13.71 thf(f15297,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X1)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f12361,f13514])).
% 92.92/13.71 thf(f12361,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),c_2Ebool_2ET) = X1)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8429])).
% 92.92/13.71 thf(f8429,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),c_2Ebool_2EF) = X2) & (vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),c_2Ebool_2ET) = X1))),
% 92.92/13.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK634])],[f5253,f8428])).
% 92.92/13.71 thf(f8428,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0] : (? [X3 : $o > X0] : ((vAPP($o,X0,X3,c_2Ebool_2EF) = X2) & (vAPP($o,X0,X3,c_2Ebool_2ET) = X1)) => ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),c_2Ebool_2EF) = X2) & (vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),c_2Ebool_2ET) = X1)))),
% 92.92/13.71 introduced(choice_axiom,[])).
% 92.92/13.71 thf(f5253,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : X0,X2 : X0] : ? [X3 : $o > X0] : ((vAPP($o,X0,X3,c_2Ebool_2EF) = X2) & (vAPP($o,X0,X3,c_2Ebool_2ET) = X1))),
% 92.92/13.71 inference(rectify,[],[f166])).
% 92.92/13.71 thf(f166,axiom,(
% 92.92/13.71 ! [X0 : $tType,X9 : X0,X10 : X0] : ? [X78 : $o > X0] : ((vAPP($o,X0,X78,c_2Ebool_2EF) = X10) & (vAPP($o,X0,X78,c_2Ebool_2ET) = X9))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EboolAxiom)).
% 92.92/13.71 thf(f41335,plain,(
% 92.92/13.71 spl854_316),
% 92.92/13.71 inference(avatar_split_clause,[],[f20007,f41333])).
% 92.92/13.71 thf(f41333,plain,(
% 92.92/13.71 spl854_316 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),$false) = X2)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_316])])).
% 92.92/13.71 thf(f20007,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),$false) = X2)) )),
% 92.92/13.71 inference(forward_demodulation,[],[f15296,f17793])).
% 92.92/13.71 thf(f15296,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X2)) )),
% 92.92/13.71 inference(definition_unfolding,[],[f12362,f13520])).
% 92.92/13.71 thf(f12362,plain,(
% 92.92/13.71 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,X0,vAPP(X0,sTfun($o,X0),vAPP(X0,sTfun(X0,sTfun($o,X0)),sK634(X0),X2),X1),c_2Ebool_2EF) = X2)) )),
% 92.92/13.71 inference(cnf_transformation,[],[f8429])).
% 92.92/13.71 thf(f41307,plain,(
% 92.92/13.71 spl854_315),
% 92.92/13.71 inference(avatar_split_clause,[],[f18578,f41305])).
% 92.92/13.71 thf(f41305,plain,(
% 92.92/13.71 spl854_315 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_315])])).
% 92.92/13.71 thf(f18578,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.92/13.71 inference(forward_demodulation,[],[f17821,f18124])).
% 92.92/13.71 thf(f17821,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.92/13.71 inference(equality_proxy_clausification,[],[f17820])).
% 92.92/13.71 thf(f17820,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.92/13.71 inference(not_proxy_clausification,[],[f14003])).
% 92.92/13.71 thf(f14003,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f9749,f13512])).
% 92.92/13.71 thf(f9749,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6794])).
% 92.92/13.71 thf(f41241,plain,(
% 92.92/13.71 spl854_305 | spl854_314 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f16614,f29086,f41239,f29086])).
% 92.92/13.71 thf(f41239,plain,(
% 92.92/13.71 spl854_314 <=> ! [X2 : $o] : (($true = X2) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,$true),X2)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_314])])).
% 92.92/13.71 thf(f16614,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X0 : $o] : (($true = X3) | ($true = X2) | ($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,$true),X2))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12593])).
% 92.92/13.71 thf(f12593,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X3) | ($true != X1) | ($true = X2) | ($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X2))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6525])).
% 92.92/13.71 thf(f6525,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X3) | ($true != X1) | (($true != X0) & ($true = X2)) | (($true != X3) & ($true = X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X2)))),
% 92.92/13.71 inference(definition_folding,[],[f6105,f6524])).
% 92.92/13.71 thf(f6524,plain,(
% 92.92/13.71 ! [X2 : $o,X1 : $o] : ((($true != X2) & ($true = X1)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X2)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f6105,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X3) | ($true != X1) | (($true != X0) & ($true = X2)) | (($true != X3) & ($true = X0)) | (($true != X2) & ($true = X1)))),
% 92.92/13.71 inference(flattening,[],[f6104])).
% 92.92/13.71 thf(f6104,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X3) | ($true != X1)) | (($true != X0) & ($true = X2))) | ((($true != X3) & ($true = X0)) | (($true != X2) & ($true = X1))))),
% 92.92/13.71 inference(ennf_transformation,[],[f4304])).
% 92.92/13.71 thf(f4304,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X0) => ($true = X3)) & (($true = X1) => ($true = X2))) => ((($true = X2) => ($true = X0)) => (($true = X1) => ($true = X3))))),
% 92.92/13.71 inference(fool_elimination,[],[f4303])).
% 92.92/13.71 thf(f4303,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X0 => X3) & (X1 => X2)) => ((X2 => X0) => (X1 => X3)))),
% 92.92/13.71 inference(rectify,[],[f151])).
% 92.92/13.71 thf(f151,axiom,(
% 92.92/13.71 ! [X68 : $o,X18 : $o,X19 : $o,X69 : $o] : (((X68 => X69) & (X18 => X19)) => ((X19 => X68) => (X18 => X69)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__IMP)).
% 92.92/13.71 thf(f41175,plain,(
% 92.92/13.71 spl854_305 | spl854_313 | spl854_305),
% 92.92/13.71 inference(avatar_split_clause,[],[f16605,f29086,f41173,f29086])).
% 92.92/13.71 thf(f41173,plain,(
% 92.92/13.71 spl854_313 <=> ! [X1 : $o] : (($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,$true),X1)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_313])])).
% 92.92/13.71 thf(f16605,plain,(
% 92.92/13.71 ( ! [X3 : $o,X0 : $o,X1 : $o] : (($true = X3) | ($true = X1) | ($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,$true),X1))) )),
% 92.92/13.71 inference(equality_resolution,[],[f12587])).
% 92.92/13.71 thf(f12587,plain,(
% 92.92/13.71 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X3) | ($true = X1) | ($true != X2) | ($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X2),X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f6523])).
% 92.92/13.71 thf(f6523,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X3) | ($true = X1) | (($true != X0) & ($true != X2)) | (($true != X3) & ($true = X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X2),X1)))),
% 92.92/13.71 inference(definition_folding,[],[f6103,f6522])).
% 92.92/13.71 thf(f6522,plain,(
% 92.92/13.71 ! [X1 : $o,X2 : $o] : ((($true != X1) & ($true = X2)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X2),X1)))),
% 92.92/13.71 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.71 thf(f6103,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (($true = X3) | ($true = X1) | (($true != X0) & ($true != X2)) | (($true != X3) & ($true = X0)) | (($true != X1) & ($true = X2)))),
% 92.92/13.71 inference(flattening,[],[f6102])).
% 92.92/13.71 thf(f6102,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X3) | ($true = X1)) | (($true != X0) & ($true != X2))) | ((($true != X3) & ($true = X0)) | (($true != X1) & ($true = X2))))),
% 92.92/13.71 inference(ennf_transformation,[],[f4302])).
% 92.92/13.71 thf(f4302,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X0) => ($true = X3)) & (($true = X2) => ($true = X1))) => ((($true = X0) | ($true = X2)) => (($true = X3) | ($true = X1))))),
% 92.92/13.71 inference(fool_elimination,[],[f4301])).
% 92.92/13.71 thf(f4301,plain,(
% 92.92/13.71 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X0 => X3) & (X2 => X1)) => ((X0 | X2) => (X3 | X1)))),
% 92.92/13.71 inference(rectify,[],[f150])).
% 92.92/13.71 thf(f150,axiom,(
% 92.92/13.71 ! [X68 : $o,X18 : $o,X19 : $o,X69 : $o] : (((X68 => X69) & (X19 => X18)) => ((X68 | X19) => (X69 | X18)))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__OR)).
% 92.92/13.71 thf(f41171,plain,(
% 92.92/13.71 spl854_312),
% 92.92/13.71 inference(avatar_split_clause,[],[f15314,f41169])).
% 92.92/13.71 thf(f41169,plain,(
% 92.92/13.71 spl854_312 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X2 : X0 > X1] : (vAPP(X0,X1,X2,X3) = vAPP(X0,X1,vAPP(sTfun(X0,X1),sTfun(X0,X1),iCOMB,X2),X3))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_312])])).
% 92.92/13.71 thf(f15314,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X3 : X0] : ((vAPP(X0,X1,X2,X3) = vAPP(X0,X1,vAPP(sTfun(X0,X1),sTfun(X0,X1),iCOMB,X2),X3))) )),
% 92.92/13.71 inference(definition_unfolding,[],[f12389,f9977])).
% 92.92/13.71 thf(f9977,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType] : ((iCOMB = c_2Ebool_2Eliteral__case(X0,X1))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f2548])).
% 92.92/13.71 thf(f2548,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : (iCOMB = c_2Ebool_2Eliteral__case(X0,X1))),
% 92.92/13.71 inference(fool_elimination,[],[f2547])).
% 92.92/13.71 thf(f2547,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType] : (c_2Ebool_2Eliteral__case(X0,X1) = (^[X2 : X0 > X1, X3 : X0] : (vAPP(X0,X1,X2,X3))))),
% 92.92/13.71 inference(rectify,[],[f32])).
% 92.92/13.71 thf(f32,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType] : (c_2Ebool_2Eliteral__case(X0,X5) = (^[X3 : X0 > X5, X4 : X0] : (vAPP(X0,X5,X3,X4))))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Eliteral__case__DEF)).
% 92.92/13.71 thf(f12389,plain,(
% 92.92/13.71 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X3 : X0] : ((vAPP(X0,X1,X2,X3) = vAPP(X0,X1,vAPP(sTfun(X0,X1),sTfun(X0,X1),c_2Ebool_2Eliteral__case(X0,X1),X2),X3))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f5261])).
% 92.92/13.71 thf(f5261,plain,(
% 92.92/13.71 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1,X3 : X0] : (vAPP(X0,X1,X2,X3) = vAPP(X0,X1,vAPP(sTfun(X0,X1),sTfun(X0,X1),c_2Ebool_2Eliteral__case(X0,X1),X2),X3))),
% 92.92/13.71 inference(rectify,[],[f180])).
% 92.92/13.71 thf(f180,axiom,(
% 92.92/13.71 ! [X0 : $tType,X5 : $tType,X3 : X0 > X5,X4 : X0] : (vAPP(X0,X5,X3,X4) = vAPP(X0,X5,vAPP(sTfun(X0,X5),sTfun(X0,X5),c_2Ebool_2Eliteral__case(X0,X5),X3),X4))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Eliteral__case__THM)).
% 92.92/13.71 thf(f37354,plain,(
% 92.92/13.71 spl854_311 | ~spl854_18 | ~spl854_132),
% 92.92/13.71 inference(avatar_split_clause,[],[f22819,f22784,f21990,f37352])).
% 92.92/13.71 thf(f21990,plain,(
% 92.92/13.71 spl854_18 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X1)) = X1)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_18])])).
% 92.92/13.71 thf(f22784,plain,(
% 92.92/13.71 spl854_132 <=> ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) != X0))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_132])])).
% 92.92/13.71 thf(f22819,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))) ) | (~spl854_18 | ~spl854_132)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f22817])).
% 92.92/13.71 thf(f22817,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0)))) ) | (~spl854_18 | ~spl854_132)),
% 92.92/13.71 inference(superposition,[],[f22785,f21991])).
% 92.92/13.71 thf(f21991,plain,(
% 92.92/13.71 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X1)) = X1)) ) | ~spl854_18),
% 92.92/13.71 inference(avatar_component_clause,[],[f21990])).
% 92.92/13.71 thf(f22785,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Emin_2Eind] : ((vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) != X0) | ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0))) ) | ~spl854_132),
% 92.92/13.71 inference(avatar_component_clause,[],[f22784])).
% 92.92/13.71 thf(f35591,plain,(
% 92.92/13.71 spl854_310 | ~spl854_5 | spl854_296),
% 92.92/13.71 inference(avatar_split_clause,[],[f26236,f23913,f21881,f35588])).
% 92.92/13.71 thf(f35588,plain,(
% 92.92/13.71 spl854_310 <=> ($false = vAPP(sTfun($o,$o),$o,sK169,sK386($o)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_310])])).
% 92.92/13.71 thf(f23913,plain,(
% 92.92/13.71 spl854_296 <=> ($true = vAPP(sTfun($o,$o),$o,sK169,sK386($o)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_296])])).
% 92.92/13.71 thf(f26236,plain,(
% 92.92/13.71 ($false = vAPP(sTfun($o,$o),$o,sK169,sK386($o))) | (~spl854_5 | spl854_296)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f26235])).
% 92.92/13.71 thf(f26235,plain,(
% 92.92/13.71 ($true != $true) | ($false = vAPP(sTfun($o,$o),$o,sK169,sK386($o))) | (~spl854_5 | spl854_296)),
% 92.92/13.71 inference(superposition,[],[f23915,f21882])).
% 92.92/13.71 thf(f23915,plain,(
% 92.92/13.71 ($true != vAPP(sTfun($o,$o),$o,sK169,sK386($o))) | spl854_296),
% 92.92/13.71 inference(avatar_component_clause,[],[f23913])).
% 92.92/13.71 thf(f35582,plain,(
% 92.92/13.71 spl854_309 | ~spl854_146 | ~spl854_168 | ~spl854_171 | ~spl854_175),
% 92.92/13.71 inference(avatar_split_clause,[],[f34667,f23087,f22996,f22983,f22890,f35579])).
% 92.92/13.71 thf(f35579,plain,(
% 92.92/13.71 spl854_309 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_309])])).
% 92.92/13.71 thf(f22996,plain,(
% 92.92/13.71 spl854_171 <=> ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_171])])).
% 92.92/13.71 thf(f23087,plain,(
% 92.92/13.71 spl854_175 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_175])])).
% 92.92/13.71 thf(f34667,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) | (~spl854_146 | ~spl854_168 | ~spl854_171 | ~spl854_175)),
% 92.92/13.71 inference(forward_demodulation,[],[f22998,f23166])).
% 92.92/13.71 thf(f23166,plain,(
% 92.92/13.71 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (~spl854_146 | ~spl854_168 | ~spl854_175)),
% 92.92/13.71 inference(forward_demodulation,[],[f23164,f22985])).
% 92.92/13.71 thf(f23164,plain,(
% 92.92/13.71 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | (~spl854_146 | ~spl854_175)),
% 92.92/13.71 inference(superposition,[],[f22891,f23089])).
% 92.92/13.71 thf(f23089,plain,(
% 92.92/13.71 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_175),
% 92.92/13.71 inference(avatar_component_clause,[],[f23087])).
% 92.92/13.71 thf(f22998,plain,(
% 92.92/13.71 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) | ~spl854_171),
% 92.92/13.71 inference(avatar_component_clause,[],[f22996])).
% 92.92/13.71 thf(f35577,plain,(
% 92.92/13.71 spl854_308 | ~spl854_9 | ~spl854_160),
% 92.92/13.71 inference(avatar_split_clause,[],[f29755,f22950,f21928,f35574])).
% 92.92/13.71 thf(f35571,plain,(
% 92.92/13.71 spl854_159 | ~spl854_9),
% 92.92/13.71 inference(avatar_split_clause,[],[f29751,f21928,f22944])).
% 92.92/13.71 thf(f22944,plain,(
% 92.92/13.71 spl854_159 <=> (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_159])])).
% 92.92/13.71 thf(f35536,plain,(
% 92.92/13.71 spl854_307 | ~spl854_5 | spl854_285),
% 92.92/13.71 inference(avatar_split_clause,[],[f25192,f23868,f21881,f35533])).
% 92.92/13.71 thf(f35533,plain,(
% 92.92/13.71 spl854_307 <=> ($false = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_307])])).
% 92.92/13.71 thf(f23868,plain,(
% 92.92/13.71 spl854_285 <=> ($true = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_285])])).
% 92.92/13.71 thf(f25192,plain,(
% 92.92/13.71 ($false = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o))) | (~spl854_5 | spl854_285)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f25191])).
% 92.92/13.71 thf(f25191,plain,(
% 92.92/13.71 ($true != $true) | ($false = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o))) | (~spl854_5 | spl854_285)),
% 92.92/13.71 inference(superposition,[],[f23870,f21882])).
% 92.92/13.71 thf(f23870,plain,(
% 92.92/13.71 ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o))) | spl854_285),
% 92.92/13.71 inference(avatar_component_clause,[],[f23868])).
% 92.92/13.71 thf(f35214,plain,(
% 92.92/13.71 spl854_306 | ~spl854_9),
% 92.92/13.71 inference(avatar_split_clause,[],[f30031,f21928,f35212])).
% 92.92/13.71 thf(f35212,plain,(
% 92.92/13.71 spl854_306 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_306])])).
% 92.92/13.71 thf(f30031,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) ) | ~spl854_9),
% 92.92/13.71 inference(forward_demodulation,[],[f30030,f21929])).
% 92.92/13.71 thf(f30030,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) ) | ~spl854_9),
% 92.92/13.71 inference(forward_demodulation,[],[f9155,f21929])).
% 92.92/13.71 thf(f9155,plain,(
% 92.92/13.71 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.92/13.71 inference(cnf_transformation,[],[f4837])).
% 92.92/13.71 thf(f4837,plain,(
% 92.92/13.71 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,c_2Enum_2E0))),
% 92.92/13.71 inference(rectify,[],[f1398])).
% 92.92/13.71 thf(f1398,axiom,(
% 92.92/13.71 ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137))) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137))) & ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)))) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,c_2Enum_2E0))),
% 92.92/13.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__div2)).
% 92.92/13.71 thf(f29249,plain,(
% 92.92/13.71 ~spl854_8 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29248])).
% 92.92/13.71 thf(f29248,plain,(
% 92.92/13.71 $false | (~spl854_8 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29119])).
% 92.92/13.71 thf(f29119,plain,(
% 92.92/13.71 ($true = $false) | (~spl854_8 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f21925,f29087])).
% 92.92/13.71 thf(f29087,plain,(
% 92.92/13.71 ( ! [X0 : $o] : (($true = X0)) ) | ~spl854_305),
% 92.92/13.71 inference(avatar_component_clause,[],[f29086])).
% 92.92/13.71 thf(f21925,plain,(
% 92.92/13.71 ($false = sK125) | ~spl854_8),
% 92.92/13.71 inference(avatar_component_clause,[],[f21923])).
% 92.92/13.71 thf(f21923,plain,(
% 92.92/13.71 spl854_8 <=> ($false = sK125)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_8])])).
% 92.92/13.71 thf(f29247,plain,(
% 92.92/13.71 spl854_2 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29246])).
% 92.92/13.71 thf(f29246,plain,(
% 92.92/13.71 $false | (spl854_2 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29120])).
% 92.92/13.71 thf(f29120,plain,(
% 92.92/13.71 ($true != $true) | (spl854_2 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f21869,f29087])).
% 92.92/13.71 thf(f21869,plain,(
% 92.92/13.71 ($true != sK125) | spl854_2),
% 92.92/13.71 inference(avatar_component_clause,[],[f21867])).
% 92.92/13.71 thf(f21867,plain,(
% 92.92/13.71 spl854_2 <=> ($true = sK125)),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_2])])).
% 92.92/13.71 thf(f29244,plain,(
% 92.92/13.71 ~spl854_48 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29243])).
% 92.92/13.71 thf(f29243,plain,(
% 92.92/13.71 $false | (~spl854_48 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29122])).
% 92.92/13.71 thf(f29122,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_48 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f22130,f29087])).
% 92.92/13.71 thf(f29241,plain,(
% 92.92/13.71 ~spl854_254 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29240])).
% 92.92/13.71 thf(f29240,plain,(
% 92.92/13.71 $false | (~spl854_254 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29124])).
% 92.92/13.71 thf(f29124,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_254 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23740,f29087])).
% 92.92/13.71 thf(f23740,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),$true))) ) | ~spl854_254),
% 92.92/13.71 inference(avatar_component_clause,[],[f23739])).
% 92.92/13.71 thf(f23739,plain,(
% 92.92/13.71 spl854_254 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_254])])).
% 92.92/13.71 thf(f29239,plain,(
% 92.92/13.71 ~spl854_252 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29238])).
% 92.92/13.71 thf(f29238,plain,(
% 92.92/13.71 $false | (~spl854_252 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29125])).
% 92.92/13.71 thf(f29125,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_252 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23731,f29087])).
% 92.92/13.71 thf(f23731,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),$true))) ) | ~spl854_252),
% 92.92/13.71 inference(avatar_component_clause,[],[f23730])).
% 92.92/13.71 thf(f23730,plain,(
% 92.92/13.71 spl854_252 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_252])])).
% 92.92/13.71 thf(f29237,plain,(
% 92.92/13.71 ~spl854_256 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29236])).
% 92.92/13.71 thf(f29236,plain,(
% 92.92/13.71 $false | (~spl854_256 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29126])).
% 92.92/13.71 thf(f29126,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_256 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23748,f29087])).
% 92.92/13.71 thf(f23748,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),$true))) ) | ~spl854_256),
% 92.92/13.71 inference(avatar_component_clause,[],[f23747])).
% 92.92/13.71 thf(f23747,plain,(
% 92.92/13.71 spl854_256 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_256])])).
% 92.92/13.71 thf(f29235,plain,(
% 92.92/13.71 ~spl854_255 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29234])).
% 92.92/13.71 thf(f29234,plain,(
% 92.92/13.71 $false | (~spl854_255 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29127])).
% 92.92/13.71 thf(f29127,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_255 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23744,f29087])).
% 92.92/13.71 thf(f23744,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),$true))) ) | ~spl854_255),
% 92.92/13.71 inference(avatar_component_clause,[],[f23743])).
% 92.92/13.71 thf(f23743,plain,(
% 92.92/13.71 spl854_255 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_255])])).
% 92.92/13.71 thf(f29233,plain,(
% 92.92/13.71 ~spl854_258 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29232])).
% 92.92/13.71 thf(f29232,plain,(
% 92.92/13.71 $false | (~spl854_258 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29128])).
% 92.92/13.71 thf(f29128,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_258 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23756,f29087])).
% 92.92/13.71 thf(f23756,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),$true))) ) | ~spl854_258),
% 92.92/13.71 inference(avatar_component_clause,[],[f23755])).
% 92.92/13.71 thf(f23755,plain,(
% 92.92/13.71 spl854_258 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_258])])).
% 92.92/13.71 thf(f29231,plain,(
% 92.92/13.71 ~spl854_257 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29230])).
% 92.92/13.71 thf(f29230,plain,(
% 92.92/13.71 $false | (~spl854_257 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29129])).
% 92.92/13.71 thf(f29129,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_257 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23752,f29087])).
% 92.92/13.71 thf(f23752,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),$true))) ) | ~spl854_257),
% 92.92/13.71 inference(avatar_component_clause,[],[f23751])).
% 92.92/13.71 thf(f23751,plain,(
% 92.92/13.71 spl854_257 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_257])])).
% 92.92/13.71 thf(f29229,plain,(
% 92.92/13.71 ~spl854_260 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29228])).
% 92.92/13.71 thf(f29228,plain,(
% 92.92/13.71 $false | (~spl854_260 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29130])).
% 92.92/13.71 thf(f29130,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_260 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23764,f29087])).
% 92.92/13.71 thf(f23764,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),$true))) ) | ~spl854_260),
% 92.92/13.71 inference(avatar_component_clause,[],[f23763])).
% 92.92/13.71 thf(f23763,plain,(
% 92.92/13.71 spl854_260 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),$true))),
% 92.92/13.71 introduced(avatar_definition,[new_symbols(naming,[spl854_260])])).
% 92.92/13.71 thf(f29227,plain,(
% 92.92/13.71 ~spl854_259 | ~spl854_305),
% 92.92/13.71 inference(avatar_contradiction_clause,[],[f29226])).
% 92.92/13.71 thf(f29226,plain,(
% 92.92/13.71 $false | (~spl854_259 | ~spl854_305)),
% 92.92/13.71 inference(trivial_inequality_removal,[],[f29131])).
% 92.92/13.71 thf(f29131,plain,(
% 92.92/13.71 ($true != $true) | (~spl854_259 | ~spl854_305)),
% 92.92/13.71 inference(superposition,[],[f23760,f29087])).
% 92.92/13.71 thf(f23760,plain,(
% 92.92/13.71 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),$true))) ) | ~spl854_259),
% 92.92/13.71 inference(avatar_component_clause,[],[f23759])).
% 92.92/13.71 thf(f23759,plain,(
% 92.92/13.71 spl854_259 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_259])])).
% 92.92/13.72 thf(f29225,plain,(
% 92.92/13.72 ~spl854_261 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29224])).
% 92.92/13.72 thf(f29224,plain,(
% 92.92/13.72 $false | (~spl854_261 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29132])).
% 92.92/13.72 thf(f29132,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_261 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23768,f29087])).
% 92.92/13.72 thf(f23768,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),$true))) ) | ~spl854_261),
% 92.92/13.72 inference(avatar_component_clause,[],[f23767])).
% 92.92/13.72 thf(f23767,plain,(
% 92.92/13.72 spl854_261 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_261])])).
% 92.92/13.72 thf(f29223,plain,(
% 92.92/13.72 ~spl854_262 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29222])).
% 92.92/13.72 thf(f29222,plain,(
% 92.92/13.72 $false | (~spl854_262 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29133])).
% 92.92/13.72 thf(f29133,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_262 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23772,f29087])).
% 92.92/13.72 thf(f23772,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),$true))) ) | ~spl854_262),
% 92.92/13.72 inference(avatar_component_clause,[],[f23771])).
% 92.92/13.72 thf(f23771,plain,(
% 92.92/13.72 spl854_262 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_262])])).
% 92.92/13.72 thf(f29221,plain,(
% 92.92/13.72 ~spl854_264 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29220])).
% 92.92/13.72 thf(f29220,plain,(
% 92.92/13.72 $false | (~spl854_264 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29134])).
% 92.92/13.72 thf(f29134,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_264 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23784,f29087])).
% 92.92/13.72 thf(f23784,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),$true))) ) | ~spl854_264),
% 92.92/13.72 inference(avatar_component_clause,[],[f23783])).
% 92.92/13.72 thf(f23783,plain,(
% 92.92/13.72 spl854_264 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_264])])).
% 92.92/13.72 thf(f29219,plain,(
% 92.92/13.72 ~spl854_263 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29218])).
% 92.92/13.72 thf(f29218,plain,(
% 92.92/13.72 $false | (~spl854_263 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29135])).
% 92.92/13.72 thf(f29135,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_263 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23776,f29087])).
% 92.92/13.72 thf(f23776,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),$true))) ) | ~spl854_263),
% 92.92/13.72 inference(avatar_component_clause,[],[f23775])).
% 92.92/13.72 thf(f23775,plain,(
% 92.92/13.72 spl854_263 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_263])])).
% 92.92/13.72 thf(f29217,plain,(
% 92.92/13.72 ~spl854_266 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29216])).
% 92.92/13.72 thf(f29216,plain,(
% 92.92/13.72 $false | (~spl854_266 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29136])).
% 92.92/13.72 thf(f29136,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_266 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23792,f29087])).
% 92.92/13.72 thf(f23792,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),$true))) ) | ~spl854_266),
% 92.92/13.72 inference(avatar_component_clause,[],[f23791])).
% 92.92/13.72 thf(f23791,plain,(
% 92.92/13.72 spl854_266 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_266])])).
% 92.92/13.72 thf(f29215,plain,(
% 92.92/13.72 ~spl854_265 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29214])).
% 92.92/13.72 thf(f29214,plain,(
% 92.92/13.72 $false | (~spl854_265 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29137])).
% 92.92/13.72 thf(f29137,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_265 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23788,f29087])).
% 92.92/13.72 thf(f23788,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),$true))) ) | ~spl854_265),
% 92.92/13.72 inference(avatar_component_clause,[],[f23787])).
% 92.92/13.72 thf(f23787,plain,(
% 92.92/13.72 spl854_265 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_265])])).
% 92.92/13.72 thf(f29213,plain,(
% 92.92/13.72 ~spl854_272 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29212])).
% 92.92/13.72 thf(f29212,plain,(
% 92.92/13.72 $false | (~spl854_272 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29138])).
% 92.92/13.72 thf(f29138,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_272 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23816,f29087])).
% 92.92/13.72 thf(f23816,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),$true))) ) | ~spl854_272),
% 92.92/13.72 inference(avatar_component_clause,[],[f23815])).
% 92.92/13.72 thf(f23815,plain,(
% 92.92/13.72 spl854_272 <=> ! [X2 : $o,X1 : $o] : ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_272])])).
% 92.92/13.72 thf(f29211,plain,(
% 92.92/13.72 ~spl854_47 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29210])).
% 92.92/13.72 thf(f29210,plain,(
% 92.92/13.72 $false | (~spl854_47 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29139])).
% 92.92/13.72 thf(f29139,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_47 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22126,f29087])).
% 92.92/13.72 thf(f29209,plain,(
% 92.92/13.72 ~spl854_49 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29208])).
% 92.92/13.72 thf(f29208,plain,(
% 92.92/13.72 $false | (~spl854_49 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29140])).
% 92.92/13.72 thf(f29140,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_49 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22134,f29087])).
% 92.92/13.72 thf(f29207,plain,(
% 92.92/13.72 ~spl854_50 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29206])).
% 92.92/13.72 thf(f29206,plain,(
% 92.92/13.72 $false | (~spl854_50 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29141])).
% 92.92/13.72 thf(f29141,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_50 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22138,f29087])).
% 92.92/13.72 thf(f29205,plain,(
% 92.92/13.72 ~spl854_51 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29204])).
% 92.92/13.72 thf(f29204,plain,(
% 92.92/13.72 $false | (~spl854_51 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29142])).
% 92.92/13.72 thf(f29142,plain,(
% 92.92/13.72 ($true != $true) | (~spl854_51 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22142,f29087])).
% 92.92/13.72 thf(f29203,plain,(
% 92.92/13.72 ~spl854_44 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29202])).
% 92.92/13.72 thf(f29202,plain,(
% 92.92/13.72 $false | (~spl854_44 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29143])).
% 92.92/13.72 thf(f29143,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_44 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22114,f29087])).
% 92.92/13.72 thf(f29201,plain,(
% 92.92/13.72 spl854_12 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29200])).
% 92.92/13.72 thf(f29200,plain,(
% 92.92/13.72 $false | (spl854_12 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29144])).
% 92.92/13.72 thf(f29144,plain,(
% 92.92/13.72 ($true != $true) | (spl854_12 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f21942,f29087])).
% 92.92/13.72 thf(f21942,plain,(
% 92.92/13.72 ($true != vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124)) | spl854_12),
% 92.92/13.72 inference(avatar_component_clause,[],[f21940])).
% 92.92/13.72 thf(f21940,plain,(
% 92.92/13.72 spl854_12 <=> ($true = vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_12])])).
% 92.92/13.72 thf(f29199,plain,(
% 92.92/13.72 ~spl854_189 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29198])).
% 92.92/13.72 thf(f29198,plain,(
% 92.92/13.72 $false | (~spl854_189 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29145])).
% 92.92/13.72 thf(f29145,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_189 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23218,f29087])).
% 92.92/13.72 thf(f23218,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X1))) ) | ~spl854_189),
% 92.92/13.72 inference(avatar_component_clause,[],[f23217])).
% 92.92/13.72 thf(f23217,plain,(
% 92.92/13.72 spl854_189 <=> ! [X0 : $tType,X1 : X0 > $o] : ($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_189])])).
% 92.92/13.72 thf(f29195,plain,(
% 92.92/13.72 ~spl854_129 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29194])).
% 92.92/13.72 thf(f29194,plain,(
% 92.92/13.72 $false | (~spl854_129 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29148])).
% 92.92/13.72 thf(f29148,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_129 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22706,f29087])).
% 92.92/13.72 thf(f22706,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) ) | ~spl854_129),
% 92.92/13.72 inference(avatar_component_clause,[],[f22705])).
% 92.92/13.72 thf(f22705,plain,(
% 92.92/13.72 spl854_129 <=> ! [X0 : tyop_2Enum_2Enum] : ($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_129])])).
% 92.92/13.72 thf(f29193,plain,(
% 92.92/13.72 ~spl854_283 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29192])).
% 92.92/13.72 thf(f29192,plain,(
% 92.92/13.72 $false | (~spl854_283 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29149])).
% 92.92/13.72 thf(f29149,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_283 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23861,f29087])).
% 92.92/13.72 thf(f23861,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) ) | ~spl854_283),
% 92.92/13.72 inference(avatar_component_clause,[],[f23860])).
% 92.92/13.72 thf(f23860,plain,(
% 92.92/13.72 spl854_283 <=> ! [X0 : tyop_2Enum_2Enum] : ($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_283])])).
% 92.92/13.72 thf(f29189,plain,(
% 92.92/13.72 ~spl854_166 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29188])).
% 92.92/13.72 thf(f29188,plain,(
% 92.92/13.72 $false | (~spl854_166 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29152])).
% 92.92/13.72 thf(f29152,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_166 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22976,f29087])).
% 92.92/13.72 thf(f22976,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : (($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)))) ) | ~spl854_166),
% 92.92/13.72 inference(avatar_component_clause,[],[f22975])).
% 92.92/13.72 thf(f22975,plain,(
% 92.92/13.72 spl854_166 <=> ! [X1 : $tType,X0 : $tType,X2 : X1] : ($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_166])])).
% 92.92/13.72 thf(f29187,plain,(
% 92.92/13.72 ~spl854_167 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29186])).
% 92.92/13.72 thf(f29186,plain,(
% 92.92/13.72 $false | (~spl854_167 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29153])).
% 92.92/13.72 thf(f29153,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_167 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22980,f29087])).
% 92.92/13.72 thf(f22980,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)))) ) | ~spl854_167),
% 92.92/13.72 inference(avatar_component_clause,[],[f22979])).
% 92.92/13.72 thf(f22979,plain,(
% 92.92/13.72 spl854_167 <=> ! [X1 : $tType,X0 : $tType,X2 : X0] : ($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_167])])).
% 92.92/13.72 thf(f29185,plain,(
% 92.92/13.72 ~spl854_30 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29184])).
% 92.92/13.72 thf(f29184,plain,(
% 92.92/13.72 $false | (~spl854_30 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29154])).
% 92.92/13.72 thf(f29154,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_30 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22049,f29087])).
% 92.92/13.72 thf(f22049,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) ) | ~spl854_30),
% 92.92/13.72 inference(avatar_component_clause,[],[f22048])).
% 92.92/13.72 thf(f22048,plain,(
% 92.92/13.72 spl854_30 <=> ! [X0 : tyop_2Enum_2Enum] : ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_30])])).
% 92.92/13.72 thf(f29183,plain,(
% 92.92/13.72 ~spl854_81 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29182])).
% 92.92/13.72 thf(f29182,plain,(
% 92.92/13.72 $false | (~spl854_81 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29155])).
% 92.92/13.72 thf(f29155,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_81 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22345,f29087])).
% 92.92/13.72 thf(f22345,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ~spl854_81),
% 92.92/13.72 inference(avatar_component_clause,[],[f22343])).
% 92.92/13.72 thf(f22343,plain,(
% 92.92/13.72 spl854_81 <=> ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_81])])).
% 92.92/13.72 thf(f29181,plain,(
% 92.92/13.72 ~spl854_28 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29180])).
% 92.92/13.72 thf(f29180,plain,(
% 92.92/13.72 $false | (~spl854_28 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29156])).
% 92.92/13.72 thf(f29156,plain,(
% 92.92/13.72 ($true = $false) | (~spl854_28 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f22033,f29087])).
% 92.92/13.72 thf(f22033,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_28),
% 92.92/13.72 inference(avatar_component_clause,[],[f22031])).
% 92.92/13.72 thf(f22031,plain,(
% 92.92/13.72 spl854_28 <=> ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_28])])).
% 92.92/13.72 thf(f29177,plain,(
% 92.92/13.72 spl854_274 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29176])).
% 92.92/13.72 thf(f29176,plain,(
% 92.92/13.72 $false | (spl854_274 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29159])).
% 92.92/13.72 thf(f29159,plain,(
% 92.92/13.72 ($true != $true) | (spl854_274 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23825,f29087])).
% 92.92/13.72 thf(f23825,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o))) | spl854_274),
% 92.92/13.72 inference(avatar_component_clause,[],[f23823])).
% 92.92/13.72 thf(f23823,plain,(
% 92.92/13.72 spl854_274 <=> ($true = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_274])])).
% 92.92/13.72 thf(f29175,plain,(
% 92.92/13.72 spl854_285 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29174])).
% 92.92/13.72 thf(f29174,plain,(
% 92.92/13.72 $false | (spl854_285 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29160])).
% 92.92/13.72 thf(f29160,plain,(
% 92.92/13.72 ($true != $true) | (spl854_285 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23870,f29087])).
% 92.92/13.72 thf(f29173,plain,(
% 92.92/13.72 spl854_296 | ~spl854_305),
% 92.92/13.72 inference(avatar_contradiction_clause,[],[f29172])).
% 92.92/13.72 thf(f29172,plain,(
% 92.92/13.72 $false | (spl854_296 | ~spl854_305)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f29161])).
% 92.92/13.72 thf(f29161,plain,(
% 92.92/13.72 ($true != $true) | (spl854_296 | ~spl854_305)),
% 92.92/13.72 inference(superposition,[],[f23915,f29087])).
% 92.92/13.72 thf(f29088,plain,(
% 92.92/13.72 spl854_304 | spl854_305),
% 92.92/13.72 inference(avatar_split_clause,[],[f11618,f29086,f29083])).
% 92.92/13.72 thf(f29083,plain,(
% 92.92/13.72 spl854_304 <=> ! [X2 : $o,X1 : $o] : (($true = X2) | ($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_304])])).
% 92.92/13.72 thf(f11618,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = X0) | ($true = X2) | ($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6443])).
% 92.92/13.72 thf(f6443,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = X0) | (($true != X0) & ($true = X2)) | (($true != X0) & ($true = X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X2)))),
% 92.92/13.72 inference(definition_folding,[],[f5952,f6442])).
% 92.92/13.72 thf(f6442,plain,(
% 92.92/13.72 ! [X2 : $o,X1 : $o] : ((($true != X2) & ($true != X1)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X2)))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f5952,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o] : (($true = X0) | (($true != X0) & ($true = X2)) | (($true != X0) & ($true = X1)) | (($true != X2) & ($true != X1)))),
% 92.92/13.72 inference(flattening,[],[f5951])).
% 92.92/13.72 thf(f5951,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o] : (((($true = X0) | (($true != X0) & ($true = X2))) | (($true != X0) & ($true = X1))) | (($true != X2) & ($true != X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f3770])).
% 92.92/13.72 thf(f3770,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o] : ((($true = X2) | ($true = X1)) => ((($true = X1) => ($true = X0)) => ((($true = X2) => ($true = X0)) => ($true = X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f3769])).
% 92.92/13.72 thf(f3769,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o] : ((X2 | X1) => ((X1 => X0) => ((X2 => X0) => X0)))),
% 92.92/13.72 inference(rectify,[],[f63])).
% 92.92/13.72 thf(f63,axiom,(
% 92.92/13.72 ! [X6 : $o,X13 : $o,X14 : $o] : ((X14 | X13) => ((X13 => X6) => ((X14 => X6) => X6)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__ELIM__THM)).
% 92.92/13.72 thf(f29081,plain,(
% 92.92/13.72 spl854_303 | ~spl854_5 | spl854_274),
% 92.92/13.72 inference(avatar_split_clause,[],[f24139,f23823,f21881,f29078])).
% 92.92/13.72 thf(f29078,plain,(
% 92.92/13.72 spl854_303 <=> ($false = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_303])])).
% 92.92/13.72 thf(f24139,plain,(
% 92.92/13.72 ($false = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o))) | (~spl854_5 | spl854_274)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f24138])).
% 92.92/13.72 thf(f24138,plain,(
% 92.92/13.72 ($true != $true) | ($false = vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o))) | (~spl854_5 | spl854_274)),
% 92.92/13.72 inference(superposition,[],[f23825,f21882])).
% 92.92/13.72 thf(f29076,plain,(
% 92.92/13.72 spl854_302),
% 92.92/13.72 inference(avatar_split_clause,[],[f11486,f29074])).
% 92.92/13.72 thf(f29074,plain,(
% 92.92/13.72 spl854_302 <=> ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2)) | ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_302])])).
% 92.92/13.72 thf(f11486,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2)) | ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3646])).
% 92.92/13.72 thf(f3646,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2)) | ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2)))),
% 92.92/13.72 inference(fool_elimination,[],[f3645])).
% 92.92/13.72 thf(f3645,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : tyop_2Esum_2Esum(X0,X1)] : (vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),X2) | vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),X2))),
% 92.92/13.72 inference(rectify,[],[f683])).
% 92.92/13.72 thf(f683,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X8 : tyop_2Esum_2Esum(X0,X5)] : (vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISR(X0,X5),X8) | vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISL(X0,X5),X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EISL__OR__ISR)).
% 92.92/13.72 thf(f29072,plain,(
% 92.92/13.72 spl854_301),
% 92.92/13.72 inference(avatar_split_clause,[],[f9632,f29070])).
% 92.92/13.72 thf(f29070,plain,(
% 92.92/13.72 spl854_301 <=> ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_301])])).
% 92.92/13.72 thf(f9632,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK167,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6703])).
% 92.92/13.72 thf(f29068,plain,(
% 92.92/13.72 spl854_300),
% 92.92/13.72 inference(avatar_split_clause,[],[f9628,f29066])).
% 92.92/13.72 thf(f29066,plain,(
% 92.92/13.72 spl854_300 <=> ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK165,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_300])])).
% 92.92/13.72 thf(f9628,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK165,X0))) | ($true != vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,sP1,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6698])).
% 92.92/13.72 thf(f26520,plain,(
% 92.92/13.72 ~spl854_299 | ~spl854_253 | spl854_296),
% 92.92/13.72 inference(avatar_split_clause,[],[f26237,f23913,f23734,f26517])).
% 92.92/13.72 thf(f26517,plain,(
% 92.92/13.72 spl854_299 <=> (vNOT = sK386($o))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_299])])).
% 92.92/13.72 thf(f23734,plain,(
% 92.92/13.72 spl854_253 <=> ($true = vAPP(sTfun($o,$o),$o,sK169,vNOT))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_253])])).
% 92.92/13.72 thf(f26237,plain,(
% 92.92/13.72 (vNOT != sK386($o)) | (~spl854_253 | spl854_296)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f26234])).
% 92.92/13.72 thf(f26234,plain,(
% 92.92/13.72 ($true != $true) | (vNOT != sK386($o)) | (~spl854_253 | spl854_296)),
% 92.92/13.72 inference(constrained_superposition,[],[f23915,f23736])).
% 92.92/13.72 thf(f23736,plain,(
% 92.92/13.72 ($true = vAPP(sTfun($o,$o),$o,sK169,vNOT)) | ~spl854_253),
% 92.92/13.72 inference(avatar_component_clause,[],[f23734])).
% 92.92/13.72 thf(f25831,plain,(
% 92.92/13.72 ~spl854_298 | ~spl854_253 | spl854_285),
% 92.92/13.72 inference(avatar_split_clause,[],[f25193,f23868,f23734,f25828])).
% 92.92/13.72 thf(f25828,plain,(
% 92.92/13.72 spl854_298 <=> (vNOT = c_2Emarker_2Estmarker($o))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_298])])).
% 92.92/13.72 thf(f25193,plain,(
% 92.92/13.72 (vNOT != c_2Emarker_2Estmarker($o)) | (~spl854_253 | spl854_285)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f25190])).
% 92.92/13.72 thf(f25190,plain,(
% 92.92/13.72 ($true != $true) | (vNOT != c_2Emarker_2Estmarker($o)) | (~spl854_253 | spl854_285)),
% 92.92/13.72 inference(constrained_superposition,[],[f23870,f23736])).
% 92.92/13.72 thf(f24289,plain,(
% 92.92/13.72 ~spl854_297 | ~spl854_253 | spl854_274),
% 92.92/13.72 inference(avatar_split_clause,[],[f24140,f23823,f23734,f24286])).
% 92.92/13.72 thf(f24286,plain,(
% 92.92/13.72 spl854_297 <=> (vNOT = c_2Emarker_2Eunint($o))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_297])])).
% 92.92/13.72 thf(f24140,plain,(
% 92.92/13.72 (vNOT != c_2Emarker_2Eunint($o)) | (~spl854_253 | spl854_274)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f24137])).
% 92.92/13.72 thf(f24137,plain,(
% 92.92/13.72 ($true != $true) | (vNOT != c_2Emarker_2Eunint($o)) | (~spl854_253 | spl854_274)),
% 92.92/13.72 inference(constrained_superposition,[],[f23825,f23736])).
% 92.92/13.72 thf(f23916,plain,(
% 92.92/13.72 ~spl854_296 | ~spl854_15 | ~spl854_190),
% 92.92/13.72 inference(avatar_split_clause,[],[f23416,f23221,f21958,f23913])).
% 92.92/13.72 thf(f21958,plain,(
% 92.92/13.72 spl854_15 <=> ! [X0 : $tType,X1 : X0] : (vAPP(X0,X0,sK386(X0),X1) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_15])])).
% 92.92/13.72 thf(f23221,plain,(
% 92.92/13.72 spl854_190 <=> ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,$false)) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_190])])).
% 92.92/13.72 thf(f23416,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,sK386($o))) | (~spl854_15 | ~spl854_190)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23415])).
% 92.92/13.72 thf(f23415,plain,(
% 92.92/13.72 ($true = $false) | ($true != vAPP(sTfun($o,$o),$o,sK169,sK386($o))) | (~spl854_15 | ~spl854_190)),
% 92.92/13.72 inference(forward_demodulation,[],[f23368,f21959])).
% 92.92/13.72 thf(f21959,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,sK386(X0),X1) = X1)) ) | ~spl854_15),
% 92.92/13.72 inference(avatar_component_clause,[],[f21958])).
% 92.92/13.72 thf(f23368,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,sK386($o))) | ($true = vAPP($o,$o,sK386($o),$false)) | (~spl854_15 | ~spl854_190)),
% 92.92/13.72 inference(superposition,[],[f23222,f21959])).
% 92.92/13.72 thf(f23222,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0))) | ($true = vAPP($o,$o,X0,$false))) ) | ~spl854_190),
% 92.92/13.72 inference(avatar_component_clause,[],[f23221])).
% 92.92/13.72 thf(f23911,plain,(
% 92.92/13.72 spl854_295),
% 92.92/13.72 inference(avatar_split_clause,[],[f19584,f23909])).
% 92.92/13.72 thf(f23909,plain,(
% 92.92/13.72 spl854_295 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_295])])).
% 92.92/13.72 thf(f19584,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0)))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f17338,f9309])).
% 92.92/13.72 thf(f17338,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0)) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17337])).
% 92.92/13.72 thf(f17337,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f11228])).
% 92.92/13.72 thf(f11228,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3566])).
% 92.92/13.72 thf(f3566,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1))))),
% 92.92/13.72 inference(fool_elimination,[],[f3565])).
% 92.92/13.72 thf(f3565,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X1),X1)))),
% 92.92/13.72 inference(rectify,[],[f1030])).
% 92.92/13.72 thf(f1030,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),X136)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X27),X27)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__ODD__EQ__EVEN)).
% 92.92/13.72 thf(f23907,plain,(
% 92.92/13.72 spl854_294),
% 92.92/13.72 inference(avatar_split_clause,[],[f18673,f23905])).
% 92.92/13.72 thf(f23905,plain,(
% 92.92/13.72 spl854_294 <=> ! [X0 : $tType] : (vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_294])])).
% 92.92/13.72 thf(f18673,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$true) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18672,f13591])).
% 92.92/13.72 thf(f18672,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),$false))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f17783,f17793])).
% 92.92/13.72 thf(f17783,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : ((vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) != vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17782])).
% 92.92/13.72 thf(f17782,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f14071])).
% 92.92/13.72 thf(f14071,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),vAPP($o,sTfun(X0,$o),c_2Ecombin_2EK($o,X0),vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9840,f13541,f13544])).
% 92.92/13.72 thf(f9840,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),c_2Epred__set_2EEMPTY(X0)),c_2Epred__set_2EUNIV(X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2520])).
% 92.92/13.72 thf(f2520,plain,(
% 92.92/13.72 ! [X0 : $tType] : ($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),vEQ(sTfun(X0,$o)),c_2Epred__set_2EEMPTY(X0)),c_2Epred__set_2EUNIV(X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f2519])).
% 92.92/13.72 thf(f2519,plain,(
% 92.92/13.72 ! [X0 : $tType] : vAPP($o,$o,vNOT,(c_2Epred__set_2EEMPTY(X0) = c_2Epred__set_2EUNIV(X0)))),
% 92.92/13.72 inference(rectify,[],[f1875])).
% 92.92/13.72 thf(f1875,axiom,(
% 92.92/13.72 ! [X0 : $tType] : vAPP($o,$o,vNOT,(c_2Epred__set_2EEMPTY(X0) = c_2Epred__set_2EUNIV(X0)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__NOT__EMPTY)).
% 92.92/13.72 thf(f23903,plain,(
% 92.92/13.72 spl854_293),
% 92.92/13.72 inference(avatar_split_clause,[],[f18654,f23901])).
% 92.92/13.72 thf(f23901,plain,(
% 92.92/13.72 spl854_293 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_293])])).
% 92.92/13.72 thf(f18654,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18653,f18124])).
% 92.92/13.72 thf(f18653,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18652,f13563])).
% 92.92/13.72 thf(f18652,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f14057,f13548])).
% 92.92/13.72 thf(f14057,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9818,f13512])).
% 92.92/13.72 thf(f9818,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2476])).
% 92.92/13.72 thf(f2476,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0))),
% 92.92/13.72 inference(fool_elimination,[],[f2475])).
% 92.92/13.72 thf(f2475,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)),
% 92.92/13.72 inference(rectify,[],[f1467])).
% 92.92/13.72 thf(f1467,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EONE__DIVIDES__ALL)).
% 92.92/13.72 thf(f23899,plain,(
% 92.92/13.72 spl854_292),
% 92.92/13.72 inference(avatar_split_clause,[],[f18401,f23897])).
% 92.92/13.72 thf(f23897,plain,(
% 92.92/13.72 spl854_292 <=> ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,X0,$true)) | ($true != vAPP($o,$o,X0,$false)) | ($true = vAPP($o,$o,X0,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_292])])).
% 92.92/13.72 thf(f18401,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,X0,$true)) | ($true != vAPP($o,$o,X0,$false)) | ($true = vAPP($o,$o,X0,X1))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18400,f13591])).
% 92.92/13.72 thf(f18400,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,X0,$false)) | ($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13836,f18095])).
% 92.92/13.72 thf(f13836,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o,X1 : $o] : (($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP($o,$o,X0,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9546,f13520,f13514])).
% 92.92/13.72 thf(f9546,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o,X1 : $o] : (($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5431])).
% 92.92/13.72 thf(f5431,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : (! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET)))),
% 92.92/13.72 inference(flattening,[],[f5430])).
% 92.92/13.72 thf(f5430,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : (! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) | (($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2154])).
% 92.92/13.72 thf(f2154,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : ((($true = vAPP($o,$o,X0,c_2Ebool_2EF)) & ($true = vAPP($o,$o,X0,c_2Ebool_2ET))) => ! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)))),
% 92.92/13.72 inference(fool_elimination,[],[f2153])).
% 92.92/13.72 thf(f2153,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : ((vAPP($o,$o,X0,c_2Ebool_2EF) & vAPP($o,$o,X0,c_2Ebool_2ET)) => ! [X1 : $o] : vAPP($o,$o,X0,X1))),
% 92.92/13.72 inference(rectify,[],[f167])).
% 92.92/13.72 thf(f167,axiom,(
% 92.92/13.72 ! [X7 : $o > $o] : ((vAPP($o,$o,X7,c_2Ebool_2EF) & vAPP($o,$o,X7,c_2Ebool_2ET)) => ! [X49 : $o] : vAPP($o,$o,X7,X49))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__INDUCT)).
% 92.92/13.72 thf(f23895,plain,(
% 92.92/13.72 spl854_291),
% 92.92/13.72 inference(avatar_split_clause,[],[f18337,f23893])).
% 92.92/13.72 thf(f23893,plain,(
% 92.92/13.72 spl854_291 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_291])])).
% 92.92/13.72 thf(f18337,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18336,f18124])).
% 92.92/13.72 thf(f18336,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18335,f13563])).
% 92.92/13.72 thf(f18335,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13733,f13548])).
% 92.92/13.72 thf(f13733,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9406,f13512])).
% 92.92/13.72 thf(f9406,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4928])).
% 92.92/13.72 thf(f23891,plain,(
% 92.92/13.72 spl854_290),
% 92.92/13.72 inference(avatar_split_clause,[],[f18306,f23889])).
% 92.92/13.72 thf(f23889,plain,(
% 92.92/13.72 spl854_290 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_290])])).
% 92.92/13.72 thf(f18306,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18305,f18124])).
% 92.92/13.72 thf(f18305,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18304,f13563])).
% 92.92/13.72 thf(f18304,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13724,f13548])).
% 92.92/13.72 thf(f13724,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9387,f13512])).
% 92.92/13.72 thf(f9387,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4924])).
% 92.92/13.72 thf(f4924,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0) = X0))),
% 92.92/13.72 inference(rectify,[],[f1591])).
% 92.92/13.72 thf(f1591,axiom,(
% 92.92/13.72 ! [X8 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X8),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X8) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X8) = X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__1)).
% 92.92/13.72 thf(f23887,plain,(
% 92.92/13.72 spl854_289),
% 92.92/13.72 inference(avatar_split_clause,[],[f18303,f23885])).
% 92.92/13.72 thf(f23885,plain,(
% 92.92/13.72 spl854_289 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_289])])).
% 92.92/13.72 thf(f18303,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18302,f18124])).
% 92.92/13.72 thf(f18302,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18301,f13563])).
% 92.92/13.72 thf(f18301,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13723,f13548])).
% 92.92/13.72 thf(f13723,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9388,f13512])).
% 92.92/13.72 thf(f9388,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4924])).
% 92.92/13.72 thf(f23883,plain,(
% 92.92/13.72 spl854_288),
% 92.92/13.72 inference(avatar_split_clause,[],[f18220,f23881])).
% 92.92/13.72 thf(f18220,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18219,f18204])).
% 92.92/13.72 thf(f18219,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18218,f18124])).
% 92.92/13.72 thf(f18218,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13689,f13563])).
% 92.92/13.72 thf(f13689,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9331,f9122])).
% 92.92/13.72 thf(f9331,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4902])).
% 92.92/13.72 thf(f4902,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0))))),
% 92.92/13.72 inference(rectify,[],[f917])).
% 92.92/13.72 thf(f917,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X136),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EBIT1)).
% 92.92/13.72 thf(f23879,plain,(
% 92.92/13.72 spl854_287),
% 92.92/13.72 inference(avatar_split_clause,[],[f18197,f23877])).
% 92.92/13.72 thf(f23877,plain,(
% 92.92/13.72 spl854_287 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_287])])).
% 92.92/13.72 thf(f18197,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18196,f18124])).
% 92.92/13.72 thf(f18196,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18195,f13563])).
% 92.92/13.72 thf(f18195,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X0) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13679,f13548])).
% 92.92/13.72 thf(f13679,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X0) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9317,f9121,f13512])).
% 92.92/13.72 thf(f9317,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4890])).
% 92.92/13.72 thf(f4890,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f994])).
% 92.92/13.72 thf(f994,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X134) = X134)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__LEFT__1)).
% 92.92/13.72 thf(f23875,plain,(
% 92.92/13.72 spl854_286),
% 92.92/13.72 inference(avatar_split_clause,[],[f18194,f23873])).
% 92.92/13.72 thf(f23873,plain,(
% 92.92/13.72 spl854_286 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_286])])).
% 92.92/13.72 thf(f18194,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18193,f18124])).
% 92.92/13.72 thf(f18193,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18192,f13563])).
% 92.92/13.72 thf(f18192,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13678,f13548])).
% 92.92/13.72 thf(f13678,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9316,f9121,f13512])).
% 92.92/13.72 thf(f9316,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4889])).
% 92.92/13.72 thf(f4889,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X0)),
% 92.92/13.72 inference(rectify,[],[f995])).
% 92.92/13.72 thf(f995,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X134),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = X134)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__RIGHT__1)).
% 92.92/13.72 thf(f23871,plain,(
% 92.92/13.72 ~spl854_285 | ~spl854_14 | ~spl854_190),
% 92.92/13.72 inference(avatar_split_clause,[],[f23414,f23221,f21954,f23868])).
% 92.92/13.72 thf(f21954,plain,(
% 92.92/13.72 spl854_14 <=> ! [X0 : $tType,X1 : X0] : (vAPP(X0,X0,c_2Emarker_2Estmarker(X0),X1) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_14])])).
% 92.92/13.72 thf(f23414,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o))) | (~spl854_14 | ~spl854_190)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23413])).
% 92.92/13.72 thf(f23413,plain,(
% 92.92/13.72 ($true = $false) | ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o))) | (~spl854_14 | ~spl854_190)),
% 92.92/13.72 inference(forward_demodulation,[],[f23367,f21955])).
% 92.92/13.72 thf(f21955,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,c_2Emarker_2Estmarker(X0),X1) = X1)) ) | ~spl854_14),
% 92.92/13.72 inference(avatar_component_clause,[],[f21954])).
% 92.92/13.72 thf(f23367,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Estmarker($o))) | ($true = vAPP($o,$o,c_2Emarker_2Estmarker($o),$false)) | (~spl854_14 | ~spl854_190)),
% 92.92/13.72 inference(superposition,[],[f23222,f21955])).
% 92.92/13.72 thf(f23866,plain,(
% 92.92/13.72 spl854_284),
% 92.92/13.72 inference(avatar_split_clause,[],[f18181,f23864])).
% 92.92/13.72 thf(f23864,plain,(
% 92.92/13.72 spl854_284 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_284])])).
% 92.92/13.72 thf(f18181,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18180,f18124])).
% 92.92/13.72 thf(f18180,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13674,f13563])).
% 92.92/13.72 thf(f13674,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9310,f9122])).
% 92.92/13.72 thf(f9310,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4884])).
% 92.92/13.72 thf(f4884,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)) = X0)),
% 92.92/13.72 inference(rectify,[],[f1157])).
% 92.92/13.72 thf(f1157,axiom,(
% 92.92/13.72 ! [X109 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV,X109),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,c_2Enum_2E0)) = X109)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__ONE)).
% 92.92/13.72 thf(f23862,plain,(
% 92.92/13.72 spl854_283),
% 92.92/13.72 inference(avatar_split_clause,[],[f18003,f23860])).
% 92.92/13.72 thf(f18003,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f13816])).
% 92.92/13.72 thf(f13816,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9524,f13519])).
% 92.92/13.72 thf(f9524,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2136])).
% 92.92/13.72 thf(f2136,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) & (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Earithmetic_2EZERO)) = $true) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) & (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Earithmetic_2EZERO) = $true))),
% 92.92/13.72 inference(fool_elimination,[],[f2135])).
% 92.92/13.72 thf(f2135,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Earithmetic_2EZERO)) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) & vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(rectify,[],[f1391])).
% 92.92/13.72 thf(f1391,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136))) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,c_2Earithmetic_2EZERO)) & vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) & vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)) & vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,c_2Earithmetic_2EZERO))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__evenodd)).
% 92.92/13.72 thf(f23858,plain,(
% 92.92/13.72 spl854_282),
% 92.92/13.72 inference(avatar_split_clause,[],[f17364,f23856])).
% 92.92/13.72 thf(f23856,plain,(
% 92.92/13.72 spl854_282 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK857(X0),X1))) | ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_282])])).
% 92.92/13.72 thf(f17364,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK857(X0),X1))) | ($true = vAPP(X0,$o,X1,X2))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f17363])).
% 92.92/13.72 thf(f17363,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK857(X0),X1))) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) )),
% 92.92/13.72 inference(sigma_clausification,[],[f17362])).
% 92.92/13.72 thf(f17362,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vPI(X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f11164])).
% 92.92/13.72 thf(f11164,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7660])).
% 92.92/13.72 thf(f7660,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) | ! [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) & (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1)))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1)))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK379])],[f7658,f7659])).
% 92.92/13.72 thf(f7659,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))) => ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1)))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f7658,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) | ! [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) & (? [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1)))))),
% 92.92/13.72 inference(rectify,[],[f7657])).
% 92.92/13.72 thf(f7657,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) | ! [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) & (? [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1)))))),
% 92.92/13.72 inference(nnf_transformation,[],[f5124])).
% 92.92/13.72 thf(f5124,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) <=> ? [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2))))),
% 92.92/13.72 inference(rectify,[],[f3460])).
% 92.92/13.72 thf(f3460,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) <=> ? [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))))),
% 92.92/13.72 inference(fool_elimination,[],[f3459])).
% 92.92/13.72 thf(f3459,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (vAPP($o,$o,vNOT,! [X2 : X0] : vAPP(X0,$o,X1,X2)) <=> ? [X3 : X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)))),
% 92.92/13.72 inference(rectify,[],[f88])).
% 92.92/13.72 thf(f88,axiom,(
% 92.92/13.72 ! [X0 : $tType,X7 : X0 > $o] : (vAPP($o,$o,vNOT,! [X4 : X0] : vAPP(X0,$o,X7,X4)) <=> ? [X19 : X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,X7,X19)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__FORALL__THM)).
% 92.92/13.72 thf(f23854,plain,(
% 92.92/13.72 spl854_281),
% 92.92/13.72 inference(avatar_split_clause,[],[f17361,f23852])).
% 92.92/13.72 thf(f23852,plain,(
% 92.92/13.72 spl854_281 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1))) | ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_281])])).
% 92.92/13.72 thf(f17361,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1))) | ($true = vAPP(X0,$o,X1,X2))) )),
% 92.92/13.72 inference(pi_clausification,[],[f17360])).
% 92.92/13.72 thf(f17360,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1))) | ($true = vAPP(sTfun(X0,$o),$o,vPI(X0),X1))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f17359])).
% 92.92/13.72 thf(f17359,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f11163])).
% 92.92/13.72 thf(f11163,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK379(X0),X1)))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vPI(X0),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7660])).
% 92.92/13.72 thf(f23850,plain,(
% 92.92/13.72 spl854_280),
% 92.92/13.72 inference(avatar_split_clause,[],[f17358,f23848])).
% 92.92/13.72 thf(f23848,plain,(
% 92.92/13.72 spl854_280 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_280])])).
% 92.92/13.72 thf(f17358,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f17357])).
% 92.92/13.72 thf(f17357,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,X2)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1))))) )),
% 92.92/13.72 inference(pi_clausification,[],[f17356])).
% 92.92/13.72 thf(f17356,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1))))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f11166])).
% 92.92/13.72 thf(f11166,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7664])).
% 92.92/13.72 thf(f7664,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) | ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1))))) & (! [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK380])],[f7662,f7663])).
% 92.92/13.72 thf(f7663,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (? [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2))) => ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK380(X0),X1)))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f7662,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) | ? [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) & (! [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)))))),
% 92.92/13.72 inference(rectify,[],[f7661])).
% 92.92/13.72 thf(f7661,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ((($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) | ? [X2 : X0] : ($true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)))) & (! [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)))))),
% 92.92/13.72 inference(nnf_transformation,[],[f5125])).
% 92.92/13.72 thf(f5125,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) <=> ! [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2))))),
% 92.92/13.72 inference(rectify,[],[f3462])).
% 92.92/13.72 thf(f3462,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) <=> ! [X3 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))))),
% 92.92/13.72 inference(fool_elimination,[],[f3461])).
% 92.92/13.72 thf(f3461,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (vAPP($o,$o,vNOT,? [X2 : X0] : vAPP(X0,$o,X1,X2)) <=> ! [X3 : X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)))),
% 92.92/13.72 inference(rectify,[],[f89])).
% 92.92/13.72 thf(f89,axiom,(
% 92.92/13.72 ! [X0 : $tType,X7 : X0 > $o] : (vAPP($o,$o,vNOT,? [X4 : X0] : vAPP(X0,$o,X7,X4)) <=> ! [X19 : X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,X7,X19)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__EXISTS__THM)).
% 92.92/13.72 thf(f23846,plain,(
% 92.92/13.72 spl854_279),
% 92.92/13.72 inference(avatar_split_clause,[],[f17355,f23844])).
% 92.92/13.72 thf(f23844,plain,(
% 92.92/13.72 spl854_279 <=> ! [X0 : $tType,X1 : X0 > $o,X3 : X0] : (($false = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK856(X0),X1))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_279])])).
% 92.92/13.72 thf(f17355,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X3 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK856(X0),X1)))) )),
% 92.92/13.72 inference(sigma_clausification,[],[f17354])).
% 92.92/13.72 thf(f17354,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X3 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,X3)) | ($true = vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f17353])).
% 92.92/13.72 thf(f17353,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X3 : X0,X1 : X0 > $o] : (($false = vAPP(X0,$o,X1,X3)) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f11165])).
% 92.92/13.72 thf(f11165,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X3 : X0,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3))) | ($true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7664])).
% 92.92/13.72 thf(f23842,plain,(
% 92.92/13.72 spl854_278),
% 92.92/13.72 inference(avatar_split_clause,[],[f17340,f23840])).
% 92.92/13.72 thf(f23840,plain,(
% 92.92/13.72 spl854_278 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_278])])).
% 92.92/13.72 thf(f17340,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17339])).
% 92.92/13.72 thf(f17339,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f14895])).
% 92.92/13.72 thf(f14895,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f11227,f9122])).
% 92.92/13.72 thf(f11227,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3564])).
% 92.92/13.72 thf(f3564,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f3563])).
% 92.92/13.72 thf(f3563,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),X0)))),
% 92.92/13.72 inference(rectify,[],[f1067])).
% 92.92/13.72 thf(f1067,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)),X134)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__EXP__0)).
% 92.92/13.72 thf(f23838,plain,(
% 92.92/13.72 spl854_277),
% 92.92/13.72 inference(avatar_split_clause,[],[f17222,f23836])).
% 92.92/13.72 thf(f23836,plain,(
% 92.92/13.72 spl854_277 <=> ! [X2 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_277])])).
% 92.92/13.72 thf(f17222,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),$true))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f16265])).
% 92.92/13.72 thf(f16265,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),$true)) | ($true != $true)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11843])).
% 92.92/13.72 thf(f11843,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0)) | ($true != X0) | ($true != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7988])).
% 92.92/13.72 thf(f23834,plain,(
% 92.92/13.72 spl854_276),
% 92.92/13.72 inference(avatar_split_clause,[],[f17221,f23832])).
% 92.92/13.72 thf(f23832,plain,(
% 92.92/13.72 spl854_276 <=> ! [X2 : $o,X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_276])])).
% 92.92/13.72 thf(f17221,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),$true),X0))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f16283])).
% 92.92/13.72 thf(f16283,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),$true),X0)) | ($true != $true)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11854])).
% 92.92/13.72 thf(f11854,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0)) | ($true != X1) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7999])).
% 92.92/13.72 thf(f23830,plain,(
% 92.92/13.72 spl854_275),
% 92.92/13.72 inference(avatar_split_clause,[],[f17220,f23828])).
% 92.92/13.72 thf(f23828,plain,(
% 92.92/13.72 spl854_275 <=> ! [X2 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_275])])).
% 92.92/13.72 thf(f17220,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),$true))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f16309])).
% 92.92/13.72 thf(f16309,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),$true)) | ($true != $true)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11883])).
% 92.92/13.72 thf(f11883,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP39,X2),X1),X0)) | ($true != X0) | ($true != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8014])).
% 92.92/13.72 thf(f23826,plain,(
% 92.92/13.72 ~spl854_274 | ~spl854_13 | ~spl854_190),
% 92.92/13.72 inference(avatar_split_clause,[],[f23412,f23221,f21950,f23823])).
% 92.92/13.72 thf(f21950,plain,(
% 92.92/13.72 spl854_13 <=> ! [X0 : $tType,X1 : X0] : (vAPP(X0,X0,c_2Emarker_2Eunint(X0),X1) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_13])])).
% 92.92/13.72 thf(f23412,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o))) | (~spl854_13 | ~spl854_190)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23411])).
% 92.92/13.72 thf(f23411,plain,(
% 92.92/13.72 ($true = $false) | ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o))) | (~spl854_13 | ~spl854_190)),
% 92.92/13.72 inference(forward_demodulation,[],[f23366,f21951])).
% 92.92/13.72 thf(f21951,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,c_2Emarker_2Eunint(X0),X1) = X1)) ) | ~spl854_13),
% 92.92/13.72 inference(avatar_component_clause,[],[f21950])).
% 92.92/13.72 thf(f23366,plain,(
% 92.92/13.72 ($true != vAPP(sTfun($o,$o),$o,sK169,c_2Emarker_2Eunint($o))) | ($true = vAPP($o,$o,c_2Emarker_2Eunint($o),$false)) | (~spl854_13 | ~spl854_190)),
% 92.92/13.72 inference(superposition,[],[f23222,f21951])).
% 92.92/13.72 thf(f23821,plain,(
% 92.92/13.72 spl854_273),
% 92.92/13.72 inference(avatar_split_clause,[],[f16984,f23819])).
% 92.92/13.72 thf(f23819,plain,(
% 92.92/13.72 spl854_273 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : X0] : (vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2) != vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_273])])).
% 92.92/13.72 thf(f16984,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : ((vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2) != vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f16983])).
% 92.92/13.72 thf(f16983,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,vAPP(tyop_2Esum_2Esum(X0,X1),sTfun(tyop_2Esum_2Esum(X0,X1),$o),vEQ(tyop_2Esum_2Esum(X0,X1)),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f13035])).
% 92.92/13.72 thf(f13035,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,vAPP(tyop_2Esum_2Esum(X0,X1),sTfun(tyop_2Esum_2Esum(X0,X1),$o),vEQ(tyop_2Esum_2Esum(X0,X1)),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4580])).
% 92.92/13.72 thf(f4580,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,vAPP(tyop_2Esum_2Esum(X0,X1),sTfun(tyop_2Esum_2Esum(X0,X1),$o),vEQ(tyop_2Esum_2Esum(X0,X1)),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3))))),
% 92.92/13.72 inference(fool_elimination,[],[f4579])).
% 92.92/13.72 thf(f4579,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : vAPP($o,$o,vNOT,(vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2) = vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3)))),
% 92.92/13.72 inference(rectify,[],[f682])).
% 92.92/13.72 thf(f682,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X8 : X0,X18 : X5] : vAPP($o,$o,vNOT,(vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X8) = vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X18)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2Esum__distinct1)).
% 92.92/13.72 thf(f23817,plain,(
% 92.92/13.72 spl854_272),
% 92.92/13.72 inference(avatar_split_clause,[],[f16691,f23815])).
% 92.92/13.72 thf(f16691,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f13120])).
% 92.92/13.72 thf(f13120,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP110,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8886])).
% 92.92/13.72 thf(f23813,plain,(
% 92.92/13.72 spl854_271),
% 92.92/13.72 inference(avatar_split_clause,[],[f16650,f23811])).
% 92.92/13.72 thf(f23811,plain,(
% 92.92/13.72 spl854_271 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_271])])).
% 92.92/13.72 thf(f16650,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12768])).
% 92.92/13.72 thf(f12768,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8610])).
% 92.92/13.72 thf(f23809,plain,(
% 92.92/13.72 spl854_270),
% 92.92/13.72 inference(avatar_split_clause,[],[f16649,f23807])).
% 92.92/13.72 thf(f23807,plain,(
% 92.92/13.72 spl854_270 <=> ! [X2 : $o,X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_270])])).
% 92.92/13.72 thf(f16649,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12769])).
% 92.92/13.72 thf(f12769,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP96,X2),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8610])).
% 92.92/13.72 thf(f23805,plain,(
% 92.92/13.72 spl854_269),
% 92.92/13.72 inference(avatar_split_clause,[],[f16648,f23803])).
% 92.92/13.72 thf(f23803,plain,(
% 92.92/13.72 spl854_269 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_269])])).
% 92.92/13.72 thf(f16648,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12764])).
% 92.92/13.72 thf(f12764,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP97,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8607])).
% 92.92/13.72 thf(f23801,plain,(
% 92.92/13.72 spl854_268),
% 92.92/13.72 inference(avatar_split_clause,[],[f16647,f23799])).
% 92.92/13.72 thf(f23799,plain,(
% 92.92/13.72 spl854_268 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_268])])).
% 92.92/13.72 thf(f16647,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12760])).
% 92.92/13.72 thf(f12760,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP98,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8604])).
% 92.92/13.72 thf(f23797,plain,(
% 92.92/13.72 spl854_267),
% 92.92/13.72 inference(avatar_split_clause,[],[f16646,f23795])).
% 92.92/13.72 thf(f23795,plain,(
% 92.92/13.72 spl854_267 <=> ! [X2 : $o,X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_267])])).
% 92.92/13.72 thf(f16646,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12757])).
% 92.92/13.72 thf(f12757,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP99,X2),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8601])).
% 92.92/13.72 thf(f23793,plain,(
% 92.92/13.72 spl854_266),
% 92.92/13.72 inference(avatar_split_clause,[],[f16628,f23791])).
% 92.92/13.72 thf(f16628,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12618])).
% 92.92/13.72 thf(f12618,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP87,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8494])).
% 92.92/13.72 thf(f23789,plain,(
% 92.92/13.72 spl854_265),
% 92.92/13.72 inference(avatar_split_clause,[],[f16627,f23787])).
% 92.92/13.72 thf(f16627,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12615])).
% 92.92/13.72 thf(f12615,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP88,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8492])).
% 92.92/13.72 thf(f23785,plain,(
% 92.92/13.72 spl854_264),
% 92.92/13.72 inference(avatar_split_clause,[],[f16624,f23783])).
% 92.92/13.72 thf(f16624,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12610])).
% 92.92/13.72 thf(f12610,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP85,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8490])).
% 92.92/13.72 thf(f23777,plain,(
% 92.92/13.72 spl854_263),
% 92.92/13.72 inference(avatar_split_clause,[],[f16623,f23775])).
% 92.92/13.72 thf(f16623,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12607])).
% 92.92/13.72 thf(f12607,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP86,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8489])).
% 92.92/13.72 thf(f23773,plain,(
% 92.92/13.72 spl854_262),
% 92.92/13.72 inference(avatar_split_clause,[],[f16579,f23771])).
% 92.92/13.72 thf(f16579,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12574])).
% 92.92/13.72 thf(f12574,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP80,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8478])).
% 92.92/13.72 thf(f23769,plain,(
% 92.92/13.72 spl854_261),
% 92.92/13.72 inference(avatar_split_clause,[],[f16570,f23767])).
% 92.92/13.72 thf(f16570,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12567])).
% 92.92/13.72 thf(f12567,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP79,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8476])).
% 92.92/13.72 thf(f23765,plain,(
% 92.92/13.72 spl854_260),
% 92.92/13.72 inference(avatar_split_clause,[],[f16566,f23763])).
% 92.92/13.72 thf(f16566,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12562])).
% 92.92/13.72 thf(f12562,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP77,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8474])).
% 92.92/13.72 thf(f23761,plain,(
% 92.92/13.72 spl854_259),
% 92.92/13.72 inference(avatar_split_clause,[],[f16565,f23759])).
% 92.92/13.72 thf(f16565,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12559])).
% 92.92/13.72 thf(f12559,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP78,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8472])).
% 92.92/13.72 thf(f23757,plain,(
% 92.92/13.72 spl854_258),
% 92.92/13.72 inference(avatar_split_clause,[],[f16561,f23755])).
% 92.92/13.72 thf(f16561,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12554])).
% 92.92/13.72 thf(f12554,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP75,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8470])).
% 92.92/13.72 thf(f23753,plain,(
% 92.92/13.72 spl854_257),
% 92.92/13.72 inference(avatar_split_clause,[],[f16560,f23751])).
% 92.92/13.72 thf(f16560,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12551])).
% 92.92/13.72 thf(f12551,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP76,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8468])).
% 92.92/13.72 thf(f23749,plain,(
% 92.92/13.72 spl854_256),
% 92.92/13.72 inference(avatar_split_clause,[],[f16555,f23747])).
% 92.92/13.72 thf(f16555,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12546])).
% 92.92/13.72 thf(f12546,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP73,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8466])).
% 92.92/13.72 thf(f23745,plain,(
% 92.92/13.72 spl854_255),
% 92.92/13.72 inference(avatar_split_clause,[],[f16554,f23743])).
% 92.92/13.72 thf(f16554,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12543])).
% 92.92/13.72 thf(f12543,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP74,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8465])).
% 92.92/13.72 thf(f23741,plain,(
% 92.92/13.72 spl854_254),
% 92.92/13.72 inference(avatar_split_clause,[],[f16549,f23739])).
% 92.92/13.72 thf(f16549,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12538])).
% 92.92/13.72 thf(f12538,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP71,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8463])).
% 92.92/13.72 thf(f23737,plain,(
% 92.92/13.72 spl854_253 | ~spl854_191),
% 92.92/13.72 inference(avatar_split_clause,[],[f23473,f23225,f23734])).
% 92.92/13.72 thf(f23225,plain,(
% 92.92/13.72 spl854_191 <=> ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,$true)) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_191])])).
% 92.92/13.72 thf(f23473,plain,(
% 92.92/13.72 ($true = vAPP(sTfun($o,$o),$o,sK169,vNOT)) | ~spl854_191),
% 92.92/13.72 inference(not_proxy_clausification,[],[f23472])).
% 92.92/13.72 thf(f23472,plain,(
% 92.92/13.72 ($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK169,vNOT))) | ~spl854_191),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23471])).
% 92.92/13.72 thf(f23471,plain,(
% 92.92/13.72 ($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK169,vNOT))) | ($true = $false) | ~spl854_191),
% 92.92/13.72 inference(boolean_simplification,[],[f23426])).
% 92.92/13.72 thf(f23426,plain,(
% 92.92/13.72 ($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK169,vNOT))) | ($true = vAPP($o,$o,vNOT,$true)) | ~spl854_191),
% 92.92/13.72 inference(primitive_instantiation,[],[f23226])).
% 92.92/13.72 thf(f23226,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0))) | ($true = vAPP($o,$o,X0,$true))) ) | ~spl854_191),
% 92.92/13.72 inference(avatar_component_clause,[],[f23225])).
% 92.92/13.72 thf(f23732,plain,(
% 92.92/13.72 spl854_252),
% 92.92/13.72 inference(avatar_split_clause,[],[f16548,f23730])).
% 92.92/13.72 thf(f16548,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12535])).
% 92.92/13.72 thf(f12535,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP72,X2),X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8461])).
% 92.92/13.72 thf(f23728,plain,(
% 92.92/13.72 spl854_251),
% 92.92/13.72 inference(avatar_split_clause,[],[f16491,f23725])).
% 92.92/13.72 thf(f16491,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(equality_resolution,[],[f16490])).
% 92.92/13.72 thf(f16490,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X1)) )),
% 92.92/13.72 inference(equality_resolution,[],[f15253])).
% 92.92/13.72 thf(f15253,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0)) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != X1)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f12298,f9122,f9122])).
% 92.92/13.72 thf(f12298,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0)) | (c_2Enum_2E0 != X0) | (c_2Enum_2E0 != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8376])).
% 92.92/13.72 thf(f8376,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0)) | (c_2Enum_2E0 != X0) | (c_2Enum_2E0 != X1)) & (((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0))))),
% 92.92/13.72 inference(rectify,[],[f8375])).
% 92.92/13.72 thf(f8375,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)) | (c_2Enum_2E0 != X0) | (c_2Enum_2E0 != X2)) & (((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0))))),
% 92.92/13.72 inference(flattening,[],[f8374])).
% 92.92/13.72 thf(f8374,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)) | ((c_2Enum_2E0 != X0) | (c_2Enum_2E0 != X2))) & (((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6487])).
% 92.92/13.72 thf(f6487,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X2),X0)) <=> ((c_2Enum_2E0 = X0) & (c_2Enum_2E0 = X2)))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f23723,plain,(
% 92.92/13.72 spl854_250),
% 92.92/13.72 inference(avatar_split_clause,[],[f16486,f23721])).
% 92.92/13.72 thf(f23721,plain,(
% 92.92/13.72 spl854_250 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,$true),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_250])])).
% 92.92/13.72 thf(f16486,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,$true),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16485])).
% 92.92/13.72 thf(f16485,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,$true),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(equality_resolution,[],[f12252])).
% 92.92/13.72 thf(f12252,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP60,X2),X1),X0)) | ($true != X2) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8349])).
% 92.92/13.72 thf(f23719,plain,(
% 92.92/13.72 spl854_249),
% 92.92/13.72 inference(avatar_split_clause,[],[f16480,f23717])).
% 92.92/13.72 thf(f23717,plain,(
% 92.92/13.72 spl854_249 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_249])])).
% 92.92/13.72 thf(f16480,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16479])).
% 92.92/13.72 thf(f16479,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f12245])).
% 92.92/13.72 thf(f12245,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP59,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8345])).
% 92.92/13.72 thf(f23715,plain,(
% 92.92/13.72 spl854_248),
% 92.92/13.72 inference(avatar_split_clause,[],[f16477,f23713])).
% 92.92/13.72 thf(f23713,plain,(
% 92.92/13.72 spl854_248 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,$true),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_248])])).
% 92.92/13.72 thf(f16477,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,$true),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16476])).
% 92.92/13.72 thf(f16476,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),$true),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f12235])).
% 92.92/13.72 thf(f12235,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0)) | ($true != X1) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8341])).
% 92.92/13.72 thf(f23711,plain,(
% 92.92/13.72 spl854_247),
% 92.92/13.72 inference(avatar_split_clause,[],[f16474,f23709])).
% 92.92/13.72 thf(f23709,plain,(
% 92.92/13.72 spl854_247 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_247])])).
% 92.92/13.72 thf(f16474,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16473])).
% 92.92/13.72 thf(f16473,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f12237])).
% 92.92/13.72 thf(f12237,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP58,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8341])).
% 92.92/13.72 thf(f23707,plain,(
% 92.92/13.72 spl854_246),
% 92.92/13.72 inference(avatar_split_clause,[],[f16436,f23705])).
% 92.92/13.72 thf(f23705,plain,(
% 92.92/13.72 spl854_246 <=> ! [X0 : $tType,X6 : X0,X2 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK578(X0),X2))) | ($true != vAPP(X0,$o,X2,X6)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_246])])).
% 92.92/13.72 thf(f16436,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X6 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK578(X0),X2))) | ($true != vAPP(X0,$o,X2,X6))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12061])).
% 92.92/13.72 thf(f12061,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X6 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK578(X0),X2))) | ($true != X1) | ($true != vAPP(X0,$o,X2,X6))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8181])).
% 92.92/13.72 thf(f23703,plain,(
% 92.92/13.72 spl854_245),
% 92.92/13.72 inference(avatar_split_clause,[],[f16427,f23701])).
% 92.92/13.72 thf(f23701,plain,(
% 92.92/13.72 spl854_245 <=> ! [X0 : $tType,X6 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK573(X0),X1))) | ($true != vAPP(X0,$o,X1,X6)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_245])])).
% 92.92/13.72 thf(f16427,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X6 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK573(X0),X1))) | ($true != vAPP(X0,$o,X1,X6))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12048])).
% 92.92/13.72 thf(f12048,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X6 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK573(X0),X1))) | ($true != X2) | ($true != vAPP(X0,$o,X1,X6))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8166])).
% 92.92/13.72 thf(f23699,plain,(
% 92.92/13.72 spl854_244),
% 92.92/13.72 inference(avatar_split_clause,[],[f16422,f23697])).
% 92.92/13.72 thf(f23697,plain,(
% 92.92/13.72 spl854_244 <=> ! [X0 : $tType,X6 : X0,X2 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK571(X0),X2))) | ($true != vAPP(X0,$o,X2,X6)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_244])])).
% 92.92/13.72 thf(f16422,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X6 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK571(X0),X2))) | ($true != vAPP(X0,$o,X2,X6))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12045])).
% 92.92/13.72 thf(f12045,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X6 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK571(X0),X2))) | ($true != vAPP(X0,$o,X2,X6)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8160])).
% 92.92/13.72 thf(f23695,plain,(
% 92.92/13.72 spl854_243),
% 92.92/13.72 inference(avatar_split_clause,[],[f16404,f23693])).
% 92.92/13.72 thf(f23693,plain,(
% 92.92/13.72 spl854_243 <=> ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK545(X0),X2))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_243])])).
% 92.92/13.72 thf(f16404,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0] : (($true = vAPP(X0,$o,X2,X3)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK545(X0),X2)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12016])).
% 92.92/13.72 thf(f12016,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : $o] : (($true = vAPP(X0,$o,X2,X3)) | ($true != X1) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK545(X0),X2)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8105])).
% 92.92/13.72 thf(f23687,plain,(
% 92.92/13.72 spl854_242),
% 92.92/13.72 inference(avatar_split_clause,[],[f16387,f23685])).
% 92.92/13.72 thf(f23685,plain,(
% 92.92/13.72 spl854_242 <=> ! [X2 : $o,X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_242])])).
% 92.92/13.72 thf(f16387,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11980])).
% 92.92/13.72 thf(f11980,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP51,X2),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8060])).
% 92.92/13.72 thf(f23683,plain,(
% 92.92/13.72 spl854_241),
% 92.92/13.72 inference(avatar_split_clause,[],[f16381,f23681])).
% 92.92/13.72 thf(f23681,plain,(
% 92.92/13.72 spl854_241 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_241])])).
% 92.92/13.72 thf(f16381,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16380])).
% 92.92/13.72 thf(f16380,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11977])).
% 92.92/13.72 thf(f11977,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP52,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8057])).
% 92.92/13.72 thf(f23679,plain,(
% 92.92/13.72 spl854_240),
% 92.92/13.72 inference(avatar_split_clause,[],[f16374,f23677])).
% 92.92/13.72 thf(f23677,plain,(
% 92.92/13.72 spl854_240 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_240])])).
% 92.92/13.72 thf(f16374,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11960])).
% 92.92/13.72 thf(f11960,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8051])).
% 92.92/13.72 thf(f23675,plain,(
% 92.92/13.72 spl854_239),
% 92.92/13.72 inference(avatar_split_clause,[],[f16373,f23673])).
% 92.92/13.72 thf(f23673,plain,(
% 92.92/13.72 spl854_239 <=> ! [X2 : $o,X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_239])])).
% 92.92/13.72 thf(f16373,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11961])).
% 92.92/13.72 thf(f11961,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP48,X2),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8051])).
% 92.92/13.72 thf(f23671,plain,(
% 92.92/13.72 spl854_238),
% 92.92/13.72 inference(avatar_split_clause,[],[f16369,f23669])).
% 92.92/13.72 thf(f23669,plain,(
% 92.92/13.72 spl854_238 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,$true),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_238])])).
% 92.92/13.72 thf(f16369,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,$true),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16368])).
% 92.92/13.72 thf(f16368,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),$true),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11957])).
% 92.92/13.72 thf(f11957,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) | ($true != X1) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8048])).
% 92.92/13.72 thf(f23667,plain,(
% 92.92/13.72 spl854_237),
% 92.92/13.72 inference(avatar_split_clause,[],[f16367,f23665])).
% 92.92/13.72 thf(f23665,plain,(
% 92.92/13.72 spl854_237 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_237])])).
% 92.92/13.72 thf(f16367,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16366])).
% 92.92/13.72 thf(f16366,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11958])).
% 92.92/13.72 thf(f11958,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP49,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8048])).
% 92.92/13.72 thf(f23663,plain,(
% 92.92/13.72 spl854_236),
% 92.92/13.72 inference(avatar_split_clause,[],[f16362,f23661])).
% 92.92/13.72 thf(f23661,plain,(
% 92.92/13.72 spl854_236 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_236])])).
% 92.92/13.72 thf(f16362,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11941])).
% 92.92/13.72 thf(f11941,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP45,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8042])).
% 92.92/13.72 thf(f23659,plain,(
% 92.92/13.72 spl854_235),
% 92.92/13.72 inference(avatar_split_clause,[],[f16357,f23656])).
% 92.92/13.72 thf(f23656,plain,(
% 92.92/13.72 spl854_235 <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,$true),$true),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_235])])).
% 92.92/13.72 thf(f16357,plain,(
% 92.92/13.72 ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,$true),$true),$true))),
% 92.92/13.72 inference(equality_resolution,[],[f16356])).
% 92.92/13.72 thf(f16356,plain,(
% 92.92/13.72 ( ! [X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),$true),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f16355])).
% 92.92/13.72 thf(f16355,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),$true)) | ($true != X1) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11939])).
% 92.92/13.72 thf(f11939,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP46,X2),X1),X0)) | ($true != X0) | ($true != X1) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8040])).
% 92.92/13.72 thf(f23654,plain,(
% 92.92/13.72 spl854_234),
% 92.92/13.72 inference(avatar_split_clause,[],[f16350,f23652])).
% 92.92/13.72 thf(f23652,plain,(
% 92.92/13.72 spl854_234 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X1),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_234])])).
% 92.92/13.72 thf(f16350,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X1),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16349])).
% 92.92/13.72 thf(f16349,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X1),X1),X2)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11924])).
% 92.92/13.72 thf(f11924,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP44,X0),X1),X2)) | (X0 != X1) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8035])).
% 92.92/13.72 thf(f23650,plain,(
% 92.92/13.72 spl854_233),
% 92.92/13.72 inference(avatar_split_clause,[],[f16346,f23648])).
% 92.92/13.72 thf(f23648,plain,(
% 92.92/13.72 spl854_233 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_233])])).
% 92.92/13.72 thf(f16346,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11920])).
% 92.92/13.72 thf(f11920,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8034])).
% 92.92/13.72 thf(f23646,plain,(
% 92.92/13.72 spl854_232 | ~spl854_57 | ~spl854_211),
% 92.92/13.72 inference(avatar_split_clause,[],[f23601,f23556,f22214,f23643])).
% 92.92/13.72 thf(f22214,plain,(
% 92.92/13.72 spl854_57 <=> ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_57])])).
% 92.92/13.72 thf(f23556,plain,(
% 92.92/13.72 spl854_211 <=> ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,c_2Enum_2EZERO__REP))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_211])])).
% 92.92/13.72 thf(f23601,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,c_2Enum_2EZERO__REP)) | (~spl854_57 | ~spl854_211)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23600])).
% 92.92/13.72 thf(f23600,plain,(
% 92.92/13.72 ($true != $true) | ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,c_2Enum_2EZERO__REP)) | (~spl854_57 | ~spl854_211)),
% 92.92/13.72 inference(superposition,[],[f22215,f23558])).
% 92.92/13.72 thf(f23558,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,c_2Enum_2EZERO__REP)) | ~spl854_211),
% 92.92/13.72 inference(avatar_component_clause,[],[f23556])).
% 92.92/13.72 thf(f22215,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0))) ) | ~spl854_57),
% 92.92/13.72 inference(avatar_component_clause,[],[f22214])).
% 92.92/13.72 thf(f23641,plain,(
% 92.92/13.72 spl854_231),
% 92.92/13.72 inference(avatar_split_clause,[],[f16345,f23639])).
% 92.92/13.72 thf(f23639,plain,(
% 92.92/13.72 spl854_231 <=> ! [X2 : $o,X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_231])])).
% 92.92/13.72 thf(f16345,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11921])).
% 92.92/13.72 thf(f11921,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8034])).
% 92.92/13.72 thf(f23637,plain,(
% 92.92/13.72 spl854_230),
% 92.92/13.72 inference(avatar_split_clause,[],[f16344,f23635])).
% 92.92/13.72 thf(f23635,plain,(
% 92.92/13.72 spl854_230 <=> ! [X2 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_230])])).
% 92.92/13.72 thf(f16344,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11922])).
% 92.92/13.72 thf(f11922,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP41,X2),X1),X0)) | ($true != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8034])).
% 92.92/13.72 thf(f23633,plain,(
% 92.92/13.72 spl854_229),
% 92.92/13.72 inference(avatar_split_clause,[],[f16343,f23631])).
% 92.92/13.72 thf(f23631,plain,(
% 92.92/13.72 spl854_229 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_229])])).
% 92.92/13.72 thf(f16343,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11916])).
% 92.92/13.72 thf(f11916,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP42,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8032])).
% 92.92/13.72 thf(f23629,plain,(
% 92.92/13.72 spl854_228),
% 92.92/13.72 inference(avatar_split_clause,[],[f16342,f23627])).
% 92.92/13.72 thf(f23627,plain,(
% 92.92/13.72 spl854_228 <=> ! [X0 : $o,X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,$true),X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_228])])).
% 92.92/13.72 thf(f16342,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,$true),X1),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11912])).
% 92.92/13.72 thf(f11912,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP43,X2),X1),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8029])).
% 92.92/13.72 thf(f23625,plain,(
% 92.92/13.72 spl854_227),
% 92.92/13.72 inference(avatar_split_clause,[],[f16318,f23623])).
% 92.92/13.72 thf(f23623,plain,(
% 92.92/13.72 spl854_227 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_227])])).
% 92.92/13.72 thf(f16318,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16317])).
% 92.92/13.72 thf(f16317,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11893])).
% 92.92/13.72 thf(f11893,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP40,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8019])).
% 92.92/13.72 thf(f23621,plain,(
% 92.92/13.72 spl854_226),
% 92.92/13.72 inference(avatar_split_clause,[],[f16278,f23619])).
% 92.92/13.72 thf(f23619,plain,(
% 92.92/13.72 spl854_226 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_226])])).
% 92.92/13.72 thf(f16278,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16277])).
% 92.92/13.72 thf(f16277,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11857])).
% 92.92/13.72 thf(f11857,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP38,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7999])).
% 92.92/13.72 thf(f23617,plain,(
% 92.92/13.72 spl854_225),
% 92.92/13.72 inference(avatar_split_clause,[],[f16271,f23615])).
% 92.92/13.72 thf(f23615,plain,(
% 92.92/13.72 spl854_225 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,$true),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_225])])).
% 92.92/13.72 thf(f16271,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,$true),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16270])).
% 92.92/13.72 thf(f16270,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),$true),X0)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11840])).
% 92.92/13.72 thf(f11840,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP37,X2),X1),X0)) | ($true != X1) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7988])).
% 92.92/13.72 thf(f23613,plain,(
% 92.92/13.72 spl854_224),
% 92.92/13.72 inference(avatar_split_clause,[],[f16243,f23611])).
% 92.92/13.72 thf(f23611,plain,(
% 92.92/13.72 spl854_224 <=> ! [X0 : $tType,X2 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK528(X0),X2))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_224])])).
% 92.92/13.72 thf(f16243,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK528(X0),X2)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11826])).
% 92.92/13.72 thf(f11826,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0 > $o,X1 : $o,X5 : X0] : (($true = vAPP(X0,$o,X2,X5)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK528(X0),X2))) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7981])).
% 92.92/13.72 thf(f23609,plain,(
% 92.92/13.72 spl854_223),
% 92.92/13.72 inference(avatar_split_clause,[],[f16236,f23607])).
% 92.92/13.72 thf(f23607,plain,(
% 92.92/13.72 spl854_223 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,$true),$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_223])])).
% 92.92/13.72 thf(f16236,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,$true),$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16235])).
% 92.92/13.72 thf(f16235,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,$true),X1),X0)) | ($true != X1)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11819])).
% 92.92/13.72 thf(f11819,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0)) | ($true != X2) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7973])).
% 92.92/13.72 thf(f23605,plain,(
% 92.92/13.72 spl854_222),
% 92.92/13.72 inference(avatar_split_clause,[],[f16234,f23603])).
% 92.92/13.72 thf(f23603,plain,(
% 92.92/13.72 spl854_222 <=> ! [X2 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),$true),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_222])])).
% 92.92/13.72 thf(f16234,plain,(
% 92.92/13.72 ( ! [X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),$true),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16233])).
% 92.92/13.72 thf(f16233,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),$true)) | ($true != X1)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11820])).
% 92.92/13.72 thf(f11820,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP36,X2),X1),X0)) | ($true != X0) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7973])).
% 92.92/13.72 thf(f23599,plain,(
% 92.92/13.72 spl854_221),
% 92.92/13.72 inference(avatar_split_clause,[],[f16232,f23597])).
% 92.92/13.72 thf(f16232,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK526(X0),X1)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11811])).
% 92.92/13.72 thf(f11811,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK526(X0),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7970])).
% 92.92/13.72 thf(f23595,plain,(
% 92.92/13.72 spl854_220),
% 92.92/13.72 inference(avatar_split_clause,[],[f16224,f23593])).
% 92.92/13.72 thf(f23593,plain,(
% 92.92/13.72 spl854_220 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,$true),X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_220])])).
% 92.92/13.72 thf(f16224,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,$true),X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16223])).
% 92.92/13.72 thf(f16223,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),$true)) | ($true != X2)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11805])).
% 92.92/13.72 thf(f11805,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0)) | ($true != X0) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7962])).
% 92.92/13.72 thf(f23591,plain,(
% 92.92/13.72 spl854_219),
% 92.92/13.72 inference(avatar_split_clause,[],[f16222,f23589])).
% 92.92/13.72 thf(f23589,plain,(
% 92.92/13.72 spl854_219 <=> ! [X2 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),$true),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_219])])).
% 92.92/13.72 thf(f16222,plain,(
% 92.92/13.72 ( ! [X2 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),$true),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16221])).
% 92.92/13.72 thf(f16221,plain,(
% 92.92/13.72 ( ! [X2 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),$true)) | ($true != X1)) )),
% 92.92/13.72 inference(equality_resolution,[],[f11806])).
% 92.92/13.72 thf(f11806,plain,(
% 92.92/13.72 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP35,X2),X1),X0)) | ($true != X0) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7962])).
% 92.92/13.72 thf(f23587,plain,(
% 92.92/13.72 spl854_218),
% 92.92/13.72 inference(avatar_split_clause,[],[f16164,f23585])).
% 92.92/13.72 thf(f16164,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X13 : X0] : (($true = vAPP(X0,$o,X1,X13)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK401(X0),X1)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11441])).
% 92.92/13.72 thf(f11441,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X13 : X0] : (($true = vAPP(X0,$o,X1,X13)) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK401(X0),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7714])).
% 92.92/13.72 thf(f23583,plain,(
% 92.92/13.72 spl854_217),
% 92.92/13.72 inference(avatar_split_clause,[],[f16161,f23581])).
% 92.92/13.72 thf(f16161,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X9 : X0] : (($true = vAPP(X0,$o,X1,X9)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK399(X0),X1)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11444])).
% 92.92/13.72 thf(f11444,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X9 : X0] : (($true = vAPP(X0,$o,X1,X9)) | ($true != X2) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK399(X0),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7714])).
% 92.92/13.72 thf(f23579,plain,(
% 92.92/13.72 spl854_216),
% 92.92/13.72 inference(avatar_split_clause,[],[f16156,f23577])).
% 92.92/13.72 thf(f16156,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK397(X0),X1)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11449])).
% 92.92/13.72 thf(f11449,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK397(X0),X1))) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7714])).
% 92.92/13.72 thf(f23575,plain,(
% 92.92/13.72 spl854_215),
% 92.92/13.72 inference(avatar_split_clause,[],[f16149,f23573])).
% 92.92/13.72 thf(f16149,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X8 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK392(X0),X1))) | ($true != vAPP(X0,$o,X1,X8))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11434])).
% 92.92/13.72 thf(f11434,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X8 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK392(X0),X1))) | ($true != X2) | ($true != vAPP(X0,$o,X1,X8))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7704])).
% 92.92/13.72 thf(f23571,plain,(
% 92.92/13.72 spl854_214),
% 92.92/13.72 inference(avatar_split_clause,[],[f16144,f23569])).
% 92.92/13.72 thf(f16144,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK390(X0),X1))) | ($true != vAPP(X0,$o,X1,X4))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11439])).
% 92.92/13.72 thf(f11439,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : $o,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK390(X0),X1))) | ($true != vAPP(X0,$o,X1,X4)) | ($true != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7704])).
% 92.92/13.72 thf(f23567,plain,(
% 92.92/13.72 spl854_213),
% 92.92/13.72 inference(avatar_split_clause,[],[f15777,f23565])).
% 92.92/13.72 thf(f23565,plain,(
% 92.92/13.72 spl854_213 <=> ! [X0 : $tType,X1 : X0 > X0,X3 : X0] : ((vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3)) = X3) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_213])])).
% 92.92/13.72 thf(f15777,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X3 : X0,X1 : X0 > X0] : ((vAPP(X0,X0,X1,vAPP(X0,X0,X1,X3)) = X3) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10291])).
% 92.92/13.72 thf(f10291,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0] : ((vAPP(X0,X0,X1,X2) = X3) | (vAPP(X0,X0,X1,X3) != X2) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6912])).
% 92.92/13.72 thf(f6912,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > X0] : (! [X2 : X0,X3 : X0] : (((vAPP(X0,X0,X1,X2) = X3) | (vAPP(X0,X0,X1,X3) != X2)) & ((vAPP(X0,X0,X1,X3) = X2) | (vAPP(X0,X0,X1,X2) != X3))) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)))),
% 92.92/13.72 inference(nnf_transformation,[],[f5669])).
% 92.92/13.72 thf(f5669,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > X0] : (! [X2 : X0,X3 : X0] : ((vAPP(X0,X0,X1,X2) = X3) <=> (vAPP(X0,X0,X1,X3) = X2)) | ($true != vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f2776])).
% 92.92/13.72 thf(f2776,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > X0] : (($true = vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1)) => ! [X2 : X0,X3 : X0] : ((vAPP(X0,X0,X1,X2) = X3) <=> (vAPP(X0,X0,X1,X3) = X2)))),
% 92.92/13.72 inference(fool_elimination,[],[f2775])).
% 92.92/13.72 thf(f2775,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > X0] : (vAPP(sTfun(X0,X0),$o,c_2Erelation_2EINVOL(X0),X1) => ! [X2 : X0,X3 : X0] : ((vAPP(X0,X0,X1,X2) = X3) <=> (vAPP(X0,X0,X1,X3) = X2)))),
% 92.92/13.72 inference(rectify,[],[f597])).
% 92.92/13.72 thf(f597,axiom,(
% 92.92/13.72 ! [X139 : $tType,X3 : X139 > X139] : (vAPP(sTfun(X139,X139),$o,c_2Erelation_2EINVOL(X139),X3) => ! [X73 : X139,X79 : X139] : ((vAPP(X139,X139,X3,X73) = X79) <=> (vAPP(X139,X139,X3,X79) = X73)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EINVOL__ONE__ENO)).
% 92.92/13.72 thf(f23563,plain,(
% 92.92/13.72 spl854_212),
% 92.92/13.72 inference(avatar_split_clause,[],[f13815,f23561])).
% 92.92/13.72 thf(f23561,plain,(
% 92.92/13.72 spl854_212 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_212])])).
% 92.92/13.72 thf(f13815,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9525,f13519])).
% 92.92/13.72 thf(f9525,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EODD,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2136])).
% 92.92/13.72 thf(f23559,plain,(
% 92.92/13.72 spl854_211 | ~spl854_181 | ~spl854_183),
% 92.92/13.72 inference(avatar_split_clause,[],[f23316,f23193,f23185,f23556])).
% 92.92/13.72 thf(f23185,plain,(
% 92.92/13.72 spl854_181 <=> ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_181])])).
% 92.92/13.72 thf(f23193,plain,(
% 92.92/13.72 spl854_183 <=> ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_183])])).
% 92.92/13.72 thf(f23316,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,c_2Enum_2EZERO__REP)) | (~spl854_181 | ~spl854_183)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23315])).
% 92.92/13.72 thf(f23315,plain,(
% 92.92/13.72 ($true != $true) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,c_2Enum_2EZERO__REP)) | (~spl854_181 | ~spl854_183)),
% 92.92/13.72 inference(duplicate_literal_removal,[],[f23312])).
% 92.92/13.72 thf(f23312,plain,(
% 92.92/13.72 ($true != $true) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,c_2Enum_2EZERO__REP)) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,c_2Enum_2EZERO__REP)) | (~spl854_181 | ~spl854_183)),
% 92.92/13.72 inference(superposition,[],[f23194,f23186])).
% 92.92/13.72 thf(f23186,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),c_2Enum_2EZERO__REP)) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) ) | ~spl854_181),
% 92.92/13.72 inference(avatar_component_clause,[],[f23185])).
% 92.92/13.72 thf(f23194,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) ) | ~spl854_183),
% 92.92/13.72 inference(avatar_component_clause,[],[f23193])).
% 92.92/13.72 thf(f23554,plain,(
% 92.92/13.72 spl854_210),
% 92.92/13.72 inference(avatar_split_clause,[],[f13716,f23552])).
% 92.92/13.72 thf(f23552,plain,(
% 92.92/13.72 spl854_210 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_210])])).
% 92.92/13.72 thf(f13716,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9376,f9122,f9122])).
% 92.92/13.72 thf(f9376,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),c_2Enum_2E0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4919])).
% 92.92/13.72 thf(f4919,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,c_2Enum_2E0),X0)) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),c_2Enum_2E0)))),
% 92.92/13.72 inference(rectify,[],[f1232])).
% 92.92/13.72 thf(f1232,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,c_2Enum_2E0),X136)) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X136),c_2Enum_2E0)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMIN__0)).
% 92.92/13.72 thf(f23550,plain,(
% 92.92/13.72 spl854_209),
% 92.92/13.72 inference(avatar_split_clause,[],[f13715,f23548])).
% 92.92/13.72 thf(f23548,plain,(
% 92.92/13.72 spl854_209 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_209])])).
% 92.92/13.72 thf(f13715,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9377,f9122,f9122])).
% 92.92/13.72 thf(f9377,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,c_2Enum_2E0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4919])).
% 92.92/13.72 thf(f23546,plain,(
% 92.92/13.72 spl854_208),
% 92.92/13.72 inference(avatar_split_clause,[],[f13712,f23544])).
% 92.92/13.72 thf(f23544,plain,(
% 92.92/13.72 spl854_208 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_208])])).
% 92.92/13.72 thf(f13712,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9372,f9122,f9122])).
% 92.92/13.72 thf(f9372,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,c_2Enum_2E0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4917])).
% 92.92/13.72 thf(f4917,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),c_2Enum_2E0)) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,c_2Enum_2E0),X0)))),
% 92.92/13.72 inference(rectify,[],[f1590])).
% 92.92/13.72 thf(f1590,axiom,(
% 92.92/13.72 ! [X8 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X8),c_2Enum_2E0)) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,c_2Enum_2E0),X8)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0)).
% 92.92/13.72 thf(f23542,plain,(
% 92.92/13.72 spl854_207),
% 92.92/13.72 inference(avatar_split_clause,[],[f13711,f23540])).
% 92.92/13.72 thf(f23540,plain,(
% 92.92/13.72 spl854_207 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_207])])).
% 92.92/13.72 thf(f13711,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9373,f9122,f9122])).
% 92.92/13.72 thf(f9373,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Elcm,X0),c_2Enum_2E0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4917])).
% 92.92/13.72 thf(f23538,plain,(
% 92.92/13.72 spl854_206),
% 92.92/13.72 inference(avatar_split_clause,[],[f13627,f23536])).
% 92.92/13.72 thf(f23536,plain,(
% 92.92/13.72 spl854_206 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_206])])).
% 92.92/13.72 thf(f13627,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9242,f9122])).
% 92.92/13.72 thf(f9242,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Etexp__help,c_2Enum_2E0),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4852])).
% 92.92/13.72 thf(f23534,plain,(
% 92.92/13.72 spl854_205),
% 92.92/13.72 inference(avatar_split_clause,[],[f13619,f23532])).
% 92.92/13.72 thf(f23532,plain,(
% 92.92/13.72 spl854_205 <=> ! [X35 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X35),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_205])])).
% 92.92/13.72 thf(f13619,plain,(
% 92.92/13.72 ( ! [X35 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X35),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9201,f9122,f9121,f9122])).
% 92.92/13.72 thf(f9201,plain,(
% 92.92/13.72 ( ! [X35 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X35),c_2Enum_2E0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6597])).
% 92.92/13.72 thf(f23530,plain,(
% 92.92/13.72 spl854_204),
% 92.92/13.72 inference(avatar_split_clause,[],[f13579,f23528])).
% 92.92/13.72 thf(f23528,plain,(
% 92.92/13.72 spl854_204 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_204])])).
% 92.92/13.72 thf(f13579,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9186,f13512])).
% 92.92/13.72 thf(f9186,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4847])).
% 92.92/13.72 thf(f23526,plain,(
% 92.92/13.72 spl854_203),
% 92.92/13.72 inference(avatar_split_clause,[],[f13578,f23524])).
% 92.92/13.72 thf(f23524,plain,(
% 92.92/13.72 spl854_203 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_203])])).
% 92.92/13.72 thf(f13578,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9182,f9122,f9121,f9122])).
% 92.92/13.72 thf(f9182,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,c_2Enum_2E0),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4846])).
% 92.92/13.72 thf(f23522,plain,(
% 92.92/13.72 spl854_202),
% 92.92/13.72 inference(avatar_split_clause,[],[f13576,f23520])).
% 92.92/13.72 thf(f23520,plain,(
% 92.92/13.72 spl854_202 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_202])])).
% 92.92/13.72 thf(f13576,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9180,f9122,f9122])).
% 92.92/13.72 thf(f9180,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4845])).
% 92.92/13.72 thf(f4845,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X0),X1)),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1)))) & ! [X2 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X2))),
% 92.92/13.72 inference(rectify,[],[f920])).
% 92.92/13.72 thf(f920,axiom,(
% 92.92/13.72 ! [X27 : tyop_2Enum_2Enum,X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X27)),X135) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X27),X135)),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X27),X135)))) & ! [X134 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,c_2Enum_2E0),X134))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB)).
% 92.92/13.72 thf(f23518,plain,(
% 92.92/13.72 spl854_201),
% 92.92/13.72 inference(avatar_split_clause,[],[f13574,f23516])).
% 92.92/13.72 thf(f23516,plain,(
% 92.92/13.72 spl854_201 <=> ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_201])])).
% 92.92/13.72 thf(f13574,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X2))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9178,f9122,f9122])).
% 92.92/13.72 thf(f9178,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,c_2Enum_2E0),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4844])).
% 92.92/13.72 thf(f4844,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,X0),X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X0),X1)),c_2Enum_2E0))) & ! [X2 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,c_2Enum_2E0),X2))),
% 92.92/13.72 inference(rectify,[],[f1711])).
% 92.92/13.72 thf(f1711,axiom,(
% 92.92/13.72 ! [X137 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)),X19) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,X137),X19)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ESBIT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,X137),X19)),c_2Enum_2E0))) & ! [X8 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EBIT__REVERSE,c_2Enum_2E0),X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EBIT__REVERSE__def)).
% 92.92/13.72 thf(f23514,plain,(
% 92.92/13.72 spl854_200),
% 92.92/13.72 inference(avatar_split_clause,[],[f11184,f23512])).
% 92.92/13.72 thf(f23512,plain,(
% 92.92/13.72 spl854_200 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,X0),X1),X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_200])])).
% 92.92/13.72 thf(f11184,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,X0),X1),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3478])).
% 92.92/13.72 thf(f3478,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,X0),X1),X1))),
% 92.92/13.72 inference(fool_elimination,[],[f3477])).
% 92.92/13.72 thf(f3477,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,X0),X1),X1)),
% 92.92/13.72 inference(rectify,[],[f1308])).
% 92.92/13.72 thf(f1308,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Earithmetic_2EMODEQ,X136),X4),X4)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__REFL)).
% 92.92/13.72 thf(f23510,plain,(
% 92.92/13.72 spl854_199),
% 92.92/13.72 inference(avatar_split_clause,[],[f11152,f23508])).
% 92.92/13.72 thf(f11152,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),X1))) | ($true != vAPP(X0,$o,X1,X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7650])).
% 92.92/13.72 thf(f23506,plain,(
% 92.92/13.72 spl854_198),
% 92.92/13.72 inference(avatar_split_clause,[],[f10393,f23504])).
% 92.92/13.72 thf(f10393,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5746])).
% 92.92/13.72 thf(f5746,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (! [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2926])).
% 92.92/13.72 thf(f2926,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1))) => ! [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)))),
% 92.92/13.72 inference(fool_elimination,[],[f2925])).
% 92.92/13.72 thf(f2925,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : (vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X1)) => ! [X2 : X0] : vAPP(X0,$o,X1,X2))),
% 92.92/13.72 inference(rectify,[],[f273])).
% 92.92/13.72 thf(f273,axiom,(
% 92.92/13.72 ! [X0 : $tType,X26 : X0 > $o] : (vAPP(X0,$o,X26,vAPP(sTfun(X0,$o),X0,c_2EnormalForms_2EUNIV__POINT(X0),X26)) => ! [X4 : X0] : vAPP(X0,$o,X26,X4))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EnormalForms_2EUNIV__POINT__DEF)).
% 92.92/13.72 thf(f23502,plain,(
% 92.92/13.72 spl854_197),
% 92.92/13.72 inference(avatar_split_clause,[],[f9822,f23500])).
% 92.92/13.72 thf(f23500,plain,(
% 92.92/13.72 spl854_197 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X0),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_197])])).
% 92.92/13.72 thf(f9822,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2484])).
% 92.92/13.72 thf(f2484,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X0),X0))),
% 92.92/13.72 inference(fool_elimination,[],[f2483])).
% 92.92/13.72 thf(f2483,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X0),X0),X0)),
% 92.92/13.72 inference(rectify,[],[f1560])).
% 92.92/13.72 thf(f1560,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),c_2Egcd_2Eis__gcd,X72),X72),X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF)).
% 92.92/13.72 thf(f23498,plain,(
% 92.92/13.72 spl854_196),
% 92.92/13.72 inference(avatar_split_clause,[],[f9797,f23496])).
% 92.92/13.72 thf(f9797,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6834])).
% 92.92/13.72 thf(f6834,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0)) = X0)),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK196,sK197])],[f4950,f6833])).
% 92.92/13.72 thf(f6833,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X2) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK196,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK197,X0)) = X0))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f4950,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ? [X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X2) = X0)),
% 92.92/13.72 inference(rectify,[],[f1677])).
% 92.92/13.72 thf(f1677,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : ? [X4 : tyop_2Enum_2Enum,X12 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X4),X12) = X136)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enpair__cases)).
% 92.92/13.72 thf(f23494,plain,(
% 92.92/13.72 spl854_195),
% 92.92/13.72 inference(avatar_split_clause,[],[f9383,f23492])).
% 92.92/13.72 thf(f23492,plain,(
% 92.92/13.72 spl854_195 <=> ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X1)) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_195])])).
% 92.92/13.72 thf(f9383,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X1)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4922])).
% 92.92/13.72 thf(f4922,plain,(
% 92.92/13.72 ! [X0 : $tType] : (! [X1 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X1)) = X1) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))))),
% 92.92/13.72 inference(rectify,[],[f713])).
% 92.92/13.72 thf(f713,axiom,(
% 92.92/13.72 ! [X0 : $tType] : (! [X8 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME(tyop_2Eoption_2Eoption(X0)),X8)) = X8) & (c_2Eoption_2ENONE(X0) = vAPP(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(tyop_2Eoption_2Eoption(X0)))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTION__JOIN__DEF)).
% 92.92/13.72 thf(f23490,plain,(
% 92.92/13.72 spl854_194),
% 92.92/13.72 inference(avatar_split_clause,[],[f9318,f23488])).
% 92.92/13.72 thf(f23488,plain,(
% 92.92/13.72 spl854_194 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_194])])).
% 92.92/13.72 thf(f9318,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4891])).
% 92.92/13.72 thf(f4891,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X0)) = X0)),
% 92.92/13.72 inference(rectify,[],[f1678])).
% 92.92/13.72 thf(f1678,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,X136)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,X136)) = X136)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enpair)).
% 92.92/13.72 thf(f23337,plain,(
% 92.92/13.72 ~spl854_193 | ~spl854_44 | ~spl854_184),
% 92.92/13.72 inference(avatar_split_clause,[],[f23322,f23197,f22112,f23334])).
% 92.92/13.72 thf(f23334,plain,(
% 92.92/13.72 spl854_193 <=> (sK124 = vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_193])])).
% 92.92/13.72 thf(f23197,plain,(
% 92.92/13.72 spl854_184 <=> ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_184])])).
% 92.92/13.72 thf(f23322,plain,(
% 92.92/13.72 (sK124 != vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)) | (~spl854_44 | ~spl854_184)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f23317])).
% 92.92/13.72 thf(f23317,plain,(
% 92.92/13.72 ($true = $false) | (sK124 != vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)) | (~spl854_44 | ~spl854_184)),
% 92.92/13.72 inference(constrained_superposition,[],[f23198,f22114])).
% 92.92/13.72 thf(f23198,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X1))) ) | ~spl854_184),
% 92.92/13.72 inference(avatar_component_clause,[],[f23197])).
% 92.92/13.72 thf(f23231,plain,(
% 92.92/13.72 spl854_192 | ~spl854_10 | ~spl854_71),
% 92.92/13.72 inference(avatar_split_clause,[],[f22358,f22298,f21932,f23229])).
% 92.92/13.72 thf(f23229,plain,(
% 92.92/13.72 spl854_192 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_192])])).
% 92.92/13.72 thf(f21932,plain,(
% 92.92/13.72 spl854_10 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_10])])).
% 92.92/13.72 thf(f22358,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))) ) | (~spl854_10 | ~spl854_71)),
% 92.92/13.72 inference(superposition,[],[f21933,f22299])).
% 92.92/13.72 thf(f21933,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != X0)) ) | ~spl854_10),
% 92.92/13.72 inference(avatar_component_clause,[],[f21932])).
% 92.92/13.72 thf(f23227,plain,(
% 92.92/13.72 spl854_191),
% 92.92/13.72 inference(avatar_split_clause,[],[f18509,f23225])).
% 92.92/13.72 thf(f18509,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,$true)) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13956,f13591])).
% 92.92/13.72 thf(f13956,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9692,f13514])).
% 92.92/13.72 thf(f9692,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,c_2Ebool_2ET)) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6748])).
% 92.92/13.72 thf(f6748,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : ((! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET))) & ((($true = vAPP($o,$o,X0,c_2Ebool_2EF)) & ($true = vAPP($o,$o,X0,c_2Ebool_2ET))) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f6746,f6747])).
% 92.92/13.72 thf(f6747,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : (? [X2 : $o] : ($true != vAPP($o,$o,X0,X2)) => ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f6746,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : ((! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET))) & ((($true = vAPP($o,$o,X0,c_2Ebool_2EF)) & ($true = vAPP($o,$o,X0,c_2Ebool_2ET))) | ? [X2 : $o] : ($true != vAPP($o,$o,X0,X2))))),
% 92.92/13.72 inference(rectify,[],[f6745])).
% 92.92/13.72 thf(f6745,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : ((! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) | ($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET))) & ((($true = vAPP($o,$o,X0,c_2Ebool_2EF)) & ($true = vAPP($o,$o,X0,c_2Ebool_2ET))) | ? [X1 : $o] : ($true != vAPP($o,$o,X0,X1))))),
% 92.92/13.72 inference(flattening,[],[f6744])).
% 92.92/13.72 thf(f6744,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : ((! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) | (($true != vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,c_2Ebool_2ET)))) & ((($true = vAPP($o,$o,X0,c_2Ebool_2EF)) & ($true = vAPP($o,$o,X0,c_2Ebool_2ET))) | ? [X1 : $o] : ($true != vAPP($o,$o,X0,X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f2318])).
% 92.92/13.72 thf(f2318,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : (! [X1 : $o] : ($true = vAPP($o,$o,X0,X1)) <=> (($true = vAPP($o,$o,X0,c_2Ebool_2EF)) & ($true = vAPP($o,$o,X0,c_2Ebool_2ET))))),
% 92.92/13.72 inference(fool_elimination,[],[f2317])).
% 92.92/13.72 thf(f2317,plain,(
% 92.92/13.72 ! [X0 : $o > $o] : (! [X1 : $o] : vAPP($o,$o,X0,X1) <=> (vAPP($o,$o,X0,c_2Ebool_2EF) & vAPP($o,$o,X0,c_2Ebool_2ET)))),
% 92.92/13.72 inference(rectify,[],[f169])).
% 92.92/13.72 thf(f169,axiom,(
% 92.92/13.72 ! [X7 : $o > $o] : (! [X49 : $o] : vAPP($o,$o,X7,X49) <=> (vAPP($o,$o,X7,c_2Ebool_2EF) & vAPP($o,$o,X7,c_2Ebool_2ET)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__BOOL)).
% 92.92/13.72 thf(f23223,plain,(
% 92.92/13.72 spl854_190),
% 92.92/13.72 inference(avatar_split_clause,[],[f18508,f23221])).
% 92.92/13.72 thf(f18508,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,$false)) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f13955,f18095])).
% 92.92/13.72 thf(f13955,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9693,f13520])).
% 92.92/13.72 thf(f9693,plain,(
% 92.92/13.72 ( ! [X0 : $o > $o] : (($true = vAPP($o,$o,X0,c_2Ebool_2EF)) | ($true != vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,sK169,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6748])).
% 92.92/13.72 thf(f23219,plain,(
% 92.92/13.72 spl854_189),
% 92.92/13.72 inference(avatar_split_clause,[],[f17351,f23217])).
% 92.92/13.72 thf(f17351,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X1))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f11193])).
% 92.92/13.72 thf(f11193,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3496])).
% 92.92/13.72 thf(f3496,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X1)))),
% 92.92/13.72 inference(fool_elimination,[],[f3495])).
% 92.92/13.72 thf(f3495,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X1),X1))),
% 92.92/13.72 inference(rectify,[],[f1894])).
% 92.92/13.72 thf(f1894,axiom,(
% 92.92/13.72 ! [X0 : $tType,X111 : X0 > $o] : vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2EPSUBSET(X0),X111),X111))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__IRREFL)).
% 92.92/13.72 thf(f23215,plain,(
% 92.92/13.72 spl854_188),
% 92.92/13.72 inference(avatar_split_clause,[],[f15255,f23213])).
% 92.92/13.72 thf(f23213,plain,(
% 92.92/13.72 spl854_188 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_188])])).
% 92.92/13.72 thf(f15255,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f12296,f9122])).
% 92.92/13.72 thf(f12296,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8376])).
% 92.92/13.72 thf(f23211,plain,(
% 92.92/13.72 spl854_187),
% 92.92/13.72 inference(avatar_split_clause,[],[f15254,f23209])).
% 92.92/13.72 thf(f23209,plain,(
% 92.92/13.72 spl854_187 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_187])])).
% 92.92/13.72 thf(f15254,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f12297,f9122])).
% 92.92/13.72 thf(f12297,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),sP61,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8376])).
% 92.92/13.72 thf(f23207,plain,(
% 92.92/13.72 spl854_186),
% 92.92/13.72 inference(avatar_split_clause,[],[f14415,f23205])).
% 92.92/13.72 thf(f23205,plain,(
% 92.92/13.72 spl854_186 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_186])])).
% 92.92/13.72 thf(f14415,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10447,f9122])).
% 92.92/13.72 thf(f10447,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6981])).
% 92.92/13.72 thf(f6981,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1)) | (X0 != X1)) & ((X0 = X1) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f5110])).
% 92.92/13.72 thf(f5110,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X1)) <=> (X0 = X1))),
% 92.92/13.72 inference(rectify,[],[f1253])).
% 92.92/13.72 thf(f1253,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X136),X27)) <=> (X27 = X136))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__EQ__0)).
% 92.92/13.72 thf(f23203,plain,(
% 92.92/13.72 spl854_185),
% 92.92/13.72 inference(avatar_split_clause,[],[f14246,f23201])).
% 92.92/13.72 thf(f23201,plain,(
% 92.92/13.72 spl854_185 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_185])])).
% 92.92/13.72 thf(f14246,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10189,f9122])).
% 92.92/13.72 thf(f10189,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5537])).
% 92.92/13.72 thf(f5537,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) != X0))),
% 92.92/13.72 inference(ennf_transformation,[],[f5104])).
% 92.92/13.72 thf(f5104,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X0),X1) = X0) => (c_2Enum_2E0 = X1))),
% 92.92/13.72 inference(rectify,[],[f975])).
% 92.92/13.72 thf(f975,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,X134),X137) = X134) => (c_2Enum_2E0 = X137))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__INV__0)).
% 92.92/13.72 thf(f23199,plain,(
% 92.92/13.72 spl854_184),
% 92.92/13.72 inference(avatar_split_clause,[],[f11183,f23197])).
% 92.92/13.72 thf(f11183,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3476])).
% 92.92/13.72 thf(f3476,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X1))),
% 92.92/13.72 inference(fool_elimination,[],[f3475])).
% 92.92/13.72 thf(f3475,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X1),X1)),
% 92.92/13.72 inference(rectify,[],[f1882])).
% 92.92/13.72 thf(f1882,axiom,(
% 92.92/13.72 ! [X0 : $tType,X111 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),X111),X111)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__REFL)).
% 92.92/13.72 thf(f23195,plain,(
% 92.92/13.72 spl854_183),
% 92.92/13.72 inference(avatar_split_clause,[],[f9720,f23193])).
% 92.92/13.72 thf(f9720,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6788])).
% 92.92/13.72 thf(f23191,plain,(
% 92.92/13.72 spl854_182 | ~spl854_29 | ~spl854_71),
% 92.92/13.72 inference(avatar_split_clause,[],[f22356,f22298,f22036,f23189])).
% 92.92/13.72 thf(f23189,plain,(
% 92.92/13.72 spl854_182 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_182])])).
% 92.92/13.72 thf(f22036,plain,(
% 92.92/13.72 spl854_29 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_29])])).
% 92.92/13.72 thf(f22356,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))) ) | (~spl854_29 | ~spl854_71)),
% 92.92/13.72 inference(superposition,[],[f22037,f22299])).
% 92.92/13.72 thf(f22037,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) ) | ~spl854_29),
% 92.92/13.72 inference(avatar_component_clause,[],[f22036])).
% 92.92/13.72 thf(f23187,plain,(
% 92.92/13.72 spl854_181),
% 92.92/13.72 inference(avatar_split_clause,[],[f9718,f23185])).
% 92.92/13.72 thf(f9718,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),sK183,X0),c_2Enum_2EZERO__REP))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6788])).
% 92.92/13.72 thf(f23183,plain,(
% 92.92/13.72 spl854_180),
% 92.92/13.72 inference(avatar_split_clause,[],[f9571,f23181])).
% 92.92/13.72 thf(f9571,plain,(
% 92.92/13.72 ( ! [X3 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6673])).
% 92.92/13.72 thf(f6673,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0)))) | ! [X3 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f6671,f6672])).
% 92.92/13.72 thf(f6672,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) => (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK155,X0)))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f6671,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) | ! [X3 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X3)))),
% 92.92/13.72 inference(rectify,[],[f5449])).
% 92.92/13.72 thf(f5449,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : (! [X3 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X3))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X2))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ! [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f2180])).
% 92.92/13.72 thf(f2180,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) => ? [X2 : tyop_2Enum_2Enum] : (! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X2)) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X3)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))))),
% 92.92/13.72 inference(fool_elimination,[],[f2179])).
% 92.92/13.72 thf(f2179,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X1) => ? [X2 : tyop_2Enum_2Enum] : (! [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X2) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X3))) & vAPP(tyop_2Enum_2Enum,$o,X0,X2)))),
% 92.92/13.72 inference(rectify,[],[f1034])).
% 92.92/13.72 thf(f1034,axiom,(
% 92.92/13.72 ! [X7 : tyop_2Enum_2Enum > $o] : (? [X137 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X137) => ? [X135 : tyop_2Enum_2Enum] : (! [X307 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X307),X135) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X7,X307))) & vAPP(tyop_2Enum_2Enum,$o,X7,X135)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EWOP)).
% 92.92/13.72 thf(f23179,plain,(
% 92.92/13.72 spl854_179),
% 92.92/13.72 inference(avatar_split_clause,[],[f9569,f23177])).
% 92.92/13.72 thf(f9569,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Enum_2Enum,X0 : tyop_2Enum_2Enum > $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0))) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6670])).
% 92.92/13.72 thf(f6670,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X1))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X1),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)))) | ! [X2 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)))),
% 92.92/13.72 inference(rectify,[],[f5448])).
% 92.92/13.72 thf(f5448,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : ((! [X2 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)))) | ! [X1 : tyop_2Enum_2Enum] : ($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f2178])).
% 92.92/13.72 thf(f2178,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) => (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0))) => ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2)))) & ($true = vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)))))),
% 92.92/13.72 inference(fool_elimination,[],[f2177])).
% 92.92/13.72 thf(f2177,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X1 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X1) => (! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0)) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X0,X2))) & vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X0))))),
% 92.92/13.72 inference(rectify,[],[f1428])).
% 92.92/13.72 thf(f1428,axiom,(
% 92.92/13.72 ! [X26 : tyop_2Enum_2Enum > $o] : (? [X137 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X26,X137) => (! [X135 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X135),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X26)) => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,X26,X135))) & vAPP(tyop_2Enum_2Enum,$o,X26,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,X26))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2ELEAST__EXISTS__IMP)).
% 92.92/13.72 thf(f23175,plain,(
% 92.92/13.72 spl854_178),
% 92.92/13.72 inference(avatar_split_clause,[],[f9563,f23173])).
% 92.92/13.72 thf(f9563,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum > $o,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6657])).
% 92.92/13.72 thf(f6657,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0))) & ! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0))))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK148])],[f6655,f6656])).
% 92.92/13.72 thf(f6656,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X2)))) => (($true != vAPP(tyop_2Enum_2Enum,$o,X0,vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0))) & ! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,sK148,X0))))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f6655,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1)) | ? [X2 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X2)) & ! [X3 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X3),X2)))))),
% 92.92/13.72 inference(rectify,[],[f5443])).
% 92.92/13.72 thf(f5443,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)) | ? [X1 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,X0,X1)) & ! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2168])).
% 92.92/13.72 thf(f2168,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1)) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X2))) => ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X1))) => ! [X3 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,X0,X3)))),
% 92.92/13.72 inference(fool_elimination,[],[f2167])).
% 92.92/13.72 thf(f2167,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum > $o] : (! [X1 : tyop_2Enum_2Enum] : (! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X2),X1) => vAPP(tyop_2Enum_2Enum,$o,X0,X2)) => vAPP(tyop_2Enum_2Enum,$o,X0,X1)) => ! [X3 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X0,X3))),
% 92.92/13.72 inference(rectify,[],[f1035])).
% 92.92/13.72 thf(f1035,axiom,(
% 92.92/13.72 ! [X7 : tyop_2Enum_2Enum > $o] : (! [X137 : tyop_2Enum_2Enum] : (! [X104 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X104),X137) => vAPP(tyop_2Enum_2Enum,$o,X7,X104)) => vAPP(tyop_2Enum_2Enum,$o,X7,X137)) => ! [X298 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,X7,X298))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ECOMPLETE__INDUCTION)).
% 92.92/13.72 thf(f23171,plain,(
% 92.92/13.72 spl854_177),
% 92.92/13.72 inference(avatar_split_clause,[],[f9484,f23169])).
% 92.92/13.72 thf(f23169,plain,(
% 92.92/13.72 spl854_177 <=> ! [X0 : $tType,X2 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X2)) = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_177])])).
% 92.92/13.72 thf(f9484,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : tyop_2Eoption_2Eoption(X0)] : ((vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X2)) = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6620])).
% 92.92/13.72 thf(f6620,plain,(
% 92.92/13.72 ! [X0 : $tType] : (! [X1 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : ((($true = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o,vAPP($o,sTfun(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o),kCOMB,c_2Ebool_2ET),X1)) | (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),X1)) != X1)) & ((vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),X1)) = X1) | ($true != vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o,vAPP($o,sTfun(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o),kCOMB,c_2Ebool_2ET),X1)))) & ! [X2 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X2)) = X2))),
% 92.92/13.72 inference(nnf_transformation,[],[f4934])).
% 92.92/13.72 thf(f4934,plain,(
% 92.92/13.72 ! [X0 : $tType] : (! [X1 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : (($true = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o,vAPP($o,sTfun(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o),kCOMB,c_2Ebool_2ET),X1)) <=> (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),X1)) = X1)) & ! [X2 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X2)) = X2))),
% 92.92/13.72 inference(rectify,[],[f2126])).
% 92.92/13.72 thf(f2126,plain,(
% 92.92/13.72 ! [X0 : $tType] : (! [X1 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : (($true = vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o,vAPP($o,sTfun(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o),kCOMB,c_2Ebool_2ET),X1)) <=> (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),X1)) = X1)) & ! [X3 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X3)) = X3))),
% 92.92/13.72 inference(fool_elimination,[],[f2125])).
% 92.92/13.72 thf(f2125,plain,(
% 92.92/13.72 ! [X0 : $tType] : (! [X1 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o,(^[X2 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : (c_2Ebool_2ET)),X1) <=> (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),X1)) = X1)) & ! [X3 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X3)) = X3))),
% 92.92/13.72 inference(rectify,[],[f704])).
% 92.92/13.72 thf(f704,axiom,(
% 92.92/13.72 ! [X0 : $tType] : (! [X112 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),$o,(^[X19 : tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone)] : (c_2Ebool_2ET)),X112) <=> (vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),X112)) = X112)) & ! [X72 : tyop_2Eoption_2Eoption(X0)] : (vAPP(tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__ABS(X0),vAPP(tyop_2Eoption_2Eoption(X0),tyop_2Esum_2Esum(X0,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP(X0),X72)) = X72))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__REP__ABS__DEF)).
% 92.92/13.72 thf(f23141,plain,(
% 92.92/13.72 spl854_176 | ~spl854_23 | ~spl854_58),
% 92.92/13.72 inference(avatar_split_clause,[],[f22270,f22218,f22010,f23139])).
% 92.92/13.72 thf(f23139,plain,(
% 92.92/13.72 spl854_176 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_176])])).
% 92.92/13.72 thf(f22218,plain,(
% 92.92/13.72 spl854_58 <=> ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_58])])).
% 92.92/13.72 thf(f22270,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))) ) | (~spl854_23 | ~spl854_58)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f22264])).
% 92.92/13.72 thf(f22264,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true != $true) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))) ) | (~spl854_23 | ~spl854_58)),
% 92.92/13.72 inference(superposition,[],[f22219,f22011])).
% 92.92/13.72 thf(f22219,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) ) | ~spl854_58),
% 92.92/13.72 inference(avatar_component_clause,[],[f22218])).
% 92.92/13.72 thf(f23090,plain,(
% 92.92/13.72 spl854_175 | ~spl854_159),
% 92.92/13.72 inference(avatar_split_clause,[],[f22948,f22944,f23087])).
% 92.92/13.72 thf(f22948,plain,(
% 92.92/13.72 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_159),
% 92.92/13.72 inference(forward_demodulation,[],[f22946,f18124])).
% 92.92/13.72 thf(f22946,plain,(
% 92.92/13.72 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ~spl854_159),
% 92.92/13.72 inference(avatar_component_clause,[],[f22944])).
% 92.92/13.72 thf(f23085,plain,(
% 92.92/13.72 spl854_174 | ~spl854_158),
% 92.92/13.72 inference(avatar_split_clause,[],[f22942,f22938,f23082])).
% 92.92/13.72 thf(f23082,plain,(
% 92.92/13.72 spl854_174 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_174])])).
% 92.92/13.72 thf(f22938,plain,(
% 92.92/13.72 spl854_158 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_158])])).
% 92.92/13.72 thf(f22942,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ~spl854_158),
% 92.92/13.72 inference(forward_demodulation,[],[f22940,f18124])).
% 92.92/13.72 thf(f22940,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) | ~spl854_158),
% 92.92/13.72 inference(avatar_component_clause,[],[f22938])).
% 92.92/13.72 thf(f23080,plain,(
% 92.92/13.72 spl854_173 | ~spl854_27 | ~spl854_58),
% 92.92/13.72 inference(avatar_split_clause,[],[f22269,f22218,f22027,f23078])).
% 92.92/13.72 thf(f23078,plain,(
% 92.92/13.72 spl854_173 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_173])])).
% 92.92/13.72 thf(f22027,plain,(
% 92.92/13.72 spl854_27 <=> ! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_27])])).
% 92.92/13.72 thf(f22269,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0)))) ) | (~spl854_27 | ~spl854_58)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f22265])).
% 92.92/13.72 thf(f22265,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true != $true) | ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0)))) ) | (~spl854_27 | ~spl854_58)),
% 92.92/13.72 inference(superposition,[],[f22219,f22028])).
% 92.92/13.72 thf(f22028,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1)))) ) | ~spl854_27),
% 92.92/13.72 inference(avatar_component_clause,[],[f22027])).
% 92.92/13.72 thf(f23018,plain,(
% 92.92/13.72 spl854_172 | ~spl854_26 | ~spl854_28),
% 92.92/13.72 inference(avatar_split_clause,[],[f22073,f22031,f22023,f23016])).
% 92.92/13.72 thf(f23016,plain,(
% 92.92/13.72 spl854_172 <=> ! [X0 : $o] : ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_172])])).
% 92.92/13.72 thf(f22073,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0)))) ) | (~spl854_26 | ~spl854_28)),
% 92.92/13.72 inference(superposition,[],[f22033,f22024])).
% 92.92/13.72 thf(f22999,plain,(
% 92.92/13.72 spl854_171),
% 92.92/13.72 inference(avatar_split_clause,[],[f21859,f22996])).
% 92.92/13.72 thf(f21859,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.72 inference(forward_demodulation,[],[f21858,f18124])).
% 92.92/13.72 thf(f21858,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.72 inference(forward_demodulation,[],[f15654,f9293])).
% 92.92/13.72 thf(f15654,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))),
% 92.92/13.72 inference(definition_unfolding,[],[f13510,f13512])).
% 92.92/13.72 thf(f13510,plain,(
% 92.92/13.72 (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = $true)),
% 92.92/13.72 inference(cnf_transformation,[],[f4832])).
% 92.92/13.72 thf(f4832,plain,(
% 92.92/13.72 (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = $true)),
% 92.92/13.72 inference(fool_elimination,[],[f4831])).
% 92.92/13.72 thf(f4831,plain,(
% 92.92/13.72 vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.92/13.72 inference(rectify,[],[f1483])).
% 92.92/13.72 thf(f1483,axiom,(
% 92.92/13.72 vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EPRIME__3)).
% 92.92/13.72 thf(f22994,plain,(
% 92.92/13.72 spl854_170),
% 92.92/13.72 inference(avatar_split_clause,[],[f19195,f22992])).
% 92.92/13.72 thf(f22992,plain,(
% 92.92/13.72 spl854_170 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true = X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_170])])).
% 92.92/13.72 thf(f19195,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true = X1)) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f19194])).
% 92.92/13.72 thf(f19194,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = $false) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true = X1)) )),
% 92.92/13.72 inference(forward_demodulation,[],[f17505,f17793])).
% 92.92/13.72 thf(f17505,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ($true = X1)) )),
% 92.92/13.72 inference(binary_proxy_clausification,[],[f17504])).
% 92.92/13.72 thf(f17504,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f14459])).
% 92.92/13.72 thf(f14459,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10524,f13520])).
% 92.92/13.72 thf(f10524,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7027])).
% 92.92/13.72 thf(f7027,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ((c_2Ebool_2EF != $true) & ($true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0))))) & ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))))),
% 92.92/13.72 inference(flattening,[],[f7026])).
% 92.92/13.72 thf(f7026,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0)) | ((c_2Ebool_2EF != $true) & ($true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0))))) & (((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP12,X1),X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6400])).
% 92.92/13.72 thf(f22990,plain,(
% 92.92/13.72 spl854_169),
% 92.92/13.72 inference(avatar_split_clause,[],[f19192,f22988])).
% 92.92/13.72 thf(f22988,plain,(
% 92.92/13.72 spl854_169 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_169])])).
% 92.92/13.72 thf(f19192,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f19191])).
% 92.92/13.72 thf(f19191,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = $false) | ($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f17509,f17793])).
% 92.92/13.72 thf(f17509,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f14457])).
% 92.92/13.72 thf(f14457,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10519,f13520])).
% 92.92/13.72 thf(f10519,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7025])).
% 92.92/13.72 thf(f7025,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ((c_2Ebool_2EF != $true) & ($true = vAPP($o,$o,vNOT,X0)) & ((c_2Ebool_2EF = $true) | ($true != X1)))) & ((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,X0)) | ((c_2Ebool_2EF != $true) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))))),
% 92.92/13.72 inference(flattening,[],[f7024])).
% 92.92/13.72 thf(f7024,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ((c_2Ebool_2EF != $true) & ($true = vAPP($o,$o,vNOT,X0)) & ((c_2Ebool_2EF = $true) | ($true != X1)))) & (((c_2Ebool_2EF = $true) | ($true != vAPP($o,$o,vNOT,X0)) | ((c_2Ebool_2EF != $true) & ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6401])).
% 92.92/13.72 thf(f22986,plain,(
% 92.92/13.72 spl854_168),
% 92.92/13.72 inference(avatar_split_clause,[],[f18124,f22983])).
% 92.92/13.72 thf(f22981,plain,(
% 92.92/13.72 spl854_167),
% 92.92/13.72 inference(avatar_split_clause,[],[f17625,f22979])).
% 92.92/13.72 thf(f17625,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10140])).
% 92.92/13.72 thf(f10140,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2602])).
% 92.92/13.72 thf(f2602,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)))) & ! [X3 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3))))),
% 92.92/13.72 inference(fool_elimination,[],[f2601])).
% 92.92/13.72 thf(f2601,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0] : vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2))) & ! [X3 : X1] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3)))),
% 92.92/13.72 inference(rectify,[],[f665])).
% 92.92/13.72 thf(f665,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType] : (! [X18 : X0] : vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISR(X0,X5),vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X18))) & ! [X8 : X5] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISR(X0,X5),vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X8)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EISR)).
% 92.92/13.72 thf(f22977,plain,(
% 92.92/13.72 spl854_166),
% 92.92/13.72 inference(avatar_split_clause,[],[f17624,f22975])).
% 92.92/13.72 thf(f17624,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : (($false = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10142])).
% 92.92/13.72 thf(f10142,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2604])).
% 92.92/13.72 thf(f2604,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)))) & ! [X3 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X3))))),
% 92.92/13.72 inference(fool_elimination,[],[f2603])).
% 92.92/13.72 thf(f2603,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1] : vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2))) & ! [X3 : X0] : vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X3)))),
% 92.92/13.72 inference(rectify,[],[f664])).
% 92.92/13.72 thf(f664,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType] : (! [X18 : X5] : vAPP($o,$o,vNOT,vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISL(X0,X5),vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X18))) & ! [X8 : X0] : vAPP(tyop_2Esum_2Esum(X0,X5),$o,c_2Esum_2EISL(X0,X5),vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X8)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EISL)).
% 92.92/13.72 thf(f22973,plain,(
% 92.92/13.72 spl854_165),
% 92.92/13.72 inference(avatar_split_clause,[],[f17531,f22971])).
% 92.92/13.72 thf(f22971,plain,(
% 92.92/13.72 spl854_165 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)) | ($true = X0) | ($true = X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_165])])).
% 92.92/13.72 thf(f17531,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)) | ($true = X0) | ($true = X1)) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f17530])).
% 92.92/13.72 thf(f17530,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)) | ($true = X0) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10430])).
% 92.92/13.72 thf(f10430,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)) | ($true != vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6971])).
% 92.92/13.72 thf(f6971,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)) | ((($true != vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) != $true)) & (($true != X0) | ($true != X1)))) & ((($true = vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) = $true)) | (($true = X0) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0))))),
% 92.92/13.72 inference(rectify,[],[f6970])).
% 92.92/13.72 thf(f6970,plain,(
% 92.92/13.72 ! [X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1)) | (((vAPP($o,$o,vNOT,X1) != $true) | ($true != vAPP($o,$o,vNOT,X0))) & (($true != X1) | ($true != X0)))) & (((vAPP($o,$o,vNOT,X1) = $true) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1))))),
% 92.92/13.72 inference(flattening,[],[f6969])).
% 92.92/13.72 thf(f6969,plain,(
% 92.92/13.72 ! [X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1)) | (((vAPP($o,$o,vNOT,X1) != $true) | ($true != vAPP($o,$o,vNOT,X0))) & (($true != X1) | ($true != X0)))) & ((((vAPP($o,$o,vNOT,X1) = $true) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6396])).
% 92.92/13.72 thf(f6396,plain,(
% 92.92/13.72 ! [X1 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1)) <=> (((vAPP($o,$o,vNOT,X1) = $true) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0))))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f22969,plain,(
% 92.92/13.72 spl854_164),
% 92.92/13.72 inference(avatar_split_clause,[],[f17528,f22967])).
% 92.92/13.72 thf(f22967,plain,(
% 92.92/13.72 spl854_164 <=> ! [X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_164])])).
% 92.92/13.72 thf(f17528,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($false = X0) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10427])).
% 92.92/13.72 thf(f10427,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | ($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6971])).
% 92.92/13.72 thf(f22965,plain,(
% 92.92/13.72 spl854_163 | ~spl854_24 | ~spl854_26),
% 92.92/13.72 inference(avatar_split_clause,[],[f22072,f22023,f22014,f22963])).
% 92.92/13.72 thf(f22963,plain,(
% 92.92/13.72 spl854_163 <=> ! [X0 : $o] : ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_163])])).
% 92.92/13.72 thf(f22072,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0)))) ) | (~spl854_24 | ~spl854_26)),
% 92.92/13.72 inference(superposition,[],[f22016,f22024])).
% 92.92/13.72 thf(f22961,plain,(
% 92.92/13.72 spl854_162),
% 92.92/13.72 inference(avatar_split_clause,[],[f17527,f22959])).
% 92.92/13.72 thf(f22959,plain,(
% 92.92/13.72 spl854_162 <=> ! [X0 : $o,X1 : $o] : (($false = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_162])])).
% 92.92/13.72 thf(f17527,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($false = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10426])).
% 92.92/13.72 thf(f10426,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X1) = $true) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6971])).
% 92.92/13.72 thf(f22957,plain,(
% 92.92/13.72 spl854_161),
% 92.92/13.72 inference(avatar_split_clause,[],[f17477,f22955])).
% 92.92/13.72 thf(f22955,plain,(
% 92.92/13.72 spl854_161 <=> ! [X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_161])])).
% 92.92/13.72 thf(f17477,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($false = X0) | ($false = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f17476])).
% 92.92/13.72 thf(f17476,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($false = X0) | (vAPP($o,$o,vNOT,X1) = $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10549])).
% 92.92/13.72 thf(f10549,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7039])).
% 92.92/13.72 thf(f7039,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0)) | (($true != vAPP($o,$o,vNOT,X0)) & (vAPP($o,$o,vNOT,X1) != $true)) | (($true != X1) & ($true != X0))) & (((($true = vAPP($o,$o,vNOT,X0)) | (vAPP($o,$o,vNOT,X1) = $true)) & (($true = X1) | ($true = X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0))))),
% 92.92/13.72 inference(rectify,[],[f7038])).
% 92.92/13.72 thf(f7038,plain,(
% 92.92/13.72 ! [X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1)) | ((vAPP($o,$o,vNOT,X1) != $true) & ($true != vAPP($o,$o,vNOT,X0))) | (($true != X0) & ($true != X1))) & ((((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0))) & (($true = X0) | ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1))))),
% 92.92/13.72 inference(flattening,[],[f7037])).
% 92.92/13.72 thf(f7037,plain,(
% 92.92/13.72 ! [X1 : $o,X0 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1)) | (((vAPP($o,$o,vNOT,X1) != $true) & ($true != vAPP($o,$o,vNOT,X0))) | (($true != X0) & ($true != X1)))) & ((((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0))) & (($true = X0) | ($true = X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6405])).
% 92.92/13.72 thf(f6405,plain,(
% 92.92/13.72 ! [X1 : $o,X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1)) <=> (((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0))) & (($true = X0) | ($true = X1))))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f22953,plain,(
% 92.92/13.72 spl854_160),
% 92.92/13.72 inference(avatar_split_clause,[],[f13710,f22950])).
% 92.92/13.72 thf(f13710,plain,(
% 92.92/13.72 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(definition_unfolding,[],[f9369,f13512,f13512])).
% 92.92/13.72 thf(f9369,plain,(
% 92.92/13.72 (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(cnf_transformation,[],[f4916])).
% 92.92/13.72 thf(f22947,plain,(
% 92.92/13.72 spl854_159),
% 92.92/13.72 inference(avatar_split_clause,[],[f13563,f22944])).
% 92.92/13.72 thf(f22941,plain,(
% 92.92/13.72 spl854_158),
% 92.92/13.72 inference(avatar_split_clause,[],[f13556,f22938])).
% 92.92/13.72 thf(f13556,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 inference(definition_unfolding,[],[f9149,f13512,f13512])).
% 92.92/13.72 thf(f9149,plain,(
% 92.92/13.72 (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),
% 92.92/13.72 inference(cnf_transformation,[],[f4836])).
% 92.92/13.72 thf(f22936,plain,(
% 92.92/13.72 spl854_157),
% 92.92/13.72 inference(avatar_split_clause,[],[f11760,f22934])).
% 92.92/13.72 thf(f22934,plain,(
% 92.92/13.72 spl854_157 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) != vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_157])])).
% 92.92/13.72 thf(f11760,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) != vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7937])).
% 92.92/13.72 thf(f7937,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0,X2 : X0] : (((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) | (X1 != X2)) & ((X1 = X2) | (vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) != vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2))))),
% 92.92/13.72 inference(nnf_transformation,[],[f5227])).
% 92.92/13.72 thf(f5227,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0,X2 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X2)) <=> (X1 = X2))),
% 92.92/13.72 inference(rectify,[],[f728])).
% 92.92/13.72 thf(f728,axiom,(
% 92.92/13.72 ! [X0 : $tType,X8 : X0,X18 : X0] : ((vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8) = vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X18)) <=> (X8 = X18))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2ESOME__11)).
% 92.92/13.72 thf(f22932,plain,(
% 92.92/13.72 spl854_156),
% 92.92/13.72 inference(avatar_split_clause,[],[f11239,f22930])).
% 92.92/13.72 thf(f22930,plain,(
% 92.92/13.72 spl854_156 <=> ! [X1 : $tType,X0 : $tType,X2 : X1] : (vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)) = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_156])])).
% 92.92/13.72 thf(f11239,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : ((vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)) = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5135])).
% 92.92/13.72 thf(f5135,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X1] : (vAPP(tyop_2Esum_2Esum(X0,X1),X1,c_2Esum_2EOUTR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X2)) = X2)),
% 92.92/13.72 inference(rectify,[],[f667])).
% 92.92/13.72 thf(f667,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X8 : X5] : (vAPP(tyop_2Esum_2Esum(X0,X5),X5,c_2Esum_2EOUTR(X0,X5),vAPP(X5,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINR(X0,X5),X8)) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EOUTR)).
% 92.92/13.72 thf(f22928,plain,(
% 92.92/13.72 spl854_155),
% 92.92/13.72 inference(avatar_split_clause,[],[f11238,f22926])).
% 92.92/13.72 thf(f22926,plain,(
% 92.92/13.72 spl854_155 <=> ! [X1 : $tType,X0 : $tType,X2 : X0] : (vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)) = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_155])])).
% 92.92/13.72 thf(f11238,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X0] : ((vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)) = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5134])).
% 92.92/13.72 thf(f5134,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X0] : (vAPP(tyop_2Esum_2Esum(X0,X1),X0,c_2Esum_2EOUTL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X2)) = X2)),
% 92.92/13.72 inference(rectify,[],[f666])).
% 92.92/13.72 thf(f666,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X8 : X0] : (vAPP(tyop_2Esum_2Esum(X0,X5),X0,c_2Esum_2EOUTL(X0,X5),vAPP(X0,tyop_2Esum_2Esum(X0,X5),c_2Esum_2EINL(X0,X5),X8)) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esum_2EOUTL)).
% 92.92/13.72 thf(f22924,plain,(
% 92.92/13.72 spl854_154),
% 92.92/13.72 inference(avatar_split_clause,[],[f10548,f22922])).
% 92.92/13.72 thf(f22922,plain,(
% 92.92/13.72 spl854_154 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_154])])).
% 92.92/13.72 thf(f10548,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7039])).
% 92.92/13.72 thf(f22920,plain,(
% 92.92/13.72 spl854_153),
% 92.92/13.72 inference(avatar_split_clause,[],[f10416,f22918])).
% 92.92/13.72 thf(f22918,plain,(
% 92.92/13.72 spl854_153 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) | ($true = X1) | ($true = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_153])])).
% 92.92/13.72 thf(f10416,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) | ($true = X1) | ($true = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6965])).
% 92.92/13.72 thf(f6965,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) | (($true != X0) & ($true = X1)) | (($true != X1) & ($true = X0))) & (((($true = X0) | ($true != X1)) & (($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0))))),
% 92.92/13.72 inference(flattening,[],[f6964])).
% 92.92/13.72 thf(f6964,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) | ((($true != X0) & ($true = X1)) | (($true != X1) & ($true = X0)))) & (((($true = X0) | ($true != X1)) & (($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6394])).
% 92.92/13.72 thf(f6394,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) <=> ((($true = X0) | ($true != X1)) & (($true = X1) | ($true != X0))))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f22916,plain,(
% 92.92/13.72 spl854_152 | ~spl854_26),
% 92.92/13.72 inference(avatar_split_clause,[],[f22071,f22023,f22914])).
% 92.92/13.72 thf(f22914,plain,(
% 92.92/13.72 spl854_152 <=> ! [X0 : $o,X1 : $o] : (vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0) = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_152])])).
% 92.92/13.72 thf(f22071,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : ((vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0) = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X1))) ) | ~spl854_26),
% 92.92/13.72 inference(superposition,[],[f22024,f22024])).
% 92.92/13.72 thf(f22912,plain,(
% 92.92/13.72 spl854_151),
% 92.92/13.72 inference(avatar_split_clause,[],[f10141,f22910])).
% 92.92/13.72 thf(f22910,plain,(
% 92.92/13.72 spl854_151 <=> ! [X1 : $tType,X0 : $tType,X3 : X0] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X3)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_151])])).
% 92.92/13.72 thf(f10141,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X3 : X0] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISL(X0,X1),vAPP(X0,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINL(X0,X1),X3)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2604])).
% 92.92/13.72 thf(f22908,plain,(
% 92.92/13.72 spl854_150),
% 92.92/13.72 inference(avatar_split_clause,[],[f10139,f22906])).
% 92.92/13.72 thf(f22906,plain,(
% 92.92/13.72 spl854_150 <=> ! [X1 : $tType,X0 : $tType,X3 : X1] : ($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_150])])).
% 92.92/13.72 thf(f10139,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X3 : X1] : (($true = vAPP(tyop_2Esum_2Esum(X0,X1),$o,c_2Esum_2EISR(X0,X1),vAPP(X1,tyop_2Esum_2Esum(X0,X1),c_2Esum_2EINR(X0,X1),X3)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2602])).
% 92.92/13.72 thf(f22904,plain,(
% 92.92/13.72 spl854_149),
% 92.92/13.72 inference(avatar_split_clause,[],[f9385,f22902])).
% 92.92/13.72 thf(f22900,plain,(
% 92.92/13.72 spl854_148),
% 92.92/13.72 inference(avatar_split_clause,[],[f9384,f22898])).
% 92.92/13.72 thf(f22898,plain,(
% 92.92/13.72 spl854_148 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_148])])).
% 92.92/13.72 thf(f9384,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4923])).
% 92.92/13.72 thf(f22896,plain,(
% 92.92/13.72 spl854_147),
% 92.92/13.72 inference(avatar_split_clause,[],[f9371,f22894])).
% 92.92/13.72 thf(f22894,plain,(
% 92.92/13.72 spl854_147 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_147])])).
% 92.92/13.72 thf(f9371,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4916])).
% 92.92/13.72 thf(f22892,plain,(
% 92.92/13.72 spl854_146),
% 92.92/13.72 inference(avatar_split_clause,[],[f9370,f22890])).
% 92.92/13.72 thf(f22888,plain,(
% 92.92/13.72 spl854_145),
% 92.92/13.72 inference(avatar_split_clause,[],[f9312,f22886])).
% 92.92/13.72 thf(f22886,plain,(
% 92.92/13.72 spl854_145 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_145])])).
% 92.92/13.72 thf(f9312,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4886])).
% 92.92/13.72 thf(f4886,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X0))))),
% 92.92/13.72 inference(rectify,[],[f380])).
% 92.92/13.72 thf(f380,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X134) = vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X134))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2ESUC__DEF)).
% 92.92/13.72 thf(f22883,plain,(
% 92.92/13.72 spl854_144),
% 92.92/13.72 inference(avatar_split_clause,[],[f9213,f22881])).
% 92.92/13.72 thf(f22881,plain,(
% 92.92/13.72 spl854_144 <=> ! [X22 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X22)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X22)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_144])])).
% 92.92/13.72 thf(f9213,plain,(
% 92.92/13.72 ( ! [X22 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X22)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,X22)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6597])).
% 92.92/13.72 thf(f22878,plain,(
% 92.92/13.72 spl854_143),
% 92.92/13.72 inference(avatar_split_clause,[],[f9211,f22876])).
% 92.92/13.72 thf(f22876,plain,(
% 92.92/13.72 spl854_143 <=> ! [X23 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X23)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X23)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_143])])).
% 92.92/13.72 thf(f9211,plain,(
% 92.92/13.72 ( ! [X23 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X23)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X23)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6597])).
% 92.92/13.72 thf(f22873,plain,(
% 92.92/13.72 spl854_142),
% 92.92/13.72 inference(avatar_split_clause,[],[f9165,f22871])).
% 92.92/13.72 thf(f22871,plain,(
% 92.92/13.72 spl854_142 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_142])])).
% 92.92/13.72 thf(f22869,plain,(
% 92.92/13.72 spl854_141 | ~spl854_5 | ~spl854_15),
% 92.92/13.72 inference(avatar_split_clause,[],[f21975,f21958,f21881,f22867])).
% 92.92/13.72 thf(f22867,plain,(
% 92.92/13.72 spl854_141 <=> ! [X0 : $o] : (($true = X0) | ($false = vAPP($o,$o,sK386($o),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_141])])).
% 92.92/13.72 thf(f21975,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP($o,$o,sK386($o),X0))) ) | (~spl854_5 | ~spl854_15)),
% 92.92/13.72 inference(superposition,[],[f21959,f21882])).
% 92.92/13.72 thf(f22863,plain,(
% 92.92/13.72 spl854_140),
% 92.92/13.72 inference(avatar_split_clause,[],[f9154,f22861])).
% 92.92/13.72 thf(f22861,plain,(
% 92.92/13.72 spl854_140 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_140])])).
% 92.92/13.72 thf(f9154,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4837])).
% 92.92/13.72 thf(f22814,plain,(
% 92.92/13.72 spl854_139),
% 92.92/13.72 inference(avatar_split_clause,[],[f17960,f22812])).
% 92.92/13.72 thf(f22812,plain,(
% 92.92/13.72 spl854_139 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_139])])).
% 92.92/13.72 thf(f17960,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0)) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17959])).
% 92.92/13.72 thf(f17959,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f13905])).
% 92.92/13.72 thf(f13905,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9622,f9122])).
% 92.92/13.72 thf(f9622,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6685])).
% 92.92/13.72 thf(f6685,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f5496,f6684])).
% 92.92/13.72 thf(f6684,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK160,X0)) = X0))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f5496,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1) = X0) | ($true != vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2270])).
% 92.92/13.72 thf(f2270,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),X0))) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1) = X0))),
% 92.92/13.72 inference(fool_elimination,[],[f2269])).
% 92.92/13.72 thf(f2269,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(c_2Enum_2E0 = X0)) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1) = X0))),
% 92.92/13.72 inference(rectify,[],[f1723])).
% 92.92/13.72 thf(f1723,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum] : (vAPP($o,$o,vNOT,(c_2Enum_2E0 = X134)) => ? [X110 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X110) = X134))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ENOT__ZERO__ADD1)).
% 92.92/13.72 thf(f22810,plain,(
% 92.92/13.72 spl854_138 | ~spl854_5 | ~spl854_14),
% 92.92/13.72 inference(avatar_split_clause,[],[f21970,f21954,f21881,f22808])).
% 92.92/13.72 thf(f22808,plain,(
% 92.92/13.72 spl854_138 <=> ! [X0 : $o] : (($true = X0) | ($false = vAPP($o,$o,c_2Emarker_2Estmarker($o),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_138])])).
% 92.92/13.72 thf(f21970,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP($o,$o,c_2Emarker_2Estmarker($o),X0))) ) | (~spl854_5 | ~spl854_14)),
% 92.92/13.72 inference(superposition,[],[f21955,f21882])).
% 92.92/13.72 thf(f22806,plain,(
% 92.92/13.72 spl854_137),
% 92.92/13.72 inference(avatar_split_clause,[],[f13824,f22804])).
% 92.92/13.72 thf(f22804,plain,(
% 92.92/13.72 spl854_137 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK130,X0)) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_137])])).
% 92.92/13.72 thf(f13824,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK130,X0)) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9531,f9122])).
% 92.92/13.72 thf(f9531,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK130,X0)) = X0) | (c_2Enum_2E0 = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6629])).
% 92.92/13.72 thf(f6629,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK130,X0)) = X0) | (c_2Enum_2E0 = X0))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK130])],[f4946,f6628])).
% 92.92/13.72 thf(f6628,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK130,X0)) = X0))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f4946,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1) = X0) | (c_2Enum_2E0 = X0))),
% 92.92/13.72 inference(rectify,[],[f951])).
% 92.92/13.72 thf(f951,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum] : (? [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137) = X134) | (c_2Enum_2E0 = X134))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2Enum__CASES)).
% 92.92/13.72 thf(f22802,plain,(
% 92.92/13.72 spl854_136),
% 92.92/13.72 inference(avatar_split_clause,[],[f13748,f22800])).
% 92.92/13.72 thf(f22800,plain,(
% 92.92/13.72 spl854_136 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_136])])).
% 92.92/13.72 thf(f13748,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = X0) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9425,f9122,f9122])).
% 92.92/13.72 thf(f9425,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6611])).
% 92.92/13.72 thf(f6611,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0))) & ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0))))),
% 92.92/13.72 inference(flattening,[],[f6610])).
% 92.92/13.72 thf(f6610,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))) & (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) | (c_2Enum_2E0 != X0)) & ((c_2Enum_2E0 = X0) | (c_2Enum_2E0 != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)))))),
% 92.92/13.72 inference(nnf_transformation,[],[f4929])).
% 92.92/13.72 thf(f4929,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) <=> (c_2Enum_2E0 = X0)) & ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) <=> (c_2Enum_2E0 = X0)))),
% 92.92/13.72 inference(rectify,[],[f1659])).
% 92.92/13.72 thf(f1659,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X136)) <=> (c_2Enum_2E0 = X136)) & ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X136)) <=> (c_2Enum_2E0 = X136)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Etri__eq__0)).
% 92.92/13.72 thf(f22798,plain,(
% 92.92/13.72 spl854_135),
% 92.92/13.72 inference(avatar_split_clause,[],[f12360,f22796])).
% 92.92/13.72 thf(f22796,plain,(
% 92.92/13.72 spl854_135 <=> ! [X1 : $tType,X0 : $tType,X2 : X1] : (vAPP(tyop_2Ebool_2Eitself(X0),X1,vAPP(X1,sTfun(tyop_2Ebool_2Eitself(X0),X1),sK633(X0,X1),X2),c_2Ebool_2Ethe__value(X0)) = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_135])])).
% 92.92/13.72 thf(f12360,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : ((vAPP(tyop_2Ebool_2Eitself(X0),X1,vAPP(X1,sTfun(tyop_2Ebool_2Eitself(X0),X1),sK633(X0,X1),X2),c_2Ebool_2Ethe__value(X0)) = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8427])).
% 92.92/13.72 thf(f8427,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X1] : (vAPP(tyop_2Ebool_2Eitself(X0),X1,vAPP(X1,sTfun(tyop_2Ebool_2Eitself(X0),X1),sK633(X0,X1),X2),c_2Ebool_2Ethe__value(X0)) = X2)),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK633])],[f5252,f8426])).
% 92.92/13.72 thf(f8426,plain,(
% 92.92/13.72 ! [X1 : $tType,X0 : $tType,X2 : X1] : (? [X3 : tyop_2Ebool_2Eitself(X0) > X1] : (vAPP(tyop_2Ebool_2Eitself(X0),X1,X3,c_2Ebool_2Ethe__value(X0)) = X2) => (vAPP(tyop_2Ebool_2Eitself(X0),X1,vAPP(X1,sTfun(tyop_2Ebool_2Eitself(X0),X1),sK633(X0,X1),X2),c_2Ebool_2Ethe__value(X0)) = X2))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f5252,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X1] : ? [X3 : tyop_2Ebool_2Eitself(X0) > X1] : (vAPP(tyop_2Ebool_2Eitself(X0),X1,X3,c_2Ebool_2Ethe__value(X0)) = X2)),
% 92.92/13.72 inference(rectify,[],[f190])).
% 92.92/13.72 thf(f190,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X90 : X5] : ? [X25 : tyop_2Ebool_2Eitself(X0) > X5] : (vAPP(tyop_2Ebool_2Eitself(X0),X5,X25,c_2Ebool_2Ethe__value(X0)) = X90)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__Axiom)).
% 92.92/13.72 thf(f22794,plain,(
% 92.92/13.72 spl854_134),
% 92.92/13.72 inference(avatar_split_clause,[],[f9756,f22792])).
% 92.92/13.72 thf(f22792,plain,(
% 92.92/13.72 spl854_134 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK186,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_134])])).
% 92.92/13.72 thf(f9756,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK186,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6799])).
% 92.92/13.72 thf(f6799,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) != X0)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK186,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK186])],[f6797,f6798])).
% 92.92/13.72 thf(f6798,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X2) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK186,X0)) = X0))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f6797,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) != X0)) & (? [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X2) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))))),
% 92.92/13.72 inference(rectify,[],[f6796])).
% 92.92/13.72 thf(f6796,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) != X0)) & (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f2388])).
% 92.92/13.72 thf(f2388,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) <=> ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0))),
% 92.92/13.72 inference(fool_elimination,[],[f2387])).
% 92.92/13.72 thf(f2387,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0) <=> ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0))),
% 92.92/13.72 inference(rectify,[],[f1498])).
% 92.92/13.72 thf(f1498,axiom,(
% 92.92/13.72 ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X26) <=> ? [X91 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X91) = X26))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EPRIME__INDEX)).
% 92.92/13.72 thf(f22790,plain,(
% 92.92/13.72 spl854_133),
% 92.92/13.72 inference(avatar_split_clause,[],[f9582,f22788])).
% 92.92/13.72 thf(f22788,plain,(
% 92.92/13.72 spl854_133 <=> ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK156,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_133])])).
% 92.92/13.72 thf(f9582,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK156,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6675])).
% 92.92/13.72 thf(f6675,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK156,X0)) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f5461,f6674])).
% 92.92/13.72 thf(f6674,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0) => (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK156,X0)) = X0))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f5461,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)))),
% 92.92/13.72 inference(ennf_transformation,[],[f2200])).
% 92.92/13.72 thf(f2200,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0))),
% 92.92/13.72 inference(fool_elimination,[],[f2199])).
% 92.92/13.72 thf(f2199,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0) => ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) = X0))),
% 92.92/13.72 inference(rectify,[],[f1497])).
% 92.92/13.72 thf(f1497,axiom,(
% 92.92/13.72 ! [X26 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X26) => ? [X91 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X91) = X26))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EPRIMES__ONTO)).
% 92.92/13.72 thf(f22786,plain,(
% 92.92/13.72 spl854_132),
% 92.92/13.72 inference(avatar_split_clause,[],[f9177,f22784])).
% 92.92/13.72 thf(f9177,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6596])).
% 92.92/13.72 thf(f6596,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : ((($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) != X0)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) = X0) | ($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)))) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X1)) = X1)),
% 92.92/13.72 inference(nnf_transformation,[],[f2036])).
% 92.92/13.72 thf(f2036,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) <=> (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) = X0)) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X1)) = X1)),
% 92.92/13.72 inference(fool_elimination,[],[f2035])).
% 92.92/13.72 thf(f2035,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0) <=> (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) = X0)) & ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X1)) = X1)),
% 92.92/13.72 inference(rectify,[],[f378])).
% 92.92/13.72 thf(f378,axiom,(
% 92.92/13.72 ! [X112 : tyop_2Emin_2Eind] : (vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X112) <=> (vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X112)) = X112)) & ! [X72 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X72)) = X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2Enum__ISO__DEF)).
% 92.92/13.72 thf(f22782,plain,(
% 92.92/13.72 spl854_131),
% 92.92/13.72 inference(avatar_split_clause,[],[f9176,f22780])).
% 92.92/13.72 thf(f9176,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : ((vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,X0)) = X0) | ($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6596])).
% 92.92/13.72 thf(f22773,plain,(
% 92.92/13.72 spl854_130 | ~spl854_5 | ~spl854_13),
% 92.92/13.72 inference(avatar_split_clause,[],[f21965,f21950,f21881,f22771])).
% 92.92/13.72 thf(f22771,plain,(
% 92.92/13.72 spl854_130 <=> ! [X0 : $o] : (($true = X0) | ($false = vAPP($o,$o,c_2Emarker_2Eunint($o),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_130])])).
% 92.92/13.72 thf(f21965,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP($o,$o,c_2Emarker_2Eunint($o),X0))) ) | (~spl854_5 | ~spl854_13)),
% 92.92/13.72 inference(superposition,[],[f21951,f21882])).
% 92.92/13.72 thf(f22707,plain,(
% 92.92/13.72 spl854_129),
% 92.92/13.72 inference(avatar_split_clause,[],[f17793,f22705])).
% 92.92/13.72 thf(f22703,plain,(
% 92.92/13.72 spl854_128),
% 92.92/13.72 inference(avatar_split_clause,[],[f17342,f22701])).
% 92.92/13.72 thf(f22701,plain,(
% 92.92/13.72 spl854_128 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_128])])).
% 92.92/13.72 thf(f17342,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17341])).
% 92.92/13.72 thf(f17341,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f14894])).
% 92.92/13.72 thf(f14894,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f11226,f9122])).
% 92.92/13.72 thf(f11226,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f3562])).
% 92.92/13.72 thf(f3562,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f3561])).
% 92.92/13.72 thf(f3561,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X1),X0)))),
% 92.92/13.72 inference(rectify,[],[f1683])).
% 92.92/13.72 thf(f1683,axiom,(
% 92.92/13.72 ! [X70 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X4),X70)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil)).
% 92.92/13.72 thf(f22699,plain,(
% 92.92/13.72 spl854_127),
% 92.92/13.72 inference(avatar_split_clause,[],[f15875,f22697])).
% 92.92/13.72 thf(f22697,plain,(
% 92.92/13.72 spl854_127 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),vAPP($o,$o,vNOT,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_127])])).
% 92.92/13.72 thf(f15875,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),vAPP($o,$o,vNOT,X0)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10554])).
% 92.92/13.72 thf(f10554,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1)) | (vAPP($o,$o,vNOT,X0) != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7040])).
% 92.92/13.72 thf(f7040,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (((vAPP($o,$o,vNOT,X0) = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1))) & (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1)) | (vAPP($o,$o,vNOT,X0) != X1)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6406])).
% 92.92/13.72 thf(f6406,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X0) = X1) <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X0),X1)))),
% 92.92/13.72 inference(definition_folding,[],[f3006,f6405])).
% 92.92/13.72 thf(f3006,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((vAPP($o,$o,vNOT,X0) = X1) <=> (((vAPP($o,$o,vNOT,X1) = $true) | ($true = vAPP($o,$o,vNOT,X0))) & (($true = X0) | ($true = X1))))),
% 92.92/13.72 inference(fool_elimination,[],[f3005])).
% 92.92/13.72 thf(f3005,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X1 <=> vAPP($o,$o,vNOT,X0)) <=> ((vAPP($o,$o,vNOT,X1) | vAPP($o,$o,vNOT,X0)) & (X0 | X1)))),
% 92.92/13.72 inference(rectify,[],[f298])).
% 92.92/13.72 thf(f298,axiom,(
% 92.92/13.72 ! [X109 : $o,X110 : $o] : ((X110 <=> vAPP($o,$o,vNOT,X109)) <=> ((vAPP($o,$o,vNOT,X110) | vAPP($o,$o,vNOT,X109)) & (X109 | X110)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg)).
% 92.92/13.72 thf(f22695,plain,(
% 92.92/13.72 spl854_126),
% 92.92/13.72 inference(avatar_split_clause,[],[f14972,f22693])).
% 92.92/13.72 thf(f22693,plain,(
% 92.92/13.72 spl854_126 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X1) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_126])])).
% 92.92/13.72 thf(f14972,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X1) = X1)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f11342,f9122])).
% 92.92/13.72 thf(f11342,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,c_2Enum_2E0),X1) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5212])).
% 92.92/13.72 thf(f5212,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X2),X0)),X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X2),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,X0),X1))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,c_2Enum_2E0),X1) = X1))),
% 92.92/13.72 inference(rectify,[],[f1691])).
% 92.92/13.72 thf(f1691,axiom,(
% 92.92/13.72 ! [X6 : tyop_2Enum_2Enum,X463 : tyop_2Enum_2Enum,X119 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X119),X6)),X463) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Encons,X119),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,X6),X463))) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enapp,c_2Enum_2E0),X463) = X463))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enapp__thm)).
% 92.92/13.72 thf(f22691,plain,(
% 92.92/13.72 spl854_125),
% 92.92/13.72 inference(avatar_split_clause,[],[f14041,f22689])).
% 92.92/13.72 thf(f22689,plain,(
% 92.92/13.72 spl854_125 <=> ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_125])])).
% 92.92/13.72 thf(f14041,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9800,f9122])).
% 92.92/13.72 thf(f9800,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),c_2Enum_2E0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2440])).
% 92.92/13.72 thf(f2440,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),c_2Enum_2E0))),
% 92.92/13.72 inference(fool_elimination,[],[f2439])).
% 92.92/13.72 thf(f2439,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),c_2Enum_2E0)),
% 92.92/13.72 inference(rectify,[],[f1463])).
% 92.92/13.72 thf(f1463,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X72),c_2Enum_2E0)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EALL__DIVIDES__0)).
% 92.92/13.72 thf(f22687,plain,(
% 92.92/13.72 spl854_124),
% 92.92/13.72 inference(avatar_split_clause,[],[f13720,f22685])).
% 92.92/13.72 thf(f22685,plain,(
% 92.92/13.72 spl854_124 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_124])])).
% 92.92/13.72 thf(f13720,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9380,f9122])).
% 92.92/13.72 thf(f9380,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),c_2Enum_2E0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4921])).
% 92.92/13.72 thf(f4921,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,c_2Enum_2E0),X0) = X0) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),c_2Enum_2E0) = X0))),
% 92.92/13.72 inference(rectify,[],[f1254])).
% 92.92/13.72 thf(f1254,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,c_2Enum_2E0),X136) = X136) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X136),c_2Enum_2E0) = X136))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__ZERO)).
% 92.92/13.72 thf(f22683,plain,(
% 92.92/13.72 spl854_123),
% 92.92/13.72 inference(avatar_split_clause,[],[f13719,f22681])).
% 92.92/13.72 thf(f22681,plain,(
% 92.92/13.72 spl854_123 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_123])])).
% 92.92/13.72 thf(f13719,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9381,f9122])).
% 92.92/13.72 thf(f9381,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,c_2Enum_2E0),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4921])).
% 92.92/13.72 thf(f22679,plain,(
% 92.92/13.72 spl854_122),
% 92.92/13.72 inference(avatar_split_clause,[],[f13718,f22677])).
% 92.92/13.72 thf(f22677,plain,(
% 92.92/13.72 spl854_122 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_122])])).
% 92.92/13.72 thf(f13718,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9378,f9122])).
% 92.92/13.72 thf(f9378,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),c_2Enum_2E0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4920])).
% 92.92/13.72 thf(f4920,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,c_2Enum_2E0),X0) = X0) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),c_2Enum_2E0) = X0))),
% 92.92/13.72 inference(rectify,[],[f1233])).
% 92.92/13.72 thf(f1233,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,c_2Enum_2E0),X136) = X136) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X136),c_2Enum_2E0) = X136))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMAX__0)).
% 92.92/13.72 thf(f22675,plain,(
% 92.92/13.72 spl854_121),
% 92.92/13.72 inference(avatar_split_clause,[],[f13717,f22673])).
% 92.92/13.72 thf(f22673,plain,(
% 92.92/13.72 spl854_121 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_121])])).
% 92.92/13.72 thf(f13717,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X0) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9379,f9122])).
% 92.92/13.72 thf(f9379,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,c_2Enum_2E0),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4920])).
% 92.92/13.72 thf(f22671,plain,(
% 92.92/13.72 spl854_120),
% 92.92/13.72 inference(avatar_split_clause,[],[f13673,f22669])).
% 92.92/13.72 thf(f22669,plain,(
% 92.92/13.72 spl854_120 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiSQR,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_120])])).
% 92.92/13.72 thf(f13673,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiSQR,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,X0),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9308,f9121])).
% 92.92/13.72 thf(f9308,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiSQR,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4882])).
% 92.92/13.72 thf(f4882,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiSQR,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X0),X0))),
% 92.92/13.72 inference(rectify,[],[f1371])).
% 92.92/13.72 thf(f1371,axiom,(
% 92.92/13.72 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiSQR,X8) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,X8),X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiSQR)).
% 92.92/13.72 thf(f22667,plain,(
% 92.92/13.72 spl854_119),
% 92.92/13.72 inference(avatar_split_clause,[],[f13670,f22665])).
% 92.92/13.72 thf(f22665,plain,(
% 92.92/13.72 spl854_119 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_119])])).
% 92.92/13.72 thf(f13670,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9300,f9122])).
% 92.92/13.72 thf(f9300,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),c_2Enum_2E0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4875])).
% 92.92/13.72 thf(f4875,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),c_2Enum_2E0) = X0)),
% 92.92/13.72 inference(rectify,[],[f1574])).
% 92.92/13.72 thf(f1574,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),c_2Enum_2E0) = X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__0R)).
% 92.92/13.72 thf(f22663,plain,(
% 92.92/13.72 spl854_118),
% 92.92/13.72 inference(avatar_split_clause,[],[f13668,f22661])).
% 92.92/13.72 thf(f22661,plain,(
% 92.92/13.72 spl854_118 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_118])])).
% 92.92/13.72 thf(f13668,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9298,f9122])).
% 92.92/13.72 thf(f9298,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4873])).
% 92.92/13.72 thf(f4873,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X0))),
% 92.92/13.72 inference(rectify,[],[f1058])).
% 92.92/13.72 thf(f1058,axiom,(
% 92.92/13.72 ! [X97 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X97),X97))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQUAL__0)).
% 92.92/13.72 thf(f22659,plain,(
% 92.92/13.72 spl854_117),
% 92.92/13.72 inference(avatar_split_clause,[],[f13667,f22657])).
% 92.92/13.72 thf(f22657,plain,(
% 92.92/13.72 spl854_117 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_117])])).
% 92.92/13.72 thf(f13667,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9297,f9122])).
% 92.92/13.72 thf(f9297,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4872])).
% 92.92/13.72 thf(f4872,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X0),X0))),
% 92.92/13.72 inference(rectify,[],[f1252])).
% 92.92/13.72 thf(f1252,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EABS__DIFF,X136),X136))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__EQS)).
% 92.92/13.72 thf(f22655,plain,(
% 92.92/13.72 spl854_116),
% 92.92/13.72 inference(avatar_split_clause,[],[f13622,f22653])).
% 92.92/13.72 thf(f22653,plain,(
% 92.92/13.72 spl854_116 <=> ! [X40 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X40) = X40)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_116])])).
% 92.92/13.72 thf(f13622,plain,(
% 92.92/13.72 ( ! [X40 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X40) = X40)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9197,f9122])).
% 92.92/13.72 thf(f9197,plain,(
% 92.92/13.72 ( ! [X40 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B,c_2Enum_2E0),X40) = X40)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6597])).
% 92.92/13.72 thf(f22651,plain,(
% 92.92/13.72 spl854_115),
% 92.92/13.72 inference(avatar_split_clause,[],[f13621,f22649])).
% 92.92/13.72 thf(f22641,plain,(
% 92.92/13.72 spl854_114),
% 92.92/13.72 inference(avatar_split_clause,[],[f13616,f22639])).
% 92.92/13.72 thf(f22639,plain,(
% 92.92/13.72 spl854_114 <=> ! [X31 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X31),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X31)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_114])])).
% 92.92/13.72 thf(f13616,plain,(
% 92.92/13.72 ( ! [X31 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X31),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)) = X31)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9204,f9122])).
% 92.92/13.72 thf(f9204,plain,(
% 92.92/13.72 ( ! [X31 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X31),c_2Enum_2E0) = X31)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6597])).
% 92.92/13.72 thf(f22637,plain,(
% 92.92/13.72 spl854_113),
% 92.92/13.72 inference(avatar_split_clause,[],[f13583,f22635])).
% 92.92/13.72 thf(f22635,plain,(
% 92.92/13.72 spl854_113 <=> ! [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X3) = X3)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_113])])).
% 92.92/13.72 thf(f13583,plain,(
% 92.92/13.72 ( ! [X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X3) = X3)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9187,f9122])).
% 92.92/13.72 thf(f9187,plain,(
% 92.92/13.72 ( ! [X3 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,c_2Enum_2E0),X3) = X3)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4848])).
% 92.92/13.72 thf(f4848,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X0),X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X1),X0)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X0),X1)))) & ! [X2 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X2)),c_2Enum_2E0)) & ! [X3 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,c_2Enum_2E0),X3) = X3)),
% 92.92/13.72 inference(rectify,[],[f1568])).
% 92.92/13.72 thf(f1568,axiom,(
% 92.92/13.72 ! [X12 : tyop_2Enum_2Enum,X15 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X15)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X12)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3C_3D,X12),X15)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X15),X12)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X12))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X15)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D,X12),X15)))) & ! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X4) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X4)),c_2Enum_2E0)) & ! [X70 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,c_2Enum_2E0),X70) = X70)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2Egcd__def)).
% 92.92/13.72 thf(f22633,plain,(
% 92.92/13.72 spl854_112),
% 92.92/13.72 inference(avatar_split_clause,[],[f13580,f22631])).
% 92.92/13.72 thf(f22631,plain,(
% 92.92/13.72 spl854_112 <=> ! [X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X4) = X4)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_112])])).
% 92.92/13.72 thf(f13580,plain,(
% 92.92/13.72 ( ! [X4 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),X4) = X4)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9184,f13512])).
% 92.92/13.72 thf(f9184,plain,(
% 92.92/13.72 ( ! [X4 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,c_2Earithmetic_2EZERO),X4) = X4)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4847])).
% 92.92/13.72 thf(f22629,plain,(
% 92.92/13.72 spl854_111),
% 92.92/13.72 inference(avatar_split_clause,[],[f12090,f22627])).
% 92.92/13.72 thf(f22627,plain,(
% 92.92/13.72 spl854_111 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_111])])).
% 92.92/13.72 thf(f12090,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8233])).
% 92.92/13.72 thf(f8233,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0,X2 : X0] : (((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true) | (X1 != X2)) & ((X1 = X2) | (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true)))),
% 92.92/13.72 inference(nnf_transformation,[],[f4040])).
% 92.92/13.72 thf(f4040,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0,X2 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true) <=> (X1 = X2))),
% 92.92/13.72 inference(fool_elimination,[],[f4039])).
% 92.92/13.72 thf(f4039,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) <=> (X1 = X2))),
% 92.92/13.72 inference(rectify,[],[f280])).
% 92.92/13.72 thf(f280,axiom,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) <=> (X1 = X2))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D)).
% 92.92/13.72 thf(f22625,plain,(
% 92.92/13.72 spl854_110),
% 92.92/13.72 inference(avatar_split_clause,[],[f11237,f22623])).
% 92.92/13.72 thf(f22623,plain,(
% 92.92/13.72 spl854_110 <=> ! [X1 : $tType,X0 : $tType,X2 : X1] : (vAPP(X1,X1,vAPP(tyop_2Ebool_2Eitself(X0),sTfun(X1,X1),c_2Ebool_2Eitself__case(X0,X1),c_2Ebool_2Ethe__value(X0)),X2) = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_110])])).
% 92.92/13.72 thf(f11237,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1] : ((vAPP(X1,X1,vAPP(tyop_2Ebool_2Eitself(X0),sTfun(X1,X1),c_2Ebool_2Eitself__case(X0,X1),c_2Ebool_2Ethe__value(X0)),X2) = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5133])).
% 92.92/13.72 thf(f5133,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X1] : (vAPP(X1,X1,vAPP(tyop_2Ebool_2Eitself(X0),sTfun(X1,X1),c_2Ebool_2Eitself__case(X0,X1),c_2Ebool_2Ethe__value(X0)),X2) = X2)),
% 92.92/13.72 inference(rectify,[],[f42])).
% 92.92/13.72 thf(f42,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X35 : X5] : (vAPP(X5,X5,vAPP(tyop_2Ebool_2Eitself(X0),sTfun(X5,X5),c_2Ebool_2Eitself__case(X0,X5),c_2Ebool_2Ethe__value(X0)),X35) = X35)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__case__thm)).
% 92.92/13.72 thf(f22621,plain,(
% 92.92/13.72 spl854_109),
% 92.92/13.72 inference(avatar_split_clause,[],[f10565,f22619])).
% 92.92/13.72 thf(f22619,plain,(
% 92.92/13.72 spl854_109 <=> ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o,X3 : tyop_2Ebool_2Eitself(X0)] : (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X3)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_109])])).
% 92.92/13.72 thf(f10565,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X3 : tyop_2Ebool_2Eitself(X0),X1 : tyop_2Ebool_2Eitself(X0) > $o] : (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X3))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7058])).
% 92.92/13.72 thf(f7058,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : ((($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,vAPP(sTfun(tyop_2Ebool_2Eitself(X0),$o),tyop_2Ebool_2Eitself(X0),sK259(X0),X1))) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0)))) & (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))) | ! [X3 : tyop_2Ebool_2Eitself(X0)] : ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X3))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK259])],[f7056,f7057])).
% 92.92/13.72 thf(f7057,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : (? [X2 : tyop_2Ebool_2Eitself(X0)] : ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) => ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,vAPP(sTfun(tyop_2Ebool_2Eitself(X0),$o),tyop_2Ebool_2Eitself(X0),sK259(X0),X1))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f7056,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : ((? [X2 : tyop_2Ebool_2Eitself(X0)] : ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0)))) & (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))) | ! [X3 : tyop_2Ebool_2Eitself(X0)] : ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X3))))),
% 92.92/13.72 inference(rectify,[],[f7055])).
% 92.92/13.72 thf(f7055,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : ((? [X2 : tyop_2Ebool_2Eitself(X0)] : ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0)))) & (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))) | ! [X2 : tyop_2Ebool_2Eitself(X0)] : ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2))))),
% 92.92/13.72 inference(nnf_transformation,[],[f3018])).
% 92.92/13.72 thf(f3018,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : (? [X2 : tyop_2Ebool_2Eitself(X0)] : ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) <=> ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f3017])).
% 92.92/13.72 thf(f3017,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : (? [X2 : tyop_2Ebool_2Eitself(X0)] : vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2) <=> vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0)))),
% 92.92/13.72 inference(rectify,[],[f193])).
% 92.92/13.72 thf(f193,axiom,(
% 92.92/13.72 ! [X0 : $tType,X7 : tyop_2Ebool_2Eitself(X0) > $o] : (? [X4 : tyop_2Ebool_2Eitself(X0)] : vAPP(tyop_2Ebool_2Eitself(X0),$o,X7,X4) <=> vAPP(tyop_2Ebool_2Eitself(X0),$o,X7,c_2Ebool_2Ethe__value(X0)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__itself)).
% 92.92/13.72 thf(f22617,plain,(
% 92.92/13.72 spl854_108),
% 92.92/13.72 inference(avatar_split_clause,[],[f10289,f22615])).
% 92.92/13.72 thf(f22615,plain,(
% 92.92/13.72 spl854_108 <=> ! [X0 : $tType,X2 : tyop_2Ebool_2Eitself(X0),X1 : tyop_2Ebool_2Eitself(X0) > $o] : (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_108])])).
% 92.92/13.72 thf(f10289,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : tyop_2Ebool_2Eitself(X0),X1 : tyop_2Ebool_2Eitself(X0) > $o] : (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5668])).
% 92.92/13.72 thf(f5668,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : (! [X2 : tyop_2Ebool_2Eitself(X0)] : ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)) | ($true != vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2774])).
% 92.92/13.72 thf(f2774,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : (($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0))) => ! [X2 : tyop_2Ebool_2Eitself(X0)] : ($true = vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2)))),
% 92.92/13.72 inference(fool_elimination,[],[f2773])).
% 92.92/13.72 thf(f2773,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0) > $o] : (vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,c_2Ebool_2Ethe__value(X0)) => ! [X2 : tyop_2Ebool_2Eitself(X0)] : vAPP(tyop_2Ebool_2Eitself(X0),$o,X1,X2))),
% 92.92/13.72 inference(rectify,[],[f191])).
% 92.92/13.72 thf(f191,axiom,(
% 92.92/13.72 ! [X0 : $tType,X7 : tyop_2Ebool_2Eitself(X0) > $o] : (vAPP(tyop_2Ebool_2Eitself(X0),$o,X7,c_2Ebool_2Ethe__value(X0)) => ! [X91 : tyop_2Ebool_2Eitself(X0)] : vAPP(tyop_2Ebool_2Eitself(X0),$o,X7,X91))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__induction)).
% 92.92/13.72 thf(f22613,plain,(
% 92.92/13.72 spl854_107),
% 92.92/13.72 inference(avatar_split_clause,[],[f10054,f22611])).
% 92.92/13.72 thf(f22611,plain,(
% 92.92/13.72 spl854_107 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1)) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_107])])).
% 92.92/13.72 thf(f10054,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5084])).
% 92.92/13.72 thf(f5084,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1)) = X1) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1)) = X0))),
% 92.92/13.72 inference(rectify,[],[f1510])).
% 92.92/13.72 thf(f1510,axiom,(
% 92.92/13.72 ! [X8 : tyop_2Enum_2Enum,X18 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X8),X18)) = X18) & (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X8),X18)) = X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2ENUMPAIR__DEST)).
% 92.92/13.72 thf(f22609,plain,(
% 92.92/13.72 spl854_106),
% 92.92/13.72 inference(avatar_split_clause,[],[f10053,f22607])).
% 92.92/13.72 thf(f22607,plain,(
% 92.92/13.72 spl854_106 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_106])])).
% 92.92/13.72 thf(f10053,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMPAIR,X0),X1)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5084])).
% 92.92/13.72 thf(f22605,plain,(
% 92.92/13.72 spl854_105),
% 92.92/13.72 inference(avatar_split_clause,[],[f10052,f22603])).
% 92.92/13.72 thf(f22603,plain,(
% 92.92/13.72 spl854_105 <=> ! [X0 : $o,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1)) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_105])])).
% 92.92/13.72 thf(f10052,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5083])).
% 92.92/13.72 thf(f5083,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1)) = X1) & (vAPP(tyop_2Enum_2Enum,$o,c_2Eind__type_2ENUMLEFT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X0),X1)) = X0))),
% 92.92/13.72 inference(rectify,[],[f1512])).
% 92.92/13.72 thf(f1512,axiom,(
% 92.92/13.72 ! [X8 : $o,X18 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X8),X18)) = X18) & (vAPP(tyop_2Enum_2Enum,$o,c_2Eind__type_2ENUMLEFT,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP($o,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSUM,X8),X18)) = X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2ENUMSUM__DEST)).
% 92.92/13.72 thf(f22601,plain,(
% 92.92/13.72 spl854_104),
% 92.92/13.72 inference(avatar_split_clause,[],[f9986,f22599])).
% 92.92/13.72 thf(f22599,plain,(
% 92.92/13.72 spl854_104 <=> ! [X0 : $tType,X1 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1)) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_104])])).
% 92.92/13.72 thf(f9986,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2566])).
% 92.92/13.72 thf(f2566,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1)) = X1)),
% 92.92/13.72 inference(fool_elimination,[],[f2565])).
% 92.92/13.72 thf(f2565,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),(^[X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)))) = X1)),
% 92.92/13.72 inference(rectify,[],[f85])).
% 92.92/13.72 thf(f85,axiom,(
% 92.92/13.72 ! [X0 : $tType,X8 : X0] : (vAPP(sTfun(X0,$o),X0,c_2Emin_2E_40(X0),(^[X18 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X8),X18)))) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESELECT__REFL__2)).
% 92.92/13.72 thf(f22597,plain,(
% 92.92/13.72 spl854_103),
% 92.92/13.72 inference(avatar_split_clause,[],[f9861,f22595])).
% 92.92/13.72 thf(f9861,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4964])).
% 92.92/13.72 thf(f4964,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X0)),
% 92.92/13.72 inference(rectify,[],[f1676])).
% 92.92/13.72 thf(f1676,axiom,(
% 92.92/13.72 ! [X70 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X4),X70)) = X70)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Ensnd__npair)).
% 92.92/13.72 thf(f22593,plain,(
% 92.92/13.72 spl854_102),
% 92.92/13.72 inference(avatar_split_clause,[],[f9860,f22591])).
% 92.92/13.72 thf(f9860,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4963])).
% 92.92/13.72 thf(f4963,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X1),X0)) = X1)),
% 92.92/13.72 inference(rectify,[],[f1675])).
% 92.92/13.72 thf(f1675,axiom,(
% 92.92/13.72 ! [X70 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enpair,X4),X70)) = X4)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enfst__npair)).
% 92.92/13.72 thf(f22589,plain,(
% 92.92/13.72 spl854_101),
% 92.92/13.72 inference(avatar_split_clause,[],[f9309,f22587])).
% 92.92/13.72 thf(f22520,plain,(
% 92.92/13.72 spl854_100 | ~spl854_9 | ~spl854_55),
% 92.92/13.72 inference(avatar_split_clause,[],[f22253,f22206,f21928,f22518])).
% 92.92/13.72 thf(f22518,plain,(
% 92.92/13.72 spl854_100 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1) != X0) | (X0 = X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_100])])).
% 92.92/13.72 thf(f22206,plain,(
% 92.92/13.72 spl854_55 <=> ! [X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : ((X18 = X19) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_55])])).
% 92.92/13.72 thf(f22253,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X1) != X0) | (X0 = X1)) ) | (~spl854_9 | ~spl854_55)),
% 92.92/13.72 inference(superposition,[],[f22207,f21929])).
% 92.92/13.72 thf(f22207,plain,(
% 92.92/13.72 ( ! [X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19)) | (X18 = X19)) ) | ~spl854_55),
% 92.92/13.72 inference(avatar_component_clause,[],[f22206])).
% 92.92/13.72 thf(f22461,plain,(
% 92.92/13.72 spl854_99),
% 92.92/13.72 inference(avatar_split_clause,[],[f17510,f22459])).
% 92.92/13.72 thf(f22459,plain,(
% 92.92/13.72 spl854_99 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($false = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_99])])).
% 92.92/13.72 thf(f17510,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($false = X0)) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f10522])).
% 92.92/13.72 thf(f10522,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($true = vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7025])).
% 92.92/13.72 thf(f22457,plain,(
% 92.92/13.72 spl854_98),
% 92.92/13.72 inference(avatar_split_clause,[],[f17481,f22455])).
% 92.92/13.72 thf(f22455,plain,(
% 92.92/13.72 spl854_98 <=> ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,$true),X0)) | ($true = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_98])])).
% 92.92/13.72 thf(f17481,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,$true),X0)) | ($true = X0)) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f15871])).
% 92.92/13.72 thf(f15871,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,$true),X0)) | ($true != vAPP($o,$o,vNOT,X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10553])).
% 92.92/13.72 thf(f10553,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0)) | ($true != vAPP($o,$o,vNOT,X0)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7039])).
% 92.92/13.72 thf(f22453,plain,(
% 92.92/13.72 spl854_97),
% 92.92/13.72 inference(avatar_split_clause,[],[f17478,f22451])).
% 92.92/13.72 thf(f22451,plain,(
% 92.92/13.72 spl854_97 <=> ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),$true)) | ($true = X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_97])])).
% 92.92/13.72 thf(f17478,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),$true)) | ($true = X1)) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f15874])).
% 92.92/13.72 thf(f15874,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),$true)) | (vAPP($o,$o,vNOT,X1) != $true)) )),
% 92.92/13.72 inference(equality_resolution,[],[f10550])).
% 92.92/13.72 thf(f10550,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP15,X1),X0)) | (vAPP($o,$o,vNOT,X1) != $true) | ($true != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7039])).
% 92.92/13.72 thf(f22449,plain,(
% 92.92/13.72 spl854_96),
% 92.92/13.72 inference(avatar_split_clause,[],[f16596,f22447])).
% 92.92/13.72 thf(f22447,plain,(
% 92.92/13.72 spl854_96 <=> ! [X1 : $o] : (($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,$true),X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_96])])).
% 92.92/13.72 thf(f16596,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,$true),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16595])).
% 92.92/13.72 thf(f16595,plain,(
% 92.92/13.72 ( ! [X3 : $o,X1 : $o] : (($true = X1) | ($true != X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,$true),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f16594])).
% 92.92/13.72 thf(f16594,plain,(
% 92.92/13.72 ( ! [X2 : $o,X3 : $o,X1 : $o] : (($true = X1) | ($true != X2) | ($true != X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X2),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12582])).
% 92.92/13.72 thf(f12582,plain,(
% 92.92/13.72 ( ! [X2 : $o,X3 : $o,X0 : $o,X1 : $o] : (($true = X1) | ($true != X0) | ($true != X2) | ($true != X3) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X2),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6521])).
% 92.92/13.72 thf(f6521,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : ((($true = X3) & ($true = X1)) | ($true != X0) | ($true != X2) | (($true != X3) & ($true = X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X2),X1)))),
% 92.92/13.72 inference(definition_folding,[],[f6101,f6520])).
% 92.92/13.72 thf(f6520,plain,(
% 92.92/13.72 ! [X1 : $o,X2 : $o] : ((($true != X1) & ($true = X2)) | ~($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X2),X1)))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f6101,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : ((($true = X3) & ($true = X1)) | ($true != X0) | ($true != X2) | (($true != X3) & ($true = X0)) | (($true != X1) & ($true = X2)))),
% 92.92/13.72 inference(flattening,[],[f6100])).
% 92.92/13.72 thf(f6100,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X3) & ($true = X1)) | (($true != X0) | ($true != X2))) | ((($true != X3) & ($true = X0)) | (($true != X1) & ($true = X2))))),
% 92.92/13.72 inference(ennf_transformation,[],[f4300])).
% 92.92/13.72 thf(f4300,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((($true = X0) => ($true = X3)) & (($true = X2) => ($true = X1))) => ((($true = X0) & ($true = X2)) => (($true = X3) & ($true = X1))))),
% 92.92/13.72 inference(fool_elimination,[],[f4299])).
% 92.92/13.72 thf(f4299,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o,X2 : $o,X3 : $o] : (((X0 => X3) & (X2 => X1)) => ((X0 & X2) => (X3 & X1)))),
% 92.92/13.72 inference(rectify,[],[f149])).
% 92.92/13.72 thf(f149,axiom,(
% 92.92/13.72 ! [X68 : $o,X18 : $o,X19 : $o,X69 : $o] : (((X68 => X69) & (X19 => X18)) => ((X68 & X19) => (X69 & X18)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__AND)).
% 92.92/13.72 thf(f22445,plain,(
% 92.92/13.72 spl854_95),
% 92.92/13.72 inference(avatar_split_clause,[],[f15938,f22443])).
% 92.92/13.72 thf(f22443,plain,(
% 92.92/13.72 spl854_95 <=> ! [X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_95])])).
% 92.92/13.72 thf(f15938,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10882])).
% 92.92/13.72 thf(f10882,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7465])).
% 92.92/13.72 thf(f7465,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) | (($true != X1) & ($true = X0))) & (($true = X1) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1))))),
% 92.92/13.72 inference(flattening,[],[f7464])).
% 92.92/13.72 thf(f7464,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) | (($true != X1) & ($true = X0))) & ((($true = X1) | ($true != X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f5794])).
% 92.92/13.72 thf(f5794,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) <=> (($true = X1) | ($true != X0)))),
% 92.92/13.72 inference(ennf_transformation,[],[f3254])).
% 92.92/13.72 thf(f3254,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) <=> (($true = X0) => ($true = X1)))),
% 92.92/13.72 inference(fool_elimination,[],[f3253])).
% 92.92/13.72 thf(f3253,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) <=> (X0 => X1))),
% 92.92/13.72 inference(rectify,[],[f202])).
% 92.92/13.72 thf(f202,axiom,(
% 92.92/13.72 ! [X1 : $o,X2 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X1),X2) <=> (X1 => X2))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E)).
% 92.92/13.72 thf(f22441,plain,(
% 92.92/13.72 spl854_94),
% 92.92/13.72 inference(avatar_split_clause,[],[f15867,f22439])).
% 92.92/13.72 thf(f22439,plain,(
% 92.92/13.72 spl854_94 <=> ! [X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,$true),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_94])])).
% 92.92/13.72 thf(f15867,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10540])).
% 92.92/13.72 thf(f10540,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7034])).
% 92.92/13.72 thf(f7034,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | (((($true != X0) & ($true != X1)) | ($true != X0)) & (($true = X0) | ($true = X1) | ($true = X0)))) & (((($true = X0) | (($true != X0) & ($true != X1))) & (($true = X0) | ($true = X1) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0))))),
% 92.92/13.72 inference(flattening,[],[f7033])).
% 92.92/13.72 thf(f7033,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | (((($true != X0) & ($true != X1)) | ($true != X0)) & ((($true = X0) | ($true = X1)) | ($true = X0)))) & (((($true = X0) | (($true != X0) & ($true != X1))) & ((($true = X0) | ($true = X1)) | ($true != X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6403])).
% 92.92/13.72 thf(f6403,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) <=> (($true = X0) <=> (($true = X0) | ($true = X1))))),
% 92.92/13.72 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 92.92/13.72 thf(f22437,plain,(
% 92.92/13.72 spl854_93),
% 92.92/13.72 inference(avatar_split_clause,[],[f15790,f22435])).
% 92.92/13.72 thf(f22435,plain,(
% 92.92/13.72 spl854_93 <=> ! [X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),$true)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_93])])).
% 92.92/13.72 thf(f15790,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10414])).
% 92.92/13.72 thf(f10414,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6965])).
% 92.92/13.72 thf(f22433,plain,(
% 92.92/13.72 spl854_92),
% 92.92/13.72 inference(avatar_split_clause,[],[f15789,f22431])).
% 92.92/13.72 thf(f22431,plain,(
% 92.92/13.72 spl854_92 <=> ! [X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,$true),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_92])])).
% 92.92/13.72 thf(f15789,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10415])).
% 92.92/13.72 thf(f10415,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6965])).
% 92.92/13.72 thf(f22429,plain,(
% 92.92/13.72 spl854_91),
% 92.92/13.72 inference(avatar_split_clause,[],[f12591,f22427])).
% 92.92/13.72 thf(f22427,plain,(
% 92.92/13.72 spl854_91 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_91])])).
% 92.92/13.72 thf(f12591,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8484])).
% 92.92/13.72 thf(f8484,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true != X0) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X0)))),
% 92.92/13.72 inference(rectify,[],[f8483])).
% 92.92/13.72 thf(f8483,plain,(
% 92.92/13.72 ! [X2 : $o,X1 : $o] : ((($true != X2) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X2)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6524])).
% 92.92/13.72 thf(f22425,plain,(
% 92.92/13.72 spl854_90),
% 92.92/13.72 inference(avatar_split_clause,[],[f12585,f22423])).
% 92.92/13.72 thf(f22423,plain,(
% 92.92/13.72 spl854_90 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_90])])).
% 92.92/13.72 thf(f12585,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8482])).
% 92.92/13.72 thf(f8482,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true != X0) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),X0)))),
% 92.92/13.72 inference(rectify,[],[f8481])).
% 92.92/13.72 thf(f8481,plain,(
% 92.92/13.72 ! [X1 : $o,X2 : $o] : ((($true != X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X2),X1)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6522])).
% 92.92/13.72 thf(f22421,plain,(
% 92.92/13.72 spl854_89 | ~spl854_35 | ~spl854_80),
% 92.92/13.72 inference(avatar_split_clause,[],[f22381,f22339,f22068,f22419])).
% 92.92/13.72 thf(f22419,plain,(
% 92.92/13.72 spl854_89 <=> ! [X0 : tyop_2Eone_2Eone,X1 : tyop_2Eone_2Eone] : (X0 = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_89])])).
% 92.92/13.72 thf(f22068,plain,(
% 92.92/13.72 spl854_35 <=> ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone,X1 : tyop_2Eone_2Eone] : (vAPP(tyop_2Eone_2Eone,tyop_2Eone_2Eone,X0,X1) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_35])])).
% 92.92/13.72 thf(f22381,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Eone_2Eone,X1 : tyop_2Eone_2Eone] : ((X0 = X1)) ) | (~spl854_35 | ~spl854_80)),
% 92.92/13.72 inference(superposition,[],[f22340,f22069])).
% 92.92/13.72 thf(f22069,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone,X1 : tyop_2Eone_2Eone] : ((vAPP(tyop_2Eone_2Eone,tyop_2Eone_2Eone,X0,X1) = X1)) ) | ~spl854_35),
% 92.92/13.72 inference(avatar_component_clause,[],[f22068])).
% 92.92/13.72 thf(f22417,plain,(
% 92.92/13.72 spl854_88),
% 92.92/13.72 inference(avatar_split_clause,[],[f12579,f22415])).
% 92.92/13.72 thf(f22415,plain,(
% 92.92/13.72 spl854_88 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_88])])).
% 92.92/13.72 thf(f12579,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8480])).
% 92.92/13.72 thf(f8480,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true != X0) & ($true = X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),X0)))),
% 92.92/13.72 inference(rectify,[],[f8479])).
% 92.92/13.72 thf(f8479,plain,(
% 92.92/13.72 ! [X1 : $o,X2 : $o] : ((($true != X1) & ($true = X2)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X2),X1)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6520])).
% 92.92/13.72 thf(f22413,plain,(
% 92.92/13.72 spl854_87),
% 92.92/13.72 inference(avatar_split_clause,[],[f10883,f22411])).
% 92.92/13.72 thf(f22411,plain,(
% 92.92/13.72 spl854_87 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) | ($true = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_87])])).
% 92.92/13.72 thf(f10883,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) | ($true = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7465])).
% 92.92/13.72 thf(f22409,plain,(
% 92.92/13.72 spl854_86),
% 92.92/13.72 inference(avatar_split_clause,[],[f10802,f22407])).
% 92.92/13.72 thf(f22407,plain,(
% 92.92/13.72 spl854_86 <=> ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_86])])).
% 92.92/13.72 thf(f10802,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7411])).
% 92.92/13.72 thf(f7411,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1)) | ($true != X1) | ($true != X0)) & ((($true = X1) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1))))),
% 92.92/13.72 inference(flattening,[],[f7410])).
% 92.92/13.72 thf(f7410,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1)) | (($true != X1) | ($true != X0))) & ((($true = X1) & ($true = X0)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f3200])).
% 92.92/13.72 thf(f3200,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1)) <=> (($true = X1) & ($true = X0)))),
% 92.92/13.72 inference(fool_elimination,[],[f3199])).
% 92.92/13.72 thf(f3199,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1) <=> (X1 & X0))),
% 92.92/13.72 inference(rectify,[],[f258])).
% 92.92/13.72 thf(f258,axiom,(
% 92.92/13.72 ! [X99 : $o,X100 : $o] : (vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X99),X100) <=> (X100 & X99))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Emarker_2EAC__DEF)).
% 92.92/13.72 thf(f22405,plain,(
% 92.92/13.72 spl854_85),
% 92.92/13.72 inference(avatar_split_clause,[],[f10801,f22403])).
% 92.92/13.72 thf(f22403,plain,(
% 92.92/13.72 spl854_85 <=> ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_85])])).
% 92.92/13.72 thf(f10801,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7411])).
% 92.92/13.72 thf(f22401,plain,(
% 92.92/13.72 spl854_84),
% 92.92/13.72 inference(avatar_split_clause,[],[f10546,f22399])).
% 92.92/13.72 thf(f22399,plain,(
% 92.92/13.72 spl854_84 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | ($true = X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_84])])).
% 92.92/13.72 thf(f10546,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | ($true = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7036])).
% 92.92/13.72 thf(f7036,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | (($true != X0) & ($true = X1))) & (($true = X0) | ($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0))))),
% 92.92/13.72 inference(flattening,[],[f7035])).
% 92.92/13.72 thf(f7035,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | (($true != X0) & ($true = X1))) & ((($true = X0) | ($true != X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6404])).
% 92.92/13.72 thf(f6404,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) <=> (($true = X0) | ($true != X1)))),
% 92.92/13.72 inference(definition_folding,[],[f5780,f6403])).
% 92.92/13.72 thf(f5780,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = X0) <=> (($true = X0) | ($true = X1))) <=> (($true = X0) | ($true != X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f3004])).
% 92.92/13.72 thf(f3004,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true = X0) <=> (($true = X0) | ($true = X1))) <=> (($true = X1) => ($true = X0)))),
% 92.92/13.72 inference(fool_elimination,[],[f3003])).
% 92.92/13.72 thf(f3003,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 <=> (X0 | X1)) <=> (X1 => X0))),
% 92.92/13.72 inference(rectify,[],[f108])).
% 92.92/13.72 thf(f108,axiom,(
% 92.92/13.72 ! [X44 : $o,X45 : $o] : ((X44 <=> (X44 | X45)) <=> (X45 => X44))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__IMP__THM)).
% 92.92/13.72 thf(f22397,plain,(
% 92.92/13.72 spl854_83),
% 92.92/13.72 inference(avatar_split_clause,[],[f9408,f22395])).
% 92.92/13.72 thf(f22395,plain,(
% 92.92/13.72 spl854_83 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_83])])).
% 92.92/13.72 thf(f9408,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(sTfun(tyop_2Enum_2Enum,$o),tyop_2Enum_2Enum,c_2Ewhile_2ELEAST,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2110])).
% 92.92/13.72 thf(f22372,plain,(
% 92.92/13.72 spl854_82),
% 92.92/13.72 inference(avatar_split_clause,[],[f18039,f22370])).
% 92.92/13.72 thf(f22370,plain,(
% 92.92/13.72 spl854_82 <=> ! [X0 : $o] : (($false = vAPP($o,$o,c_2Emarker_2ECong,X0)) | ($true = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_82])])).
% 92.92/13.72 thf(f18039,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($false = vAPP($o,$o,c_2Emarker_2ECong,X0)) | ($true = X0)) )),
% 92.92/13.72 inference(binary_proxy_clausification,[],[f9289])).
% 92.92/13.72 thf(f9289,plain,(
% 92.92/13.72 ( ! [X0 : $o] : ((vAPP($o,$o,c_2Emarker_2ECong,X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4864])).
% 92.92/13.72 thf(f4864,plain,(
% 92.92/13.72 ! [X0 : $o] : (vAPP($o,$o,c_2Emarker_2ECong,X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f259])).
% 92.92/13.72 thf(f259,axiom,(
% 92.92/13.72 ! [X8 : $o] : (vAPP($o,$o,c_2Emarker_2ECong,X8) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Emarker_2ECong__def)).
% 92.92/13.72 thf(f22346,plain,(
% 92.92/13.72 spl854_81),
% 92.92/13.72 inference(avatar_split_clause,[],[f21857,f22343])).
% 92.92/13.72 thf(f21857,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 inference(forward_demodulation,[],[f21856,f18124])).
% 92.92/13.72 thf(f21856,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 inference(forward_demodulation,[],[f21855,f13563])).
% 92.92/13.72 thf(f21855,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 inference(forward_demodulation,[],[f16820,f13548])).
% 92.92/13.72 thf(f16820,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))))),
% 92.92/13.72 inference(not_proxy_clausification,[],[f15653])).
% 92.92/13.72 thf(f15653,plain,(
% 92.92/13.72 ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))))),
% 92.92/13.72 inference(definition_unfolding,[],[f13509,f13512])).
% 92.92/13.72 thf(f13509,plain,(
% 92.92/13.72 (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = $true)),
% 92.92/13.72 inference(cnf_transformation,[],[f4830])).
% 92.92/13.72 thf(f4830,plain,(
% 92.92/13.72 (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = $true)),
% 92.92/13.72 inference(fool_elimination,[],[f4829])).
% 92.92/13.72 thf(f4829,plain,(
% 92.92/13.72 vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.92/13.72 inference(rectify,[],[f1481])).
% 92.92/13.72 thf(f1481,axiom,(
% 92.92/13.72 vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2ENOT__PRIME__1)).
% 92.92/13.72 thf(f22341,plain,(
% 92.92/13.72 spl854_80),
% 92.92/13.72 inference(avatar_split_clause,[],[f15313,f22339])).
% 92.92/13.72 thf(f15313,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : ((vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),c_2Ecombin_2EK(X0,X1),X3),X2) = X3)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f12387,f13539])).
% 92.92/13.72 thf(f13539,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType] : ((c_2Ecombin_2EFAIL(X0,X1) = c_2Ecombin_2EK(X0,X1))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9971,f9976])).
% 92.92/13.72 thf(f9971,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType] : ((c_2Ecombin_2EFAIL(X0,X1) = kCOMB)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2536])).
% 92.92/13.72 thf(f2536,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType] : (c_2Ecombin_2EFAIL(X0,X1) = kCOMB)),
% 92.92/13.72 inference(fool_elimination,[],[f2535])).
% 92.92/13.72 thf(f2535,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType] : (c_2Ecombin_2EFAIL(X0,X1) = (^[X2 : X0, X3 : X1] : (X2)))),
% 92.92/13.72 inference(rectify,[],[f328])).
% 92.92/13.72 thf(f328,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType] : (c_2Ecombin_2EFAIL(X0,X5) = (^[X8 : X0, X18 : X5] : (X8)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EFAIL__DEF)).
% 92.92/13.72 thf(f12387,plain,(
% 92.92/13.72 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : ((vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),c_2Ecombin_2EFAIL(X0,X1),X3),X2) = X3)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5259])).
% 92.92/13.72 thf(f5259,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0] : (vAPP(X1,X0,vAPP(X0,sTfun(X1,X0),c_2Ecombin_2EFAIL(X0,X1),X3),X2) = X3)),
% 92.92/13.72 inference(rectify,[],[f366])).
% 92.92/13.72 thf(f366,axiom,(
% 92.92/13.72 ! [X0 : $tType,X5 : $tType,X70 : X5,X4 : X0] : (vAPP(X5,X0,vAPP(X0,sTfun(X5,X0),c_2Ecombin_2EFAIL(X0,X5),X4),X70) = X4)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecombin_2EFAIL__THM)).
% 92.92/13.72 thf(f22337,plain,(
% 92.92/13.72 spl854_79),
% 92.92/13.72 inference(avatar_split_clause,[],[f18038,f22335])).
% 92.92/13.72 thf(f22335,plain,(
% 92.92/13.72 spl854_79 <=> ! [X0 : $o] : (($true = vAPP($o,$o,c_2Emarker_2ECong,X0)) | ($false = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_79])])).
% 92.92/13.72 thf(f18038,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,c_2Emarker_2ECong,X0)) | ($false = X0)) )),
% 92.92/13.72 inference(binary_proxy_clausification,[],[f9289])).
% 92.92/13.72 thf(f22333,plain,(
% 92.92/13.72 spl854_78),
% 92.92/13.72 inference(avatar_split_clause,[],[f13722,f22330])).
% 92.92/13.72 thf(f22330,plain,(
% 92.92/13.72 spl854_78 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_78])])).
% 92.92/13.72 thf(f13722,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(definition_unfolding,[],[f9386,f13512,f13512])).
% 92.92/13.72 thf(f9386,plain,(
% 92.92/13.72 (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(cnf_transformation,[],[f4923])).
% 92.92/13.72 thf(f22328,plain,(
% 92.92/13.72 spl854_77),
% 92.92/13.72 inference(avatar_split_clause,[],[f13559,f22325])).
% 92.92/13.72 thf(f22325,plain,(
% 92.92/13.72 spl854_77 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_77])])).
% 92.92/13.72 thf(f13559,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(definition_unfolding,[],[f9156,f9122,f9122])).
% 92.92/13.72 thf(f9156,plain,(
% 92.92/13.72 (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,c_2Enum_2E0))),
% 92.92/13.72 inference(cnf_transformation,[],[f4838])).
% 92.92/13.72 thf(f22323,plain,(
% 92.92/13.72 spl854_76),
% 92.92/13.72 inference(avatar_split_clause,[],[f13558,f22320])).
% 92.92/13.72 thf(f22320,plain,(
% 92.92/13.72 spl854_76 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_76])])).
% 92.92/13.72 thf(f13558,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(definition_unfolding,[],[f9153,f9122,f9122])).
% 92.92/13.72 thf(f9153,plain,(
% 92.92/13.72 (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,c_2Enum_2E0))),
% 92.92/13.72 inference(cnf_transformation,[],[f4837])).
% 92.92/13.72 thf(f22318,plain,(
% 92.92/13.72 spl854_75),
% 92.92/13.72 inference(avatar_split_clause,[],[f13557,f22315])).
% 92.92/13.72 thf(f22315,plain,(
% 92.92/13.72 spl854_75 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_75])])).
% 92.92/13.72 thf(f13557,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(definition_unfolding,[],[f9148,f13512,f13512])).
% 92.92/13.72 thf(f9148,plain,(
% 92.92/13.72 (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(cnf_transformation,[],[f4836])).
% 92.92/13.72 thf(f22313,plain,(
% 92.92/13.72 spl854_74),
% 92.92/13.72 inference(avatar_split_clause,[],[f13555,f22310])).
% 92.92/13.72 thf(f22310,plain,(
% 92.92/13.72 spl854_74 <=> (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_74])])).
% 92.92/13.72 thf(f13555,plain,(
% 92.92/13.72 (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(definition_unfolding,[],[f9145,f13512,f13512])).
% 92.92/13.72 thf(f9145,plain,(
% 92.92/13.72 (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(cnf_transformation,[],[f4835])).
% 92.92/13.72 thf(f4835,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sCOMB,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),cCOMB,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),vAPP(sTfun($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),bCOMB,c_2Ebool_2ECOND(tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Emin_2E_3D(tyop_2Enum_2Enum)),c_2Earithmetic_2EZERO))),c_2Earithmetic_2EZERO)),c_2Earithmetic_2EBIT1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X0),c_2Earithmetic_2EZERO))) & ! [X1 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(rectify,[],[f2032])).
% 92.92/13.72 thf(f2032,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sCOMB,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),cCOMB,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),vAPP(sTfun($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),bCOMB,c_2Ebool_2ECOND(tyop_2Enum_2Enum)),vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vAPP(sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o)),cCOMB,c_2Emin_2E_3D(tyop_2Enum_2Enum)),c_2Earithmetic_2EZERO))),c_2Earithmetic_2EZERO)),c_2Earithmetic_2EBIT1)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X0),c_2Earithmetic_2EZERO))) & ! [X2 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(fool_elimination,[],[f2031])).
% 92.92/13.72 thf(f2031,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET(tyop_2Enum_2Enum,tyop_2Enum_2Enum),(^[X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X1),c_2Earithmetic_2EZERO)),c_2Earithmetic_2EZERO),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X0),c_2Earithmetic_2EZERO))) & ! [X2 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X2))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,c_2Earithmetic_2EZERO))),
% 92.92/13.72 inference(rectify,[],[f1374])).
% 92.92/13.72 thf(f1374,axiom,(
% 92.92/13.72 ! [X137 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X137)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET(tyop_2Enum_2Enum,tyop_2Enum_2Enum),(^[X19 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),vAPP($o,sTfun(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Emin_2E_3D(tyop_2Enum_2Enum),X19),c_2Earithmetic_2EZERO)),c_2Earithmetic_2EZERO),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X19))))),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eonecount,X137),c_2Earithmetic_2EZERO))) & ! [X136 : tyop_2Enum_2Enum] : (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136))) & (c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,c_2Earithmetic_2EZERO))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Eexactlog__def)).
% 92.92/13.72 thf(f22308,plain,(
% 92.92/13.72 spl854_73),
% 92.92/13.72 inference(avatar_split_clause,[],[f13554,f22306])).
% 92.92/13.72 thf(f22306,plain,(
% 92.92/13.72 spl854_73 <=> ! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_73])])).
% 92.92/13.72 thf(f13554,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9146,f13512])).
% 92.92/13.72 thf(f9146,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4835])).
% 92.92/13.72 thf(f22304,plain,(
% 92.92/13.72 spl854_72),
% 92.92/13.72 inference(avatar_split_clause,[],[f9859,f22302])).
% 92.92/13.72 thf(f22302,plain,(
% 92.92/13.72 spl854_72 <=> ! [X0 : $tType,X1 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_72])])).
% 92.92/13.72 thf(f9859,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4962])).
% 92.92/13.72 thf(f4962,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X1)) = X1)),
% 92.92/13.72 inference(rectify,[],[f711])).
% 92.92/13.72 thf(f711,axiom,(
% 92.92/13.72 ! [X0 : $tType,X8 : X0] : (vAPP(tyop_2Eoption_2Eoption(X0),X0,c_2Eoption_2ETHE(X0),vAPP(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME(X0),X8)) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2ETHE__DEF)).
% 92.92/13.72 thf(f22300,plain,(
% 92.92/13.72 spl854_71),
% 92.92/13.72 inference(avatar_split_clause,[],[f9305,f22298])).
% 92.92/13.72 thf(f9305,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4880])).
% 92.92/13.72 thf(f4880,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X0))),
% 92.92/13.72 inference(rectify,[],[f1367])).
% 92.92/13.72 thf(f1367,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EiiSUC)).
% 92.92/13.72 thf(f22296,plain,(
% 92.92/13.72 spl854_70),
% 92.92/13.72 inference(avatar_split_clause,[],[f9164,f22294])).
% 92.92/13.72 thf(f22292,plain,(
% 92.92/13.72 spl854_69),
% 92.92/13.72 inference(avatar_split_clause,[],[f9152,f22290])).
% 92.92/13.72 thf(f22290,plain,(
% 92.92/13.72 spl854_69 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_69])])).
% 92.92/13.72 thf(f9152,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4836])).
% 92.92/13.72 thf(f22288,plain,(
% 92.92/13.72 spl854_68),
% 92.92/13.72 inference(avatar_split_clause,[],[f18037,f22286])).
% 92.92/13.72 thf(f22286,plain,(
% 92.92/13.72 spl854_68 <=> ! [X0 : $o] : (($false = vAPP($o,$o,c_2Emarker_2EAbbrev,X0)) | ($true = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_68])])).
% 92.92/13.72 thf(f18037,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($false = vAPP($o,$o,c_2Emarker_2EAbbrev,X0)) | ($true = X0)) )),
% 92.92/13.72 inference(binary_proxy_clausification,[],[f9290])).
% 92.92/13.72 thf(f9290,plain,(
% 92.92/13.72 ( ! [X0 : $o] : ((vAPP($o,$o,c_2Emarker_2EAbbrev,X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4865])).
% 92.92/13.72 thf(f4865,plain,(
% 92.92/13.72 ! [X0 : $o] : (vAPP($o,$o,c_2Emarker_2EAbbrev,X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f256])).
% 92.92/13.72 thf(f256,axiom,(
% 92.92/13.72 ! [X8 : $o] : (vAPP($o,$o,c_2Emarker_2EAbbrev,X8) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Emarker_2EAbbrev__def)).
% 92.92/13.72 thf(f22261,plain,(
% 92.92/13.72 spl854_67),
% 92.92/13.72 inference(avatar_split_clause,[],[f18036,f22259])).
% 92.92/13.72 thf(f22259,plain,(
% 92.92/13.72 spl854_67 <=> ! [X0 : $o] : (($true = vAPP($o,$o,c_2Emarker_2EAbbrev,X0)) | ($false = X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_67])])).
% 92.92/13.72 thf(f18036,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,c_2Emarker_2EAbbrev,X0)) | ($false = X0)) )),
% 92.92/13.72 inference(binary_proxy_clausification,[],[f9290])).
% 92.92/13.72 thf(f22252,plain,(
% 92.92/13.72 spl854_66),
% 92.92/13.72 inference(avatar_split_clause,[],[f16440,f22250])).
% 92.92/13.72 thf(f22250,plain,(
% 92.92/13.72 spl854_66 <=> ! [X0 : $tType,X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_66])])).
% 92.92/13.72 thf(f16440,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12091])).
% 92.92/13.72 thf(f12091,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true) | (X1 != X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8233])).
% 92.92/13.72 thf(f22248,plain,(
% 92.92/13.72 spl854_65),
% 92.92/13.72 inference(avatar_split_clause,[],[f11236,f22246])).
% 92.92/13.72 thf(f22246,plain,(
% 92.92/13.72 spl854_65 <=> ! [X0 : $tType,X2 : X0,X1 : tyop_2Eone_2Eone] : (vAPP(X0,X0,vAPP(tyop_2Eone_2Eone,sTfun(X0,X0),c_2Eone_2Eone__CASE(X0),X1),X2) = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_65])])).
% 92.92/13.72 thf(f11236,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X2 : X0,X1 : tyop_2Eone_2Eone] : ((vAPP(X0,X0,vAPP(tyop_2Eone_2Eone,sTfun(X0,X0),c_2Eone_2Eone__CASE(X0),X1),X2) = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5132])).
% 92.92/13.72 thf(f5132,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Eone_2Eone,X2 : X0] : (vAPP(X0,X0,vAPP(tyop_2Eone_2Eone,sTfun(X0,X0),c_2Eone_2Eone__CASE(X0),X1),X2) = X2)),
% 92.92/13.72 inference(rectify,[],[f393])).
% 92.92/13.72 thf(f393,axiom,(
% 92.92/13.72 ! [X0 : $tType,X82 : tyop_2Eone_2Eone,X4 : X0] : (vAPP(X0,X0,vAPP(tyop_2Eone_2Eone,sTfun(X0,X0),c_2Eone_2Eone__CASE(X0),X82),X4) = X4)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eone_2Eone__case__def)).
% 92.92/13.72 thf(f22244,plain,(
% 92.92/13.72 spl854_64),
% 92.92/13.72 inference(avatar_split_clause,[],[f10437,f22242])).
% 92.92/13.72 thf(f22242,plain,(
% 92.92/13.72 spl854_64 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_64])])).
% 92.92/13.72 thf(f10437,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6975])).
% 92.92/13.72 thf(f6975,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X1)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X1))))),
% 92.92/13.72 inference(nnf_transformation,[],[f5106])).
% 92.92/13.72 thf(f5106,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X1)) <=> (X0 = X1))),
% 92.92/13.72 inference(rectify,[],[f1662])).
% 92.92/13.72 thf(f1662,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X137)) <=> (X134 = X137))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Etri__11)).
% 92.92/13.72 thf(f22240,plain,(
% 92.92/13.72 spl854_63),
% 92.92/13.72 inference(avatar_split_clause,[],[f10187,f22238])).
% 92.92/13.72 thf(f22238,plain,(
% 92.92/13.72 spl854_63 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_63])])).
% 92.92/13.72 thf(f10187,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5535])).
% 92.92/13.72 thf(f5535,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f5102])).
% 92.92/13.72 thf(f5102,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X1)) => (X0 = X1))),
% 92.92/13.72 inference(rectify,[],[f382])).
% 92.92/13.72 thf(f382,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X137)) => (X134 = X137))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EINV__SUC)).
% 92.92/13.72 thf(f22236,plain,(
% 92.92/13.72 spl854_62),
% 92.92/13.72 inference(avatar_split_clause,[],[f10186,f22234])).
% 92.92/13.72 thf(f22234,plain,(
% 92.92/13.72 spl854_62 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_62])])).
% 92.92/13.72 thf(f10186,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5534])).
% 92.92/13.72 thf(f5534,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1)))),
% 92.92/13.72 inference(ennf_transformation,[],[f5101])).
% 92.92/13.72 thf(f5101,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1)) => (X0 = X1))),
% 92.92/13.72 inference(rectify,[],[f1492])).
% 92.92/13.72 thf(f1492,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum,X137 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X134) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X137)) => (X134 = X137))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EPRIMES__11)).
% 92.92/13.72 thf(f22232,plain,(
% 92.92/13.72 spl854_61),
% 92.92/13.72 inference(avatar_split_clause,[],[f10097,f22230])).
% 92.92/13.72 thf(f22230,plain,(
% 92.92/13.72 spl854_61 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_61])])).
% 92.92/13.72 thf(f10097,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6836])).
% 92.92/13.72 thf(f6836,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))),
% 92.92/13.72 inference(flattening,[],[f6835])).
% 92.92/13.72 thf(f6835,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (X0 != X1)) & ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)))) & (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) & (((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) & (((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) & (((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) & (((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))))),
% 92.92/13.72 inference(nnf_transformation,[],[f2586])).
% 92.92/13.72 thf(f2586,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)) <=> (X0 = X1)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> (X0 = X1)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) <=> (c_2Ebool_2EF = $true)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> (c_2Ebool_2EF = $true)) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) <=> (c_2Ebool_2EF = $true)) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) <=> (c_2Ebool_2EF = $true)) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> (c_2Ebool_2EF = $true)) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> (c_2Ebool_2EF = $true)))),
% 92.92/13.72 inference(fool_elimination,[],[f2585])).
% 92.92/13.72 thf(f2585,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1)) <=> (X0 = X1)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> (X0 = X1)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1)) <=> c_2Ebool_2EF) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X1) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) <=> c_2Ebool_2EF))),
% 92.92/13.72 inference(rectify,[],[f1380])).
% 92.92/13.72 thf(f1380,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum,X27 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)) <=> (X27 = X136)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X27)) <=> (X27 = X136)) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X27)) <=> c_2Ebool_2EF) & ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136) = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X27)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X136)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)) <=> c_2Ebool_2EF) & ((c_2Earithmetic_2EZERO = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X136)) <=> c_2Ebool_2EF))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2Enumeral__eq)).
% 92.92/13.72 thf(f22228,plain,(
% 92.92/13.72 spl854_60),
% 92.92/13.72 inference(avatar_split_clause,[],[f10095,f22226])).
% 92.92/13.72 thf(f22226,plain,(
% 92.92/13.72 spl854_60 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_60])])).
% 92.92/13.72 thf(f10095,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((X0 = X1) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6836])).
% 92.92/13.72 thf(f22224,plain,(
% 92.92/13.72 spl854_59),
% 92.92/13.72 inference(avatar_split_clause,[],[f9755,f22222])).
% 92.92/13.72 thf(f22222,plain,(
% 92.92/13.72 spl854_59 <=> ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_59])])).
% 92.92/13.72 thf(f9755,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6795])).
% 92.92/13.72 thf(f6795,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ((($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,sP3,X0))) & (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6385])).
% 92.92/13.72 thf(f6385,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) <=> ($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)))),
% 92.92/13.72 inference(definition_folding,[],[f5514,f6384])).
% 92.92/13.72 thf(f5514,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) <=> (! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))))),
% 92.92/13.72 inference(flattening,[],[f5513])).
% 92.92/13.72 thf(f5513,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) <=> (! [X1 : tyop_2Enum_2Enum] : (((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1)) | ($true != vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2386])).
% 92.92/13.72 thf(f2386,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) <=> (! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0)) => ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1))) & ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),X0)))))),
% 92.92/13.72 inference(fool_elimination,[],[f2385])).
% 92.92/13.72 thf(f2385,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0) <=> (! [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X1),X0) => ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X1) | (X0 = X1))) & vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X0))))),
% 92.92/13.72 inference(rectify,[],[f1461])).
% 92.92/13.72 thf(f1461,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X72) <=> (! [X49 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X49),X72) => ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X49) | (X49 = X72))) & vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = X72))))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2Eprime__def)).
% 92.92/13.72 thf(f22220,plain,(
% 92.92/13.72 spl854_58),
% 92.92/13.72 inference(avatar_split_clause,[],[f9754,f22218])).
% 92.92/13.72 thf(f9754,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,sP3,X0)) | ($true != vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6795])).
% 92.92/13.72 thf(f22216,plain,(
% 92.92/13.72 spl854_57),
% 92.92/13.72 inference(avatar_split_clause,[],[f9722,f22214])).
% 92.92/13.72 thf(f9722,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6789])).
% 92.92/13.72 thf(f6789,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : ((($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,sP2,X0))) & (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0))))),
% 92.92/13.72 inference(nnf_transformation,[],[f6383])).
% 92.92/13.72 thf(f6383,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) <=> ($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)))),
% 92.92/13.72 inference(definition_folding,[],[f5512,f6382])).
% 92.92/13.72 thf(f5512,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) <=> ! [X1 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,X0)) | ? [X2 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 inference(flattening,[],[f5511])).
% 92.92/13.72 thf(f5511,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) <=> ! [X1 : tyop_2Emin_2Eind > $o] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,X0)) | (? [X2 : tyop_2Emin_2Eind] : (($true != vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,X2))) | ($true != vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP)))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2332])).
% 92.92/13.72 thf(f2332,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0)) <=> ! [X1 : tyop_2Emin_2Eind > $o] : ((! [X2 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,X1,X2)) => ($true = vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2)))) & ($true = vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP))) => ($true = vAPP(tyop_2Emin_2Eind,$o,X1,X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f2331])).
% 92.92/13.72 thf(f2331,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : (vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0) <=> ! [X1 : tyop_2Emin_2Eind > $o] : ((! [X2 : tyop_2Emin_2Eind] : (vAPP(tyop_2Emin_2Eind,$o,X1,X2) => vAPP(tyop_2Emin_2Eind,$o,X1,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X2))) & vAPP(tyop_2Emin_2Eind,$o,X1,c_2Enum_2EZERO__REP)) => vAPP(tyop_2Emin_2Eind,$o,X1,X0)))),
% 92.92/13.72 inference(rectify,[],[f376])).
% 92.92/13.72 thf(f376,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Emin_2Eind] : (vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X134) <=> ! [X43 : tyop_2Emin_2Eind > $o] : ((! [X135 : tyop_2Emin_2Eind] : (vAPP(tyop_2Emin_2Eind,$o,X43,X135) => vAPP(tyop_2Emin_2Eind,$o,X43,vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X135))) & vAPP(tyop_2Emin_2Eind,$o,X43,c_2Enum_2EZERO__REP)) => vAPP(tyop_2Emin_2Eind,$o,X43,X134)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EIS__NUM__REP)).
% 92.92/13.72 thf(f22212,plain,(
% 92.92/13.72 spl854_56),
% 92.92/13.72 inference(avatar_split_clause,[],[f9721,f22210])).
% 92.92/13.72 thf(f9721,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP(tyop_2Emin_2Eind,$o,sP2,X0)) | ($true != vAPP(tyop_2Emin_2Eind,$o,c_2Enum_2EIS__NUM__REP,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6789])).
% 92.92/13.72 thf(f22208,plain,(
% 92.92/13.72 spl854_55),
% 92.92/13.72 inference(avatar_split_clause,[],[f9218,f22206])).
% 92.92/13.72 thf(f9218,plain,(
% 92.92/13.72 ( ! [X18 : tyop_2Enum_2Enum,X19 : tyop_2Enum_2Enum] : ((X18 = X19) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X18) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,X19))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6597])).
% 92.92/13.72 thf(f22172,plain,(
% 92.92/13.72 spl854_54 | ~spl854_4 | ~spl854_16),
% 92.92/13.72 inference(avatar_split_clause,[],[f21980,f21977,f21876,f22170])).
% 92.92/13.72 thf(f22170,plain,(
% 92.92/13.72 spl854_54 <=> ! [X0 : tyop_2Enum_2Enum > tyop_2Eone_2Eone,X1 : tyop_2Enum_2Enum] : (c_2Ebool_2EARB(tyop_2Eone_2Eone) = vAPP(tyop_2Enum_2Enum,tyop_2Eone_2Eone,X0,X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_54])])).
% 92.92/13.72 thf(f21980,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum > tyop_2Eone_2Eone,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EARB(tyop_2Eone_2Eone) = vAPP(tyop_2Enum_2Enum,tyop_2Eone_2Eone,X0,X1))) ) | (~spl854_4 | ~spl854_16)),
% 92.92/13.72 inference(superposition,[],[f21978,f21877])).
% 92.92/13.72 thf(f22151,plain,(
% 92.92/13.72 spl854_53),
% 92.92/13.72 inference(avatar_split_clause,[],[f19190,f22149])).
% 92.92/13.72 thf(f22149,plain,(
% 92.92/13.72 spl854_53 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,$true),X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_53])])).
% 92.92/13.72 thf(f19190,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,$true),X0))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f19189])).
% 92.92/13.72 thf(f19189,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = $false) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,$true),X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f15860,f17793])).
% 92.92/13.72 thf(f15860,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,$true),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f14455])).
% 92.92/13.72 thf(f14455,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != X1)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10521,f13520])).
% 92.92/13.72 thf(f10521,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP13,X1),X0)) | (c_2Ebool_2EF = $true) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7025])).
% 92.92/13.72 thf(f22147,plain,(
% 92.92/13.72 spl854_52),
% 92.92/13.72 inference(avatar_split_clause,[],[f17483,f22145])).
% 92.92/13.72 thf(f22145,plain,(
% 92.92/13.72 spl854_52 <=> ! [X1 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_52])])).
% 92.92/13.72 thf(f17483,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),$true))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f15863])).
% 92.92/13.72 thf(f15863,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),$true)) | ($true != $true)) )),
% 92.92/13.72 inference(equality_resolution,[],[f10544])).
% 92.92/13.72 thf(f10544,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP14,X1),X0)) | ($true != X0) | ($true != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7034])).
% 92.92/13.72 thf(f22143,plain,(
% 92.92/13.72 spl854_51),
% 92.92/13.72 inference(avatar_split_clause,[],[f16606,f22141])).
% 92.92/13.72 thf(f16606,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12592])).
% 92.92/13.72 thf(f12592,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP83,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8484])).
% 92.92/13.72 thf(f22139,plain,(
% 92.92/13.72 spl854_50),
% 92.92/13.72 inference(avatar_split_clause,[],[f16599,f22137])).
% 92.92/13.72 thf(f16599,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12586])).
% 92.92/13.72 thf(f12586,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP82,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8482])).
% 92.92/13.72 thf(f22135,plain,(
% 92.92/13.72 spl854_49),
% 92.92/13.72 inference(avatar_split_clause,[],[f16588,f22133])).
% 92.92/13.72 thf(f16588,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f12580])).
% 92.92/13.72 thf(f12580,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP81,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f8480])).
% 92.92/13.72 thf(f22131,plain,(
% 92.92/13.72 spl854_48),
% 92.92/13.72 inference(avatar_split_clause,[],[f16173,f22129])).
% 92.92/13.72 thf(f16173,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,$true),X0))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11616])).
% 92.92/13.72 thf(f11616,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true != X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7834])).
% 92.92/13.72 thf(f7834,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((($true != X0) & ($true != X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X0)))),
% 92.92/13.72 inference(rectify,[],[f7833])).
% 92.92/13.72 thf(f7833,plain,(
% 92.92/13.72 ! [X2 : $o,X1 : $o] : ((($true != X2) & ($true != X1)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X2)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6442])).
% 92.92/13.72 thf(f22127,plain,(
% 92.92/13.72 spl854_47),
% 92.92/13.72 inference(avatar_split_clause,[],[f16172,f22125])).
% 92.92/13.72 thf(f16172,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11617])).
% 92.92/13.72 thf(f11617,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true != X0) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP34,X1),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7834])).
% 92.92/13.72 thf(f22123,plain,(
% 92.92/13.72 spl854_46),
% 92.92/13.72 inference(avatar_split_clause,[],[f16041,f22121])).
% 92.92/13.72 thf(f16041,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X1),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f11042])).
% 92.92/13.72 thf(f11042,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Earithmetic_2E_3E_3D,X0),X1)) | (X0 != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7570])).
% 92.92/13.72 thf(f22119,plain,(
% 92.92/13.72 spl854_45),
% 92.92/13.72 inference(avatar_split_clause,[],[f15937,f22117])).
% 92.92/13.72 thf(f22117,plain,(
% 92.92/13.72 spl854_45 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_45])])).
% 92.92/13.72 thf(f15937,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10884])).
% 92.92/13.72 thf(f10884,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)) | ($true != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7465])).
% 92.92/13.72 thf(f22115,plain,(
% 92.92/13.72 spl854_44 | ~spl854_5 | spl854_12),
% 92.92/13.72 inference(avatar_split_clause,[],[f21945,f21940,f21881,f22112])).
% 92.92/13.72 thf(f21945,plain,(
% 92.92/13.72 ($false = vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124)) | (~spl854_5 | spl854_12)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f21944])).
% 92.92/13.72 thf(f21944,plain,(
% 92.92/13.72 ($true != $true) | ($false = vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124)) | (~spl854_5 | spl854_12)),
% 92.92/13.72 inference(superposition,[],[f21942,f21882])).
% 92.92/13.72 thf(f22110,plain,(
% 92.92/13.72 spl854_43),
% 92.92/13.72 inference(avatar_split_clause,[],[f15884,f22107])).
% 92.92/13.72 thf(f15884,plain,(
% 92.92/13.72 ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,$true),$true))),
% 92.92/13.72 inference(equality_resolution,[],[f15883])).
% 92.92/13.72 thf(f15883,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),$true)) | ($true != X0)) )),
% 92.92/13.72 inference(equality_resolution,[],[f10803])).
% 92.92/13.72 thf(f10803,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emarker_2EAC,X0),X1)) | ($true != X1) | ($true != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7411])).
% 92.92/13.72 thf(f22105,plain,(
% 92.92/13.72 spl854_42),
% 92.92/13.72 inference(avatar_split_clause,[],[f15796,f22103])).
% 92.92/13.72 thf(f15796,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X1),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10431])).
% 92.92/13.72 thf(f10431,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1)) | (X0 != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6972])).
% 92.92/13.72 thf(f6972,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (((X0 = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1))) & (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1)) | (X0 != X1)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6397])).
% 92.92/13.72 thf(f6397,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP10,X0),X1)))),
% 92.92/13.72 inference(definition_folding,[],[f2972,f6396])).
% 92.92/13.72 thf(f2972,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> (((vAPP($o,$o,vNOT,X1) = $true) & ($true = vAPP($o,$o,vNOT,X0))) | (($true = X1) & ($true = X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f2971])).
% 92.92/13.72 thf(f2971,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ((vAPP($o,$o,vNOT,X1) & vAPP($o,$o,vNOT,X0)) | (X1 & X0)))),
% 92.92/13.72 inference(rectify,[],[f124])).
% 92.92/13.72 thf(f124,axiom,(
% 92.92/13.72 ! [X9 : $o,X10 : $o] : ((X9 = X10) <=> ((vAPP($o,$o,vNOT,X10) & vAPP($o,$o,vNOT,X9)) | (X10 & X9)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__EXPAND)).
% 92.92/13.72 thf(f22101,plain,(
% 92.92/13.72 spl854_41),
% 92.92/13.72 inference(avatar_split_clause,[],[f15791,f22099])).
% 92.92/13.72 thf(f15791,plain,(
% 92.92/13.72 ( ! [X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X1))) )),
% 92.92/13.72 inference(equality_resolution,[],[f10420])).
% 92.92/13.72 thf(f10420,plain,(
% 92.92/13.72 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) | (X0 != X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6966])).
% 92.92/13.72 thf(f6966,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : (((X0 = X1) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0))) & (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)) | (X0 != X1)))),
% 92.92/13.72 inference(nnf_transformation,[],[f6395])).
% 92.92/13.72 thf(f6395,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP9,X1),X0)))),
% 92.92/13.72 inference(definition_folding,[],[f5769,f6394])).
% 92.92/13.72 thf(f5769,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ((($true = X0) | ($true != X1)) & (($true = X1) | ($true != X0))))),
% 92.92/13.72 inference(ennf_transformation,[],[f2968])).
% 92.92/13.72 thf(f2968,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ((($true = X1) => ($true = X0)) & (($true = X0) => ($true = X1))))),
% 92.92/13.72 inference(fool_elimination,[],[f2967])).
% 92.92/13.72 thf(f2967,plain,(
% 92.92/13.72 ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ((X1 => X0) & (X0 => X1)))),
% 92.92/13.72 inference(rectify,[],[f123])).
% 92.92/13.72 thf(f123,axiom,(
% 92.92/13.72 ! [X9 : $o,X10 : $o] : ((X9 = X10) <=> ((X10 => X9) & (X9 => X10)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__IMP__THM)).
% 92.92/13.72 thf(f22097,plain,(
% 92.92/13.72 spl854_40),
% 92.92/13.72 inference(avatar_split_clause,[],[f9803,f22095])).
% 92.92/13.72 thf(f9803,plain,(
% 92.92/13.72 ( ! [X0 : $tType] : ((vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),c_2Erelation_2EEMPTY__REL(X0)) = $true)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2446])).
% 92.92/13.72 thf(f2446,plain,(
% 92.92/13.72 ! [X0 : $tType] : (vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),c_2Erelation_2EEMPTY__REL(X0)) = $true)),
% 92.92/13.72 inference(fool_elimination,[],[f2445])).
% 92.92/13.72 thf(f2445,plain,(
% 92.92/13.72 ! [X0 : $tType] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),c_2Erelation_2EEMPTY__REL(X0))),
% 92.92/13.72 inference(rectify,[],[f557])).
% 92.92/13.72 thf(f557,axiom,(
% 92.92/13.72 ! [X0 : $tType] : vAPP(sTfun(X0,sTfun(X0,$o)),$o,c_2Erelation_2EWF(X0),c_2Erelation_2EEMPTY__REL(X0))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EWF__EMPTY__REL)).
% 92.92/13.72 thf(f22093,plain,(
% 92.92/13.72 spl854_39),
% 92.92/13.72 inference(avatar_split_clause,[],[f9801,f22091])).
% 92.92/13.72 thf(f9801,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2442])).
% 92.92/13.72 thf(f2442,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X0))),
% 92.92/13.72 inference(fool_elimination,[],[f2441])).
% 92.92/13.72 thf(f2441,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X0),X0)),
% 92.92/13.72 inference(rectify,[],[f1465])).
% 92.92/13.72 thf(f1465,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Edivides_2Edivides,X72),X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EDIVIDES__REFL)).
% 92.92/13.72 thf(f22089,plain,(
% 92.92/13.72 spl854_38),
% 92.92/13.72 inference(avatar_split_clause,[],[f9304,f22087])).
% 92.92/13.72 thf(f22087,plain,(
% 92.92/13.72 spl854_38 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_38])])).
% 92.92/13.72 thf(f9304,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4879])).
% 92.92/13.72 thf(f4879,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X0),X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f1572])).
% 92.92/13.72 thf(f1572,axiom,(
% 92.92/13.72 ! [X72 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Egcd_2Egcd,X72),X72) = X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__REF)).
% 92.92/13.72 thf(f22085,plain,(
% 92.92/13.72 spl854_37),
% 92.92/13.72 inference(avatar_split_clause,[],[f9303,f22083])).
% 92.92/13.72 thf(f22083,plain,(
% 92.92/13.72 spl854_37 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_37])])).
% 92.92/13.72 thf(f9303,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4878])).
% 92.92/13.72 thf(f4878,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X0),X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f1236])).
% 92.92/13.72 thf(f1236,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN,X136),X136) = X136)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMIN__IDEM)).
% 92.92/13.72 thf(f22081,plain,(
% 92.92/13.72 spl854_36),
% 92.92/13.72 inference(avatar_split_clause,[],[f9302,f22079])).
% 92.92/13.72 thf(f22079,plain,(
% 92.92/13.72 spl854_36 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_36])])).
% 92.92/13.72 thf(f9302,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4877])).
% 92.92/13.72 thf(f4877,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X0),X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f1237])).
% 92.92/13.72 thf(f1237,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX,X136),X136) = X136)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMAX__IDEM)).
% 92.92/13.72 thf(f22070,plain,(
% 92.92/13.72 spl854_35 | ~spl854_4 | ~spl854_13),
% 92.92/13.72 inference(avatar_split_clause,[],[f21961,f21950,f21876,f22068])).
% 92.92/13.72 thf(f21961,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Eone_2Eone > tyop_2Eone_2Eone,X1 : tyop_2Eone_2Eone] : ((vAPP(tyop_2Eone_2Eone,tyop_2Eone_2Eone,X0,X1) = X1)) ) | (~spl854_4 | ~spl854_13)),
% 92.92/13.72 inference(superposition,[],[f21951,f21877])).
% 92.92/13.72 thf(f22066,plain,(
% 92.92/13.72 spl854_34),
% 92.92/13.72 inference(avatar_split_clause,[],[f18905,f22064])).
% 92.92/13.72 thf(f22064,plain,(
% 92.92/13.72 spl854_34 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_34])])).
% 92.92/13.72 thf(f18905,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f18904])).
% 92.92/13.72 thf(f18904,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = $false) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f14197,f17793])).
% 92.92/13.72 thf(f14197,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10085,f13520,f13512])).
% 92.92/13.72 thf(f10085,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6836])).
% 92.92/13.72 thf(f22062,plain,(
% 92.92/13.72 spl854_33),
% 92.92/13.72 inference(avatar_split_clause,[],[f18901,f22060])).
% 92.92/13.72 thf(f22060,plain,(
% 92.92/13.72 spl854_33 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_33])])).
% 92.92/13.72 thf(f18901,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f18900])).
% 92.92/13.72 thf(f18900,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = $false) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f14193,f17793])).
% 92.92/13.72 thf(f14193,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10089,f13520,f13512])).
% 92.92/13.72 thf(f10089,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((c_2Ebool_2EF = $true) | (c_2Earithmetic_2EZERO != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6836])).
% 92.92/13.72 thf(f22058,plain,(
% 92.92/13.72 spl854_32),
% 92.92/13.72 inference(avatar_split_clause,[],[f18897,f22056])).
% 92.92/13.72 thf(f22056,plain,(
% 92.92/13.72 spl854_32 <=> ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_32])])).
% 92.92/13.72 thf(f18897,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) )),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f18896])).
% 92.92/13.72 thf(f18896,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = $false) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f14189,f17793])).
% 92.92/13.72 thf(f14189,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f10093,f13520])).
% 92.92/13.72 thf(f10093,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EF = $true) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6836])).
% 92.92/13.72 thf(f22054,plain,(
% 92.92/13.72 spl854_31),
% 92.92/13.72 inference(avatar_split_clause,[],[f18582,f22052])).
% 92.92/13.72 thf(f22052,plain,(
% 92.92/13.72 spl854_31 <=> ! [X1 : tyop_2Enum_2Enum] : ($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X1)))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_31])])).
% 92.92/13.72 thf(f18582,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB,X1)))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f18581,f18222])).
% 92.92/13.72 thf(f18581,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))),X1)))) )),
% 92.92/13.72 inference(forward_demodulation,[],[f15734,f13567])).
% 92.92/13.72 thf(f15734,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f14006])).
% 92.92/13.72 thf(f14006,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Einternal__mult,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),X1) != X0)) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9761,f9121,f13512])).
% 92.92/13.72 thf(f9761,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),X1) != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6804])).
% 92.92/13.72 thf(f22050,plain,(
% 92.92/13.72 spl854_30),
% 92.92/13.72 inference(avatar_split_clause,[],[f18001,f22048])).
% 92.92/13.72 thf(f18001,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f9522])).
% 92.92/13.72 thf(f9522,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2136])).
% 92.92/13.72 thf(f22038,plain,(
% 92.92/13.72 spl854_29),
% 92.92/13.72 inference(avatar_split_clause,[],[f17787,f22036])).
% 92.92/13.72 thf(f17787,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) != vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17786])).
% 92.92/13.72 thf(f17786,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f14069])).
% 92.92/13.72 thf(f14069,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9838,f9122])).
% 92.92/13.72 thf(f9838,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2516])).
% 92.92/13.72 thf(f2516,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),c_2Enum_2E0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f2515])).
% 92.92/13.72 thf(f2515,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)))),
% 92.92/13.72 inference(rectify,[],[f381])).
% 92.92/13.72 thf(f381,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2ENOT__SUC)).
% 92.92/13.72 thf(f22034,plain,(
% 92.92/13.72 spl854_28),
% 92.92/13.72 inference(avatar_split_clause,[],[f16821,f22031])).
% 92.92/13.72 thf(f16821,plain,(
% 92.92/13.72 ($false = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)))),
% 92.92/13.72 inference(not_proxy_clausification,[],[f15644])).
% 92.92/13.72 thf(f15644,plain,(
% 92.92/13.72 ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))))),
% 92.92/13.72 inference(definition_unfolding,[],[f13500,f9122])).
% 92.92/13.72 thf(f13500,plain,(
% 92.92/13.72 (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,c_2Enum_2E0)) = $true)),
% 92.92/13.72 inference(cnf_transformation,[],[f4812])).
% 92.92/13.72 thf(f4812,plain,(
% 92.92/13.72 (vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,c_2Enum_2E0)) = $true)),
% 92.92/13.72 inference(fool_elimination,[],[f4811])).
% 92.92/13.72 thf(f4811,plain,(
% 92.92/13.72 vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,c_2Enum_2E0))),
% 92.92/13.72 inference(rectify,[],[f1480])).
% 92.92/13.72 thf(f1480,axiom,(
% 92.92/13.72 vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,c_2Enum_2E0))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2ENOT__PRIME__0)).
% 92.92/13.72 thf(f22029,plain,(
% 92.92/13.72 spl854_27),
% 92.92/13.72 inference(avatar_split_clause,[],[f15733,f22027])).
% 92.92/13.72 thf(f15733,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1)))) )),
% 92.92/13.72 inference(equality_resolution,[],[f9757])).
% 92.92/13.72 thf(f9757,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X0)) | (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Edivides_2EPRIMES,X1) != X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6799])).
% 92.92/13.72 thf(f22025,plain,(
% 92.92/13.72 spl854_26),
% 92.92/13.72 inference(avatar_split_clause,[],[f13665,f22023])).
% 92.92/13.72 thf(f13665,plain,(
% 92.92/13.72 ( ! [X0 : $o] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9288,f9122])).
% 92.92/13.72 thf(f9288,plain,(
% 92.92/13.72 ( ! [X0 : $o] : ((c_2Enum_2E0 = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4863])).
% 92.92/13.72 thf(f4863,plain,(
% 92.92/13.72 ! [X0 : $o] : (c_2Enum_2E0 = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X0))),
% 92.92/13.72 inference(rectify,[],[f1448])).
% 92.92/13.72 thf(f1448,axiom,(
% 92.92/13.72 ! [X35 : $o] : (c_2Enum_2E0 = vAPP($o,tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size,X35))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def)).
% 92.92/13.72 thf(f22021,plain,(
% 92.92/13.72 spl854_25),
% 92.92/13.72 inference(avatar_split_clause,[],[f13664,f22019])).
% 92.92/13.72 thf(f22019,plain,(
% 92.92/13.72 spl854_25 <=> ! [X0 : tyop_2Eone_2Eone] : (vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Eone_2Eone,tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_25])])).
% 92.92/13.72 thf(f13664,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Eone_2Eone] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP) = vAPP(tyop_2Eone_2Eone,tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size,X0))) )),
% 92.92/13.72 inference(definition_unfolding,[],[f9287,f9122])).
% 92.92/13.72 thf(f9287,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Eone_2Eone] : ((c_2Enum_2E0 = vAPP(tyop_2Eone_2Eone,tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size,X0))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4862])).
% 92.92/13.72 thf(f4862,plain,(
% 92.92/13.72 ! [X0 : tyop_2Eone_2Eone] : (c_2Enum_2E0 = vAPP(tyop_2Eone_2Eone,tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size,X0))),
% 92.92/13.72 inference(rectify,[],[f1450])).
% 92.92/13.72 thf(f1450,axiom,(
% 92.92/13.72 ! [X8 : tyop_2Eone_2Eone] : (c_2Enum_2E0 = vAPP(tyop_2Eone_2Eone,tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size,X8))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def)).
% 92.92/13.72 thf(f22017,plain,(
% 92.92/13.72 spl854_24),
% 92.92/13.72 inference(avatar_split_clause,[],[f13591,f22014])).
% 92.92/13.72 thf(f22012,plain,(
% 92.92/13.72 spl854_23),
% 92.92/13.72 inference(avatar_split_clause,[],[f9789,f22010])).
% 92.92/13.72 thf(f9789,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6820])).
% 92.92/13.72 thf(f6820,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0))))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK189])],[f2424,f6819])).
% 92.92/13.72 thf(f6819,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (? [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X0),X1))) => (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0))) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X0),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,sK189,X0)))))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f2424,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ? [X1 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1)) & ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X0),X1)))),
% 92.92/13.72 inference(fool_elimination,[],[f2423])).
% 92.92/13.72 thf(f2423,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ? [X1 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X1) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X0),X1))),
% 92.92/13.72 inference(rectify,[],[f1488])).
% 92.92/13.72 thf(f1488,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : ? [X110 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,$o,c_2Edivides_2Eprime,X110) & vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Eprim__rec_2E_3C,X136),X110))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Edivides_2EEUCLID)).
% 92.92/13.72 thf(f22008,plain,(
% 92.92/13.72 spl854_22),
% 92.92/13.72 inference(avatar_split_clause,[],[f9521,f22006])).
% 92.92/13.72 thf(f9521,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP(tyop_2Enum_2Enum,$o,c_2Earithmetic_2EEVEN,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2,X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2136])).
% 92.92/13.72 thf(f22004,plain,(
% 92.92/13.72 spl854_21),
% 92.92/13.72 inference(avatar_split_clause,[],[f9295,f22002])).
% 92.92/13.72 thf(f22002,plain,(
% 92.92/13.72 spl854_21 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_21])])).
% 92.92/13.72 thf(f9295,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4870])).
% 92.92/13.72 thf(f4870,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X0)) = X0)),
% 92.92/13.72 inference(rectify,[],[f1670])).
% 92.92/13.72 thf(f1670,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Einvtri,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Etri,X136)) = X136)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Einvtri__linverse)).
% 92.92/13.72 thf(f22000,plain,(
% 92.92/13.72 spl854_20),
% 92.92/13.72 inference(avatar_split_clause,[],[f9294,f21998])).
% 92.92/13.72 thf(f21998,plain,(
% 92.92/13.72 spl854_20 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_20])])).
% 92.92/13.72 thf(f9294,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4869])).
% 92.92/13.72 thf(f4869,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X0)) = X0)),
% 92.92/13.72 inference(rectify,[],[f1405])).
% 92.92/13.72 thf(f1405,axiom,(
% 92.92/13.72 ! [X8 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1,X8)) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumeral_2EDIV2__BIT1)).
% 92.92/13.72 thf(f21996,plain,(
% 92.92/13.72 spl854_19 | ~spl854_3),
% 92.92/13.72 inference(avatar_split_clause,[],[f21879,f21872,f21994])).
% 92.92/13.72 thf(f21994,plain,(
% 92.92/13.72 spl854_19 <=> ! [X0 : $tType,X2 : tyop_2Ebool_2Eitself(X0),X1 : tyop_2Ebool_2Eitself(X0)] : (X1 = X2)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_19])])).
% 92.92/13.72 thf(f21872,plain,(
% 92.92/13.72 spl854_3 <=> ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0)] : (c_2Ebool_2Ethe__value(X0) = X1)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_3])])).
% 92.92/13.72 thf(f21879,plain,(
% 92.92/13.72 ( ! [X2 : tyop_2Ebool_2Eitself(X0),X1 : tyop_2Ebool_2Eitself(X0)] : ((X1 = X2)) ) | ~spl854_3),
% 92.92/13.72 inference(superposition,[],[f21873,f21873])).
% 92.92/13.72 thf(f21873,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0)] : ((c_2Ebool_2Ethe__value(X0) = X1)) ) | ~spl854_3),
% 92.92/13.72 inference(avatar_component_clause,[],[f21872])).
% 92.92/13.72 thf(f21992,plain,(
% 92.92/13.72 spl854_18),
% 92.92/13.72 inference(avatar_split_clause,[],[f9175,f21990])).
% 92.92/13.72 thf(f9175,plain,(
% 92.92/13.72 ( ! [X1 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,vAPP(tyop_2Enum_2Enum,tyop_2Emin_2Eind,c_2Enum_2EREP__num,X1)) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f6596])).
% 92.92/13.72 thf(f21988,plain,(
% 92.92/13.72 spl854_17),
% 92.92/13.72 inference(avatar_split_clause,[],[f9162,f21986])).
% 92.92/13.72 thf(f21986,plain,(
% 92.92/13.72 spl854_17 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_17])])).
% 92.92/13.72 thf(f9162,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4840])).
% 92.92/13.72 thf(f4840,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)) = X0) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Enum_2E0))),
% 92.92/13.72 inference(rectify,[],[f870])).
% 92.92/13.72 thf(f870,axiom,(
% 92.92/13.72 ! [X134 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X134)) = X134) & (c_2Enum_2E0 = vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE,c_2Enum_2E0))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2EPRE)).
% 92.92/13.72 thf(f21979,plain,(
% 92.92/13.72 spl854_16),
% 92.92/13.72 inference(avatar_split_clause,[],[f9855,f21977])).
% 92.92/13.72 thf(f9855,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EARB(X0) = vAPP(tyop_2Enum_2Enum,X0,c_2Eind__type_2EFNIL(X0),X1))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4958])).
% 92.92/13.72 thf(f4958,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : (c_2Ebool_2EARB(X0) = vAPP(tyop_2Enum_2Enum,X0,c_2Eind__type_2EFNIL(X0),X1))),
% 92.92/13.72 inference(rectify,[],[f1525])).
% 92.92/13.72 thf(f1525,axiom,(
% 92.92/13.72 ! [X0 : $tType,X136 : tyop_2Enum_2Enum] : (c_2Ebool_2EARB(X0) = vAPP(tyop_2Enum_2Enum,X0,c_2Eind__type_2EFNIL(X0),X136))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EFNIL)).
% 92.92/13.72 thf(f21960,plain,(
% 92.92/13.72 spl854_15),
% 92.92/13.72 inference(avatar_split_clause,[],[f11177,f21958])).
% 92.92/13.72 thf(f11177,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,sK386(X0),X1) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f7678])).
% 92.92/13.72 thf(f7678,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (vAPP(X0,X0,sK386(X0),X1) = X1)),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK386])],[f5128,f7677])).
% 92.92/13.72 thf(f7677,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : (X1 = X2) => (vAPP(X0,X0,sK386(X0),X1) = X1))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f5128,plain,(
% 92.92/13.72 ! [X0,X1 : X0] : ? [X2 : X0] : (X1 = X2)),
% 92.92/13.72 inference(rectify,[],[f157])).
% 92.92/13.72 thf(f157,axiom,(
% 92.92/13.72 ! [X0 : $tType,X72 : X0] : ? [X4 : X0] : (X4 = X72)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__REFL)).
% 92.92/13.72 thf(f21956,plain,(
% 92.92/13.72 spl854_14),
% 92.92/13.72 inference(avatar_split_clause,[],[f9854,f21954])).
% 92.92/13.72 thf(f9854,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,c_2Emarker_2Estmarker(X0),X1) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4957])).
% 92.92/13.72 thf(f4957,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (vAPP(X0,X0,c_2Emarker_2Estmarker(X0),X1) = X1)),
% 92.92/13.72 inference(rectify,[],[f254])).
% 92.92/13.72 thf(f254,axiom,(
% 92.92/13.72 ! [X0 : $tType,X8 : X0] : (vAPP(X0,X0,c_2Emarker_2Estmarker(X0),X8) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Emarker_2Estmarker__def)).
% 92.92/13.72 thf(f21952,plain,(
% 92.92/13.72 spl854_13),
% 92.92/13.72 inference(avatar_split_clause,[],[f9852,f21950])).
% 92.92/13.72 thf(f9852,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : X0] : ((vAPP(X0,X0,c_2Emarker_2Eunint(X0),X1) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4955])).
% 92.92/13.72 thf(f4955,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : X0] : (vAPP(X0,X0,c_2Emarker_2Eunint(X0),X1) = X1)),
% 92.92/13.72 inference(rectify,[],[f255])).
% 92.92/13.72 thf(f255,axiom,(
% 92.92/13.72 ! [X0 : $tType,X8 : X0] : (vAPP(X0,X0,c_2Emarker_2Eunint(X0),X8) = X8)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Emarker_2Eunint__def)).
% 92.92/13.72 thf(f21943,plain,(
% 92.92/13.72 ~spl854_12),
% 92.92/13.72 inference(avatar_split_clause,[],[f9118,f21940])).
% 92.92/13.72 thf(f9118,plain,(
% 92.92/13.72 ($true != vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124))),
% 92.92/13.72 inference(cnf_transformation,[],[f6595])).
% 92.92/13.72 thf(f6595,plain,(
% 92.92/13.72 ($true != vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK123,sK124])],[f5418,f6594])).
% 92.92/13.72 thf(f6594,plain,(
% 92.92/13.72 ? [X0 : $tType,X1 : X0 > $o] : ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1)),X1)) => ($true != vAPP(sTfun(sK123,$o),$o,vAPP(sTfun(sK123,$o),sTfun(sTfun(sK123,$o),$o),c_2Epred__set_2ESUBSET(sK123),vAPP(sTfun(sK123,$o),sTfun(sK123,$o),c_2Epred__set_2EREST(sK123),sK124)),sK124))),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f5418,plain,(
% 92.92/13.72 ? [X0 : $tType,X1 : X0 > $o] : ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1)),X1))),
% 92.92/13.72 inference(ennf_transformation,[],[f2002])).
% 92.92/13.72 thf(f2002,plain,(
% 92.92/13.72 ~! [X0 : $tType,X1 : X0 > $o] : ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1)),X1))),
% 92.92/13.72 inference(fool_elimination,[],[f2001])).
% 92.92/13.72 thf(f2001,plain,(
% 92.92/13.72 ~! [X0 : $tType,X1 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X1)),X1)),
% 92.92/13.72 inference(rectify,[],[f1998])).
% 92.92/13.72 thf(f1998,negated_conjecture,(
% 92.92/13.72 ~! [X0 : $tType,X111 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X111)),X111)),
% 92.92/13.72 inference(negated_conjecture,[],[f1997])).
% 92.92/13.72 thf(f1997,conjecture,(
% 92.92/13.72 ! [X0 : $tType,X111 : X0 > $o] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),c_2Epred__set_2ESUBSET(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),c_2Epred__set_2EREST(X0),X111)),X111)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET)).
% 92.92/13.72 thf(f21938,plain,(
% 92.92/13.72 spl854_11),
% 92.92/13.72 inference(avatar_split_clause,[],[f17789,f21936])).
% 92.92/13.72 thf(f21936,plain,(
% 92.92/13.72 spl854_11 <=> ! [X0 : tyop_2Emin_2Eind] : (c_2Enum_2EZERO__REP != vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X0))),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_11])])).
% 92.92/13.72 thf(f17789,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : ((c_2Enum_2EZERO__REP != vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X0))) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17788])).
% 92.92/13.72 thf(f17788,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($false = vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),vEQ(tyop_2Emin_2Eind),c_2Enum_2EZERO__REP),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X0)))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f9837])).
% 92.92/13.72 thf(f9837,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Emin_2Eind] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),vEQ(tyop_2Emin_2Eind),c_2Enum_2EZERO__REP),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X0))))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2514])).
% 92.92/13.72 thf(f2514,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Emin_2Eind,$o,vAPP(tyop_2Emin_2Eind,sTfun(tyop_2Emin_2Eind,$o),vEQ(tyop_2Emin_2Eind),c_2Enum_2EZERO__REP),vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X0))))),
% 92.92/13.72 inference(fool_elimination,[],[f2513])).
% 92.92/13.72 thf(f2513,plain,(
% 92.92/13.72 ! [X0 : tyop_2Emin_2Eind] : vAPP($o,$o,vNOT,(c_2Enum_2EZERO__REP = vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X0)))),
% 92.92/13.72 inference(rectify,[],[f375])).
% 92.92/13.72 thf(f375,axiom,(
% 92.92/13.72 ! [X70 : tyop_2Emin_2Eind] : vAPP($o,$o,vNOT,(c_2Enum_2EZERO__REP = vAPP(tyop_2Emin_2Eind,tyop_2Emin_2Eind,c_2Enum_2ESUC__REP,X70)))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EZERO__REP__DEF)).
% 92.92/13.72 thf(f21934,plain,(
% 92.92/13.72 spl854_10),
% 92.92/13.72 inference(avatar_split_clause,[],[f17779,f21932])).
% 92.92/13.72 thf(f17779,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) != X0)) )),
% 92.92/13.72 inference(equality_proxy_clausification,[],[f17778])).
% 92.92/13.72 thf(f17778,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($false = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0))) )),
% 92.92/13.72 inference(not_proxy_clausification,[],[f9842])).
% 92.92/13.72 thf(f9842,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : (($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0)))) )),
% 92.92/13.72 inference(cnf_transformation,[],[f2524])).
% 92.92/13.72 thf(f2524,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : ($true = vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),vEQ(tyop_2Enum_2Enum),vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0)),X0)))),
% 92.92/13.72 inference(fool_elimination,[],[f2523])).
% 92.92/13.72 thf(f2523,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X0) = X0))),
% 92.92/13.72 inference(rectify,[],[f889])).
% 92.92/13.72 thf(f889,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : vAPP($o,$o,vNOT,(vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC,X136) = X136))),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ESUC__ID)).
% 92.92/13.72 thf(f21930,plain,(
% 92.92/13.72 spl854_9),
% 92.92/13.72 inference(avatar_split_clause,[],[f9293,f21928])).
% 92.92/13.72 thf(f21926,plain,(
% 92.92/13.72 spl854_8 | spl854_2 | ~spl854_5),
% 92.92/13.72 inference(avatar_split_clause,[],[f21895,f21881,f21867,f21923])).
% 92.92/13.72 thf(f21895,plain,(
% 92.92/13.72 ($false = sK125) | (spl854_2 | ~spl854_5)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f21893])).
% 92.92/13.72 thf(f21893,plain,(
% 92.92/13.72 ($true != $true) | ($false = sK125) | (spl854_2 | ~spl854_5)),
% 92.92/13.72 inference(superposition,[],[f21869,f21882])).
% 92.92/13.72 thf(f21921,plain,(
% 92.92/13.72 spl854_7),
% 92.92/13.72 inference(avatar_split_clause,[],[f9292,f21919])).
% 92.92/13.72 thf(f21919,plain,(
% 92.92/13.72 spl854_7 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ,X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_7])])).
% 92.92/13.72 thf(f21917,plain,(
% 92.92/13.72 spl854_6),
% 92.92/13.72 inference(avatar_split_clause,[],[f9291,f21915])).
% 92.92/13.72 thf(f21915,plain,(
% 92.92/13.72 spl854_6 <=> ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic,X0) = X0)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_6])])).
% 92.92/13.72 thf(f9291,plain,(
% 92.92/13.72 ( ! [X0 : tyop_2Enum_2Enum] : ((vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic,X0) = X0)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4866])).
% 92.92/13.72 thf(f4866,plain,(
% 92.92/13.72 ! [X0 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic,X0) = X0)),
% 92.92/13.72 inference(rectify,[],[f919])).
% 92.92/13.72 thf(f919,axiom,(
% 92.92/13.72 ! [X136 : tyop_2Enum_2Enum] : (vAPP(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic,X136) = X136)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2Enat__elim____magic)).
% 92.92/13.72 thf(f21883,plain,(
% 92.92/13.72 spl854_5),
% 92.92/13.72 inference(avatar_split_clause,[],[f2000,f21881])).
% 92.92/13.72 thf(f2000,plain,(
% 92.92/13.72 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 92.92/13.72 introduced(fool_axiom,[])).
% 92.92/13.72 thf(f21878,plain,(
% 92.92/13.72 spl854_4),
% 92.92/13.72 inference(avatar_split_clause,[],[f11234,f21876])).
% 92.92/13.72 thf(f11234,plain,(
% 92.92/13.72 ( ! [X2 : X0 > tyop_2Eone_2Eone,X1 : X0 > tyop_2Eone_2Eone] : ((X1 = X2)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f5130])).
% 92.92/13.72 thf(f5130,plain,(
% 92.92/13.72 ! [X0,X1 : X0 > tyop_2Eone_2Eone,X2 : X0 > tyop_2Eone_2Eone] : (X1 = X2)),
% 92.92/13.72 inference(rectify,[],[f394])).
% 92.92/13.72 thf(f394,axiom,(
% 92.92/13.72 ! [X0 : $tType,X3 : X0 > tyop_2Eone_2Eone,X38 : X0 > tyop_2Eone_2Eone] : (X3 = X38)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eone_2Eone__axiom)).
% 92.92/13.72 thf(f21874,plain,(
% 92.92/13.72 spl854_3),
% 92.92/13.72 inference(avatar_split_clause,[],[f9849,f21872])).
% 92.92/13.72 thf(f9849,plain,(
% 92.92/13.72 ( ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0)] : ((c_2Ebool_2Ethe__value(X0) = X1)) )),
% 92.92/13.72 inference(cnf_transformation,[],[f4952])).
% 92.92/13.72 thf(f4952,plain,(
% 92.92/13.72 ! [X0 : $tType,X1 : tyop_2Ebool_2Eitself(X0)] : (c_2Ebool_2Ethe__value(X0) = X1)),
% 92.92/13.72 inference(rectify,[],[f189])).
% 92.92/13.72 thf(f189,axiom,(
% 92.92/13.72 ! [X0 : $tType,X89 : tyop_2Ebool_2Eitself(X0)] : (c_2Ebool_2Ethe__value(X0) = X89)),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EITSELF__UNIQUE)).
% 92.92/13.72 thf(f21870,plain,(
% 92.92/13.72 ~spl854_2),
% 92.92/13.72 inference(avatar_split_clause,[],[f18172,f21867])).
% 92.92/13.72 thf(f18172,plain,(
% 92.92/13.72 ($true != sK125)),
% 92.92/13.72 inference(trivial_inequality_removal,[],[f18171])).
% 92.92/13.72 thf(f18171,plain,(
% 92.92/13.72 ($true = $false) | ($true != sK125)),
% 92.92/13.72 inference(forward_demodulation,[],[f13658,f18095])).
% 92.92/13.72 thf(f13658,plain,(
% 92.92/13.72 ($true = vAPP(tyop_2Enum_2Enum,$o,vAPP(tyop_2Enum_2Enum,sTfun(tyop_2Enum_2Enum,$o),c_2Ebit_2EBIT,vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP)),vAPP(tyop_2Emin_2Eind,tyop_2Enum_2Enum,c_2Enum_2EABS__num,c_2Enum_2EZERO__REP))) | ($true != sK125)),
% 92.92/13.72 inference(definition_unfolding,[],[f9282,f13520])).
% 92.92/13.72 thf(f9282,plain,(
% 92.92/13.72 (c_2Ebool_2EF = $true) | ($true != sK125)),
% 92.92/13.72 inference(cnf_transformation,[],[f6604])).
% 92.92/13.72 thf(f6604,plain,(
% 92.92/13.72 ((c_2Ebool_2EF = $true) | ($true != sK125)) & (! [X1 : $o] : ($true = X1) | (c_2Ebool_2EF != $true))),
% 92.92/13.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK125])],[f6602,f6603])).
% 92.92/13.72 thf(f6603,plain,(
% 92.92/13.72 ? [X0 : $o] : ($true != X0) => ($true != sK125)),
% 92.92/13.72 introduced(choice_axiom,[])).
% 92.92/13.72 thf(f6602,plain,(
% 92.92/13.72 ((c_2Ebool_2EF = $true) | ? [X0 : $o] : ($true != X0)) & (! [X1 : $o] : ($true = X1) | (c_2Ebool_2EF != $true))),
% 92.92/13.72 inference(rectify,[],[f6601])).
% 92.92/13.72 thf(f6601,plain,(
% 92.92/13.72 ((c_2Ebool_2EF = $true) | ? [X0 : $o] : ($true != X0)) & (! [X0 : $o] : ($true = X0) | (c_2Ebool_2EF != $true))),
% 92.92/13.72 inference(nnf_transformation,[],[f2058])).
% 92.92/13.72 thf(f2058,plain,(
% 92.92/13.72 (c_2Ebool_2EF = $true) <=> ! [X0 : $o] : ($true = X0)),
% 92.92/13.72 inference(fool_elimination,[],[f2057])).
% 92.92/13.72 thf(f2057,plain,(
% 92.92/13.72 c_2Ebool_2EF <=> ! [X0 : $o] : X0),
% 92.92/13.72 inference(rectify,[],[f24])).
% 92.92/13.72 thf(f24,axiom,(
% 92.92/13.72 c_2Ebool_2EF <=> ! [X6 : $o] : X6),
% 92.92/13.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__DEF)).
% 92.92/13.72 thf(f21865,plain,(
% 92.92/13.72 ~spl854_1),
% 92.92/13.72 inference(avatar_split_clause,[],[f1999,f21862])).
% 92.92/13.72 thf(f21862,plain,(
% 92.92/13.72 spl854_1 <=> ($true = $false)),
% 92.92/13.72 introduced(avatar_definition,[new_symbols(naming,[spl854_1])])).
% 92.92/13.72 thf(f1999,plain,(
% 92.92/13.72 ($true != $false)),
% 92.92/13.72 introduced(fool_axiom,[])).
% 92.92/13.72 % SZS output end Proof for theBenchmark
% 92.92/13.72 % (9733)------------------------------
% 92.92/13.72 % (9733)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 92.92/13.72 % (9733)Termination reason: Refutation
% 92.92/13.72
% 92.92/13.72 % (9733)Memory used [KB]: 45101
% 92.92/13.72 % (9733)Time elapsed: 13.170 s
% 92.92/13.72 % (9733)Instructions burned: 55892 (million)
% 92.92/13.72 % (9728)Success in time 13.34 s
%------------------------------------------------------------------------------